different types of problem solving heuristic

Heuristics: Definition, Examples, And How They Work

Benjamin Frimodig

Science Expert

B.A., History and Science, Harvard University

Ben Frimodig is a 2021 graduate of Harvard College, where he studied the History of Science.

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Saul McLeod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul McLeod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

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Every day our brains must process and respond to thousands of problems, both large and small, at a moment’s notice. It might even be overwhelming to consider the sheer volume of complex problems we regularly face in need of a quick solution.

While one might wish there was time to methodically and thoughtfully evaluate the fine details of our everyday tasks, the cognitive demands of daily life often make such processing logistically impossible.

Therefore, the brain must develop reliable shortcuts to keep up with the stimulus-rich environments we inhabit. Psychologists refer to these efficient problem-solving techniques as heuristics.

Heuristics can be thought of as general cognitive frameworks humans rely on regularly to reach a solution quickly.

For example, if a student needs to decide what subject she will study at university, her intuition will likely be drawn toward the path that she envisions as most satisfying, practical, and interesting.

She may also think back on her strengths and weaknesses in secondary school or perhaps even write out a pros and cons list to facilitate her choice.

It’s important to note that these heuristics broadly apply to everyday problems, produce sound solutions, and helps simplify otherwise complicated mental tasks. These are the three defining features of a heuristic.

While the concept of heuristics dates back to Ancient Greece (the term is derived from the Greek word for “to discover”), most of the information known today on the subject comes from prominent twentieth-century social scientists.

Herbert Simon’s study of a notion he called “bounded rationality” focused on decision-making under restrictive cognitive conditions, such as limited time and information.

This concept of optimizing an inherently imperfect analysis frames the contemporary study of heuristics and leads many to credit Simon as a foundational figure in the field.

Kahneman’s Theory of Decision Making

The immense contributions of psychologist Daniel Kahneman to our understanding of cognitive problem-solving deserve special attention.

As context for his theory, Kahneman put forward the estimate that an individual makes around 35,000 decisions each day! To reach these resolutions, the mind relies on either “fast” or “slow” thinking.

The fast thinking pathway (system 1) operates mostly unconsciously and aims to reach reliable decisions with as minimal cognitive strain as possible.

While system 1 relies on broad observations and quick evaluative techniques (heuristics!), system 2 (slow thinking) requires conscious, continuous attention to carefully assess the details of a given problem and logically reach a solution.

Given the sheer volume of daily decisions, it’s no surprise that around 98% of problem-solving uses system 1.

Thus, it is crucial that the human mind develops a toolbox of effective, efficient heuristics to support this fast-thinking pathway.

Heuristics vs. Algorithms

Those who’ve studied the psychology of decision-making might notice similarities between heuristics and algorithms. However, remember that these are two distinct modes of cognition.

Heuristics are methods or strategies which often lead to problem solutions but are not guaranteed to succeed.

They can be distinguished from algorithms, which are methods or procedures that will always produce a solution sooner or later.

An algorithm is a step-by-step procedure that can be reliably used to solve a specific problem. While the concept of an algorithm is most commonly used in reference to technology and mathematics, our brains rely on algorithms every day to resolve issues (Kahneman, 2011).

The important thing to remember is that algorithms are a set of mental instructions unique to specific situations, while heuristics are general rules of thumb that can help the mind process and overcome various obstacles.

For example, if you are thoughtfully reading every line of this article, you are using an algorithm.

On the other hand, if you are quickly skimming each section for important information or perhaps focusing only on sections you don’t already understand, you are using a heuristic!

Why Heuristics Are Used

Heuristics usually occurs when one of five conditions is met (Pratkanis, 1989):

• When one is faced with too much information
• When the time to make a decision is limited
• When the decision to be made is unimportant
• When there is access to very little information to use in making the decision
• When an appropriate heuristic happens to come to mind at the same moment

When studying heuristics, keep in mind both the benefits and unavoidable drawbacks of their application. The ubiquity of these techniques in human society makes such weaknesses especially worthy of evaluation.

More specifically, in expediting decision-making processes, heuristics also predispose us to a number of cognitive biases .

A cognitive bias is an incorrect but pervasive judgment derived from an illogical pattern of cognition. In simple terms, a cognitive bias occurs when one internalizes a subjective perception as a reliable and objective truth.

Heuristics are reliable but imperfect; In the application of broad decision-making “shortcuts” to guide one’s response to specific situations, occasional errors are both inevitable and have the potential to catalyze persistent mistakes.

For example, consider the risks of faulty applications of the representative heuristic discussed above. While the technique encourages one to assign situations into broad categories based on superficial characteristics and one’s past experiences for the sake of cognitive expediency, such thinking is also the basis of stereotypes and discrimination.

In practice, these errors result in the disproportionate favoring of one group and/or the oppression of other groups within a given society.

Indeed, the most impactful research relating to heuristics often centers on the connection between them and systematic discrimination.

The tradeoff between thoughtful rationality and cognitive efficiency encompasses both the benefits and pitfalls of heuristics and represents a foundational concept in psychological research.

When learning about heuristics, keep in mind their relevance to all areas of human interaction. After all, the study of social psychology is intrinsically interdisciplinary.

Many of the most important studies on heuristics relate to flawed decision-making processes in high-stakes fields like law, medicine, and politics.

Researchers often draw on a distinct set of already established heuristics in their analysis. While dozens of unique heuristics have been observed, brief descriptions of those most central to the field are included below:

Availability Heuristic

The availability heuristic describes the tendency to make choices based on information that comes to mind readily.

For example, children of divorced parents are more likely to have pessimistic views towards marriage as adults.

Of important note, this heuristic can also involve assigning more importance to more recently learned information, largely due to the easier recall of such information.

Representativeness Heuristic

This technique allows one to quickly assign probabilities to and predict the outcome of new scenarios using psychological prototypes derived from past experiences.

For example, juries are less likely to convict individuals who are well-groomed and wearing formal attire (under the assumption that stylish, well-kempt individuals typically do not commit crimes).

This is one of the most studied heuristics by social psychologists for its relevance to the development of stereotypes.

Scarcity Heuristic

This method of decision-making is predicated on the perception of less abundant, rarer items as inherently more valuable than more abundant items.

We rely on the scarcity heuristic when we must make a fast selection with incomplete information. For example, a student deciding between two universities may be drawn toward the option with the lower acceptance rate, assuming that this exclusivity indicates a more desirable experience.

The concept of scarcity is central to behavioral economists’ study of consumer behavior (a field that evaluates economics through the lens of human psychology).

Trial and Error

This is the most basic and perhaps frequently cited heuristic. Trial and error can be used to solve a problem that possesses a discrete number of possible solutions and involves simply attempting each possible option until the correct solution is identified.

For example, if an individual was putting together a jigsaw puzzle, he or she would try multiple pieces until locating a proper fit.

This technique is commonly taught in introductory psychology courses due to its simple representation of the central purpose of heuristics: the use of reliable problem-solving frameworks to reduce cognitive load.

Anchoring and Adjustment Heuristic

Anchoring refers to the tendency to formulate expectations relating to new scenarios relative to an already ingrained piece of information.

Put simply, this anchoring one to form reasonable estimations around uncertainties. For example, if asked to estimate the number of days in a year on Mars, many people would first call to mind the fact the Earth’s year is 365 days (the “anchor”) and adjust accordingly.

This tendency can also help explain the observation that ingrained information often hinders the learning of new information, a concept known as retroactive inhibition.

Familiarity Heuristic

This technique can be used to guide actions in cognitively demanding situations by simply reverting to previous behaviors successfully utilized under similar circumstances.

The familiarity heuristic is most useful in unfamiliar, stressful environments.

For example, a job seeker might recall behavioral standards in other high-stakes situations from her past (perhaps an important presentation at university) to guide her behavior in a job interview.

Many psychologists interpret this technique as a slightly more specific variation of the availability heuristic.

How to Make Better Decisions

Heuristics are ingrained cognitive processes utilized by all humans and can lead to various biases.

Both of these statements are established facts. However, this does not mean that the biases that heuristics produce are unavoidable. As the wide-ranging impacts of such biases on societal institutions have become a popular research topic, psychologists have emphasized techniques for reaching more sound, thoughtful and fair decisions in our daily lives.

Ironically, many of these techniques are themselves heuristics!

To focus on the key details of a given problem, one might create a mental list of explicit goals and values. To clearly identify the impacts of choice, one should imagine its impacts one year in the future and from the perspective of all parties involved.

Most importantly, one must gain a mindful understanding of the problem-solving techniques used by our minds and the common mistakes that result. Mindfulness of these flawed yet persistent pathways allows one to quickly identify and remedy the biases (or otherwise flawed thinking) they tend to create!

Further Information

• Shah, A. K., & Oppenheimer, D. M. (2008). Heuristics made easy: an effort-reduction framework. Psychological bulletin, 134(2), 207.
• Marewski, J. N., & Gigerenzer, G. (2012). Heuristic decision making in medicine. Dialogues in clinical neuroscience, 14(1), 77.
• Del Campo, C., Pauser, S., Steiner, E., & Vetschera, R. (2016). Decision making styles and the use of heuristics in decision making. Journal of Business Economics, 86(4), 389-412.

What is a heuristic in psychology?

A heuristic in psychology is a mental shortcut or rule of thumb that simplifies decision-making and problem-solving. Heuristics often speed up the process of finding a satisfactory solution, but they can also lead to cognitive biases.

Bobadilla-Suarez, S., & Love, B. C. (2017, May 29). Fast or Frugal, but Not Both: Decision Heuristics Under Time Pressure. Journal of Experimental Psychology: Learning, Memory, and Cognition .

Bowes, S. M., Ammirati, R. J., Costello, T. H., Basterfield, C., & Lilienfeld, S. O. (2020). Cognitive biases, heuristics, and logical fallacies in clinical practice: A brief field guide for practicing clinicians and supervisors. Professional Psychology: Research and Practice, 51 (5), 435–445.

Dietrich, C. (2010). “Decision Making: Factors that Influence Decision Making, Heuristics Used, and Decision Outcomes.” Inquiries Journal/Student Pulse, 2(02).

Groenewegen, A. (2021, September 1). Kahneman Fast and slow thinking: System 1 and 2 explained by Sue. SUE Behavioral Design. Retrieved March 26, 2022, from https://suebehaviouraldesign.com/kahneman-fast-slow-thinking/

Kahneman, D., Lovallo, D., & Sibony, O. (2011). Before you make that big decision .

Kahneman, D. (2011). Thinking, fast and slow . Macmillan.

Pratkanis, A. (1989). The cognitive representation of attitudes. In A. R. Pratkanis, S. J. Breckler, & A. G. Greenwald (Eds.), Attitude structure and function (pp. 71–98). Hillsdale, NJ: Erlbaum.

Simon, H.A., 1956. Rational choice and the structure of the environment. Psychological Review .

Tversky, A., & Kahneman, D. (1974). Judgment under Uncertainty: Heuristics and Biases. Science, 185 (4157), 1124–1131.

22 Heuristics Examples (The Types of Heuristics)

Chris Drew (PhD)

Dr. Chris Drew is the founder of the Helpful Professor. He holds a PhD in education and has published over 20 articles in scholarly journals. He is the former editor of the Journal of Learning Development in Higher Education. [Image Descriptor: Photo of Chris]

Learn about our Editorial Process

A heuristic is a mental shortcut that enables people to make quick but less-than-optimal decisions.

The benefit of heuristics is that they allow us to make fast decisions based upon approximations, fast cognitive strategies, and educated guesses. The downside is that they often lead us to come to inaccurate conclusions and make flawed decisions.

The most common examples of heuristics are the availability, representativeness, and affect heuristics. However, there are many more possible examples, as shown in the 23 listed below.

Heuristics Definition

Psychologists Amos Tversky and Daniel Kahneman created the concept of heuristics in the early 1970s. They can be described in the following way:

“[They are] judgmental shortcuts that generally get us where we need to go – and quickly – but at the cost of occasionally sending us off course.”

Thus, we can see heuristics as being both positive and negative for our lives. But most interestingly, they can be leveraged in marketing situations to manipulate people’s purchasing decisions, as discussed below.

Types of Heuristics with Examples

1. availability heuristic.

Quick Definition: Making decisions based upon information that is easily available.

We often rely upon and place greater emphasis upon information that is easily available when making decisions.

We might make a decision based solely on what we know about a topic rather than conducting deeper research in order to make a more informed decision. This causes mistakes in our thinking and leads us to make decisions that are flawed or not sufficiently thought out.

This bias is one reason why political parties try to be the last person who talks to a voter before they go into a polling booth. The newness of the information may cause someone to vote for that part because the party’s arguments are closest to the top of mind.

> Check out these 15 availability heuristic examples

2. Representativeness Heuristic

Quick Definition: Making judgments based upon the similarity of one thing to its archetype. In social situations, this leads to prejudice.

We often make a snap judgment about something by placing it into a category based on its surface appearance. For example, we might see a tree and immediately assume it’s in the oak family based upon the color of its bark or size of its leaves.

In social sciences, we can also see that people make judgements about other people based upon their race, gender, class, or other aspects of their identity. In these situations, we are using stereotypes to come to snap judgements about others.

In these situations, our stereotypical assumptions about others can lead to bias, prejudice , and even discrimination .

> Check out these 11 representativeness heuristic examples

3. Affect Heuristic

Quick Definition: We often make decisions based on emotions, moods, and “gut feelings” rather than logic.

Emotions, moods, and feelings impact our thoughts. This simple fact can lead people into making emotional decisions that they may regret later on when they reflect using logic.

One affect heuristic example is the fact that we often make emotional outbursts that we regret later on. Yelling at a cashier at the shops, for example, may be followed up with regret when we reflect and realize it really wasn’t the cashier’s fault.

Similarly, shoppers make impulse purchases based on the feelings they have about the handbag or new dress. These purchases may be regretted later on when we use logic and realize we have overspent our budgets.

4. Anchoring Heuristic

Quick Definition: We often make decisions based upon a subjective anchoring point that influences all subsequent thinking on a topic.

An anchoring point is often the original piece of information that we are given. Based upon this original piece of information, all future thinking and decisions look good or bad.

An anchoring heuristic example is when a company sets the cost of their goods high before setting a discount. If a high price is set, then a discount is applied, then people would see the price as a bargain rather than high .

Similarly, if you were looking at two highly-priced products, the product that is a few dollars less than the other is seen as a good deal, even if its price is also inflated.

5. Base Rate Heuristic

Quick Definition: We neglect the base statistics in favor of other more proximate statistics when making a judgment.

Base rate neglect occurs when someone forgets the base rate, or a basic fact about information, and instead makes decisions based upon other information that they place too much importance upon.

For example, we may predict that the next person to walk into a hospital is a man if the last three people who entered were all males.

This assumption neglects the fact that 50% of all people who enter hospitals are women.

Here, we are privileging immediate information: that there appears to be a lot of men entering the hospital right now., instead of the base rate fact: that you’ve generally got a 50% chance of a woman walking into the store.

6. Absurdity Heuristic

Quick Definition: We tend to classify things that are improbably as absurd rather than giving them proper consideration.

Many people who believe themselves to be highly logical fall prey to the absurdity heuristic. This occurs when you hear a claim that is improbable, so you instantly dismiss it out of hand.

The ability to filter out absurdity has been highly useful to humans – allowing us to keep our focus on reality and not get caught up in conspiracy theories day and night.

But this becomes a problem when we dismiss things that are serious problems. For example, rejection of climate change science based on the fact that it seems extreme, or a doctor dismissing symptoms of a rare disease, are cases when absurdity bias leads us to make overly dismissive decisions.

7. Contagion Heuristic

Quick Definition: We can sometimes see people, ideas, and things as being either positively or negatively contagious despite lack of logic.

Sometimes, people will try to avoid contact with something or someone that has been the victim of bad luck. For example, a person may feel uncomfortable touching a cancer patient despite the fact they are not at all contagious.

On the positive end, we may believe lucky people will remain lucky and may even spread good luck if we spend time with them. Sometimes, this could be called the halo effect and horns effect.

8. Effort Heuristic

Quick Definition: Assuming the quality of something correlates with the amount of effort put into it.

We will often think something is more valuable or higher quality if it took a great deal of effort to create it. This assumption may be correct, but it doesn’t always turn out to be true.

For example, a person may spend 20 hours a day, 365 days a year, working on a startup business and it may still fail due to flaws in the business model. Another person may build a business in a week and see instant success.

Here, there is no positive correlation between effort and quality.

Nevertheless, the effort heuristic is utilized by advertisers all the time. Advertisements might talk about the amount of hours spent testing products, the research and development money put into it, and so on, in order to show that a lot of effort was put into it. The insinuation here is that the effort has led to a higher-quality product, when this is not necessarily always true.

9. Familiarity Heuristic

Quick Definition: We can often take mental shortcuts where we decide things that are most familiar to us are better than things that are less familiar.

Humans tend to see safety in the familiar and risk in the unfamiliar. In reality, familiar things may be just as risky, if not more, than unfamiliar things. Nevertheless, we know how to navigate familiar situations and therefore find them less risky.

A good example of this is travel. We may look to a country overseas and see it as potentially dangerous or scary. But, looking at data, our hometown or home city may be far more dangerous!

Similarly, we’re much more likely to die in a car crash than a plane crash. Nevertheless, fear may overcome you getting on a plane despite the fact that you didn’t put a moment’s thought into the drive to the airport.

10. Fluency Heuristic

Quick Definition: If an idea is communicated more fluently or skillfully then it is given more credence than an idea that is clumsily communicated, regardless of the merit of the idea.

The fluency with which an idea is communicated can directly impact how we perceive the idea. This mental shortcut allows us to bypass direct assessment of the merits of a case. Instead, we rely more on the charisma of the communicator.

For example, leaders with charismatic authority can often command a high vote during elections because of their ability to connect with voters moreso than their actual policy positions.

11. Gaze Heuristic

Quick Definition: Animals and humans have developed the ability to fixate on an estimated position rather than conducting complex calculations. Generally, this is in relation to motion.

The most common example of the gaze heuristic is the process humans go through to estimate where a ball will land. We don’t do all the calculations to understand trajectory and angle. Instead, we’ve developed an uncanny ability to identify where the ball will land through mental shortcuts based on previous experience.

Similarly, predatory animals can predict where their prey will flee to in order to intercept it, bats can use it during echolocation to estimate the location of obstacles, and hockey goalkeepers can use it to estimate the eventual position of a puck flying towards the goals.

12. Recognition Heuristic

Quick Definition: We assume that things we recognize have more value than things we do not recognize.

Recognition is an important facet of product marketing. Brand recognition alone can help a brand to thrive among a field of other products on a shelf.

The recognition heuristic states that we take mental shortcuts when looking at a range of options by assuming that the most recognizable option holds greater value. Thus, we assume a well-known household brand is higher-quality than a lesser-known brand.

Similarly, a study in psychology found that people assume cities whose names they recognize have larger populations than those that they don’t recognize. This assumption is based on the mental shortcut that larger cities are more likely to have recognizable names than smaller cities. This mental shortcut is often accurate, showing how heuristics can be beneficial (we call this the “less is more effect”).

13. Scarcity Heuristic

Quick Definition: When something is scarce , we see it as more valuable.

False scarcity is a widely-utilized method in marketing psychology because it encourages consumers to see a product as having greater value than it really does.

When a product is framed as being scarce, it is seen as having value because only a certain number of people can have it. As a result, people want it more. Sometimes, we call this the framing effect .

One way marketers use false scarcity is that they create limited-time discounts. In this case, the low price is a point of scarcity. Another way they can create false scarcity is to have open and closed cart periods so the product is only available for a short period of time.

This is a heuristic because people are encouraged to bypass making cold contemplative decisions about the product and, instead, make rushed decisions based on fear of missing out.

14. Similarity Heuristic

Quick Definition: Similarity between past and present situations impacts decision-making, allowing people to bypass making objective comparisons of two alternatives.

We tend to rely on past experiences to shape future experiences. If we liked something previously, then we may seek out similar situations in the future. If we didn’t like it in the past ,then we may avoid those situations in the future.

This logic allows people to bypass a thorough assessment of something and, instead, make fast decisions based on past experience.

Marketers can take advantage of this tendency. For example, a new fast food restaurant may use colors and a menu similar to McDonald;s in order to lull consumers into seeing the restaurant as similar to their previous positive experiences at McDonald’s, and therefore more likely to give it a go.

Similarly, Netflix may show you shows and movies similar to previous ones you watched to the end, because Netflix knows that you are going to be partisan toward a similar experience to the ones you previously enjoyed.

15. Simulation Heuristic

Quick Definition: We tend to overestimate the likelihood of an event based upon how easy it is to visualize it.

If our minds are able to visualize something happening, then we overstimate its probability.

Generally, the simulation heuristic occurs in relation to regret or near misses. A great example of this is buying a lottery ticket. If you found out that someone bought a winning lottery ticket one hour after you bought your ticket, then you’d easily be able to visualize the potentiality that you had gotten stuck in traffic that day and turned up to buy the ticket an hour later.

In this example, the probability of you ever turning up to buy the lottery ticket at the right time and place remains extremely low. However, because you can so easily visualize that eventuality, it feels as if you were truly very close to winning the lottery.

16. Social Proof Heuristic

Quick Definition: We use social proof as a mental shortcut to verify the quality or veracity of something instead of investigating it ourselves.

The social proof heuristic occurs both in social norms and product marketing.

In social norms, people tend to accept something as normal, correct, or appropriate because the rest of society does.

We could imagine, for example, 200 years ago many people thought the idea of the women’s right to vote as an idea that is strange or worthy of serious critique before being implemented. There weren’t many people supportive of the idea, so it was unquestioned. Today, because women’s right to vote is a social norm, it seems absurd that anyone would take it away.

In both of the above situations, people relied on broader society’s views (i.e. social proof) as an anchoring point for their own thinking on the topic.

Similarly, in marketing, marketers often go to great lengths to get quotes from “average joes” who have used a product in order to provide social proof in their advertisements.

17. Authority Heuristic

Quick Definition: We tend to defer to authorities as a shortcut rather than doing the thinking and research ourselves.

Society is structured in such a way that we defer to authorities and experts constantly. For example, we will defer to doctors on medical issues, engineers when building bridges, and lawyers on legal issues.

It’s just impossible to go about life trying to be an expert and authority on every topic. Instead, we will need to team up with authorities to make intelligent decisions. So, this heuristic is necessary.

However, mistakes can often be made when we see a person as an authority in one topic and, therefore, assume they’re an authority in entirely unrelated topics.

18. Hot-Hand Fallacy

Quick Definition: We overestimate our chances of success after a string of recent successes.

The hot-hand fallacy assumes that successful people will continue to experience success in the future.

The phrase “hot-hand” refers to gambling where a person rolling a dice has a “hot-hand” if they keep rolling the right numbers.

But we can apply this concept to a range of other situations. For example, we can apply it to investment funds, where investors will invest in a fund if it recently saw a lot of success.

However, past success does not guarantee future results. The more important thing would be to look at their investment philosophy rather than take the mental shortcut of “if they have recently been successful, then they will be in the future, too.”

19. Occam’s Razor

Quick Definition: The assumption that the most straightforward explanation is the most accurate.

Occam’s razor refers to the preferencing of more straightforward explanations as opposed to more complex ones. One logical justification for this is that the straightforward explanation has the least possible variables where mistakes in logic can occur.

However, critics of this approach highlight that, by definition, Occam’s razor fails to contemplate all possible variables and therefore causes oversimplification of explanations. Nevertheless, invoking Occam’s razor allows people to step back from a situation and contemplate whether they have over-complicated a simple situation.

>Check out these 15 occam’s razor examples

20. Naive Diversification

Quick Definition: Longer-term planning tends to involve more diversification than shorter-term planning.

Consider a situation where you are asked to purchase 5 weeks’ worth of groceries at once. In this situation, you’re more likely to buy a diverse range of fruit and vegetables for the forthcoming five weeks.

By contrast, if you were to go shopping once a week for five weeks, you’re less likely to diversify. Rather, you would buy a narrow range of products that you want in the short term.

In this example, people tend to diversify when faced with longer-term plans than shorter-term plans.

Naive diversification teaches us a lesson in business and investment. It teaches us that sometimes we are too soon to diversify when making plans because of our inability to make longer-term decisions in the shorter-term. As a result, we try to hedge by diversifying.

21. Peak–End Rule

Quick Definition: People tend to remember and pass judgment on an event based upon its most intense moment of finality rather than the average.

The peak-end rule refers to situations where the peak and end of a situation are the most important in our memories. When describing situations in the past tense, our minds shortcut to the peak and the end and fail to contemplate the other parts of the memory.

For example, a book or movie may be boring for 75% of the film, but the last 25% are excellent. You then go away and tell people how excellent it was, forgetting that there were long boring periods.

This is because our minds are most stimulated at the highly emotive parts of a situation, searing them in our memories.

This rule can be applied in vacation packages, movies, and other experince-based services where the experience is curated so the peak (and end) are highly stimulating to create a ‘wow experience’ that shapes people’s memories.

22. Mere Exposure Effect

Quick Definition: The mere exposure effect occurs when people develop a preference for a stimulus (such as a brand) simply because it is familiar. It is sometimes referred to as the familiarity principle.

The more frequently a person sees, experiences, or is otherwise exposed to something, the more likely it is that they will begin to like and favor it.

This is a cognitive heuristic because it involves a mental shortcut where something that is familiar is assumed to be safer and more trustworthy than unfamiliar things, regardless of the facts of the case.

This is used extensively in advertising, for example, where repeated exposure to advertisements from a particular brand, such as a restaurant, might make people more inclined to go to that restaurant next time they are hungry.

>See our full article on the Mere Exposure Effect

Heuristics are rules of thumb that help us make decisions quickly. They are useful in many situations, and in fact have helped us evolutionarily by filtering out bad information and making decisions quickly.

However, they can can also lead to biases and errors in our thinking. In the worst-case scenarios they can lead to stereotyping and significant social harm. The most common types of heuristics are availability heuristics, representativeness heuristics, and anchoring and adjustment.

Knowing about these biases in our thinking can help marketers to sell products and help reflective people to make better decisions by knowing when and when not to use heuristics.

See Also: Fundamental Attribution Error Examples

• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd-2/ 10 Reasons you’re Perpetually Single
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd-2/ 20 Montessori Toddler Bedrooms (Design Inspiration)
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd-2/ 21 Montessori Homeschool Setups
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd-2/ 101 Hidden Talents Examples

2 thoughts on “22 Heuristics Examples (The Types of Heuristics)”

Really interesting reading about the types of Heuristics and thank you for the concise explanations.

The information was very concise is used it for a presentation I had. Thank you

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What Are Heuristics?

These mental shortcuts lead to fast decisions—and biased thinking

Verywell / Cindy Chung 

• History and Origins
• Heuristics vs. Algorithms
• Heuristics and Bias

How to Make Better Decisions

If you need to make a quick decision, there's a good chance you'll rely on a heuristic to come up with a speedy solution. Heuristics are mental shortcuts that allow people to solve problems and make judgments quickly and efficiently. Common types of heuristics rely on availability, representativeness, familiarity, anchoring effects, mood, scarcity, and trial-and-error.

Think of these as mental "rule-of-thumb" strategies that shorten decision-making time. Such shortcuts allow us to function without constantly stopping to think about our next course of action.

However, heuristics have both benefits and drawbacks. These strategies can be handy in many situations but can also lead to  cognitive biases . Becoming aware of this might help you make better and more accurate decisions.

Press Play for Advice On Making Decisions

Hosted by therapist Amy Morin, LCSW, this episode of The Verywell Mind Podcast shares a simple way to make a tough decision. Click below to listen now.

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History of the Research on Heuristics

Nobel-prize winning economist and cognitive psychologist Herbert Simon originally introduced the concept of heuristics in psychology in the 1950s. He suggested that while people strive to make rational choices, human judgment is subject to cognitive limitations. Purely rational decisions would involve weighing every alternative's potential costs and possible benefits.

However, people are limited by the amount of time they have to make a choice and the amount of information they have at their disposal. Other factors, such as overall intelligence and accuracy of perceptions, also influence the decision-making process.

In the 1970s, psychologists Amos Tversky and Daniel Kahneman presented their research on cognitive biases. They proposed that these biases influence how people think and make judgments.

Because of these limitations, we must rely on mental shortcuts to help us make sense of the world.

Simon's research demonstrated that humans were limited in their ability to make rational decisions, but it was Tversky and Kahneman's work that introduced the study of heuristics and the specific ways of thinking that people rely on to simplify the decision-making process.

How Heuristics Are Used

Heuristics play important roles in both  problem-solving  and  decision-making , as we often turn to these mental shortcuts when we need a quick solution.

Here are a few different theories from psychologists about why we rely on heuristics.

• Attribute substitution : People substitute simpler but related questions in place of more complex and difficult questions.
• Effort reduction : People use heuristics as a type of cognitive laziness to reduce the mental effort required to make choices and decisions.
• Fast and frugal : People use heuristics because they can be fast and correct in certain contexts. Some theories argue that heuristics are actually more accurate than they are biased.

In order to cope with the tremendous amount of information we encounter and to speed up the decision-making process, our brains rely on these mental strategies to simplify things so we don't have to spend endless amounts of time analyzing every detail.

You probably make hundreds or even thousands of decisions every day. What should you have for breakfast? What should you wear today? Should you drive or take the bus? Fortunately, heuristics allow you to make such decisions with relative ease and without a great deal of agonizing.

There are many heuristics examples in everyday life. When trying to decide if you should drive or ride the bus to work, for instance, you might remember that there is road construction along the bus route. You realize that this might slow the bus and cause you to be late for work. So you leave earlier and drive to work on an alternate route.

Heuristics allow you to think through the possible outcomes quickly and arrive at a solution.

Are Heuristics Good or Bad?

Heuristics aren't inherently good or bad, but there are pros and cons to using them to make decisions. While they can help us figure out a solution to a problem faster, they can also lead to inaccurate judgments about others or situations. Understanding these pros and cons may help you better use heuristics to make better decisions.

Types of Heuristics

There are many different kinds of heuristics. While each type plays a role in decision-making, they occur during different contexts. Understanding the types can help you better understand which one you are using and when.

Availability

The availability heuristic  involves making decisions based upon how easy it is to bring something to mind. When you are trying to make a decision, you might quickly remember a number of relevant examples.

Since these are more readily available in your memory, you will likely judge these outcomes as being more common or frequently occurring.

For example, imagine you are planning to fly somewhere on vacation. As you are preparing for your trip, you might start to think of a number of recent airline accidents. You might feel like air travel is too dangerous and decide to travel by car instead. Because those examples of air disasters came to mind so easily, the availability heuristic leads you to think that plane crashes are more common than they really are.

Familiarity

The familiarity heuristic refers to how people tend to have more favorable opinions of things, people, or places they've experienced before as opposed to new ones. In fact, given two options, people may choose something they're more familiar with even if the new option provides more benefits.

Representativeness

The representativeness heuristic  involves making a decision by comparing the present situation to the most representative mental prototype. When you are trying to decide if someone is trustworthy, you might compare aspects of the individual to other mental examples you hold.

A soft-spoken older woman might remind you of your grandmother, so you might immediately assume she is kind, gentle, and trustworthy. However, this is an example of a heuristic bias, as you can't know someone trustworthy based on their age alone.

The affect heuristic involves making choices that are influenced by an individual's emotions at that moment. For example, research has shown that people are more likely to see decisions as having benefits and lower risks when in a positive mood.

Negative emotions, on the other hand, lead people to focus on the potential downsides of a decision rather than the possible benefits.

The anchoring bias involves the tendency to be overly influenced by the first bit of information we hear or learn. This can make it more difficult to consider other factors and lead to poor choices. For example, anchoring bias can influence how much you are willing to pay for something, causing you to jump at the first offer without shopping around for a better deal.

Scarcity is a heuristic principle in which we view things that are scarce or less available to us as inherently more valuable. Marketers often use the scarcity heuristic to influence people to buy certain products. This is why you'll often see signs that advertise "limited time only," or that tell you to "get yours while supplies last."

Trial and Error

Trial and error is another type of heuristic in which people use a number of different strategies to solve something until they find what works. Examples of this type of heuristic are evident in everyday life.

People use trial and error when playing video games, finding the fastest driving route to work, or learning to ride a bike (or any new skill).

Difference Between Heuristics and Algorithms

Though the terms are often confused, heuristics and algorithms are two distinct terms in psychology.

Algorithms are step-by-step instructions that lead to predictable, reliable outcomes, whereas heuristics are mental shortcuts that are basically best guesses. Algorithms always lead to accurate outcomes, whereas, heuristics do not.

Examples of algorithms include instructions for how to put together a piece of furniture or a recipe for cooking a certain dish. Health professionals also create algorithms or processes to follow in order to determine what type of treatment to use on a patient.

How Heuristics Can Lead to Bias

Heuristics can certainly help us solve problems and speed up our decision-making process, but that doesn't mean they are always a good thing. They can also introduce errors, bias, and irrational decision-making. As in the examples above, heuristics can lead to inaccurate judgments about how commonly things occur and how representative certain things may be.

Just because something has worked in the past does not mean that it will work again, and relying on a heuristic can make it difficult to see alternative solutions or come up with new ideas.

Heuristics can also contribute to stereotypes and  prejudice . Because people use mental shortcuts to classify and categorize people, they often overlook more relevant information and create stereotyped categorizations that are not in tune with reality.

While heuristics can be a useful tool, there are ways you can improve your decision-making and avoid cognitive bias at the same time.

We are more likely to make an error in judgment if we are trying to make a decision quickly or are under pressure to do so. Taking a little more time to make a decision can help you see things more clearly—and make better choices.

Whenever possible, take a few deep breaths and do something to distract yourself from the decision at hand. When you return to it, you may find a fresh perspective or notice something you didn't before.

Identify the Goal

We tend to focus automatically on what works for us and make decisions that serve our best interest. But take a moment to know what you're trying to achieve. Consider some of the following questions:

• Are there other people who will be affected by this decision?
• What's best for them?
• Is there a common goal that can be achieved that will serve all parties?

Thinking through these questions can help you figure out your goals and the impact that these decisions may have.

Process Your Emotions

Fast decision-making is often influenced by emotions from past experiences that bubble to the surface. Anger, sadness, love, and other powerful feelings can sometimes lead us to decisions we might not otherwise make.

Is your decision based on facts or emotions? While emotions can be helpful, they may affect decisions in a negative way if they prevent us from seeing the full picture.

Recognize All-or-Nothing Thinking

When making a decision, it's a common tendency to believe you have to pick a single, well-defined path, and there's no going back. In reality, this often isn't the case.

Sometimes there are compromises involving two choices, or a third or fourth option that we didn't even think of at first. Try to recognize the nuances and possibilities of all choices involved, instead of using all-or-nothing thinking .

Heuristics are common and often useful. We need this type of decision-making strategy to help reduce cognitive load and speed up many of the small, everyday choices we must make as we live, work, and interact with others.

But it pays to remember that heuristics can also be flawed and lead to irrational choices if we rely too heavily on them. If you are making a big decision, give yourself a little extra time to consider your options and try to consider the situation from someone else's perspective. Thinking things through a bit instead of relying on your mental shortcuts can help ensure you're making the right choice.

Vlaev I. Local choices: Rationality and the contextuality of decision-making .  Brain Sci . 2018;8(1):8. doi:10.3390/brainsci8010008

Hjeij M, Vilks A. A brief history of heuristics: how did research on heuristics evolve? Humanit Soc Sci Commun . 2023;10(1):64. doi:10.1057/s41599-023-01542-z

Brighton H, Gigerenzer G. Homo heuristicus: Less-is-more effects in adaptive cognition .  Malays J Med Sci . 2012;19(4):6-16.

Schwartz PH. Comparative risk: Good or bad heuristic?   Am J Bioeth . 2016;16(5):20-22. doi:10.1080/15265161.2016.1159765

Schwikert SR, Curran T. Familiarity and recollection in heuristic decision making .  J Exp Psychol Gen . 2014;143(6):2341-2365. doi:10.1037/xge0000024

AlKhars M, Evangelopoulos N, Pavur R, Kulkarni S. Cognitive biases resulting from the representativeness heuristic in operations management: an experimental investigation .  Psychol Res Behav Manag . 2019;12:263-276. doi:10.2147/PRBM.S193092

Finucane M, Alhakami A, Slovic P, Johnson S. The affect heuristic in judgments of risks and benefits . J Behav Decis Mak . 2000; 13(1):1-17. doi:10.1002/(SICI)1099-0771(200001/03)13:1<1::AID-BDM333>3.0.CO;2-S

Teovanović P. Individual differences in anchoring effect: Evidence for the role of insufficient adjustment .  Eur J Psychol . 2019;15(1):8-24. doi:10.5964/ejop.v15i1.1691

Cheung TT, Kroese FM, Fennis BM, De Ridder DT. Put a limit on it: The protective effects of scarcity heuristics when self-control is low . Health Psychol Open . 2015;2(2):2055102915615046. doi:10.1177/2055102915615046

Mohr H, Zwosta K, Markovic D, Bitzer S, Wolfensteller U, Ruge H. Deterministic response strategies in a trial-and-error learning task . Inman C, ed. PLoS Comput Biol. 2018;14(11):e1006621. doi:10.1371/journal.pcbi.1006621

Grote T, Berens P. On the ethics of algorithmic decision-making in healthcare .  J Med Ethics . 2020;46(3):205-211. doi:10.1136/medethics-2019-105586

Bigler RS, Clark C. The inherence heuristic: A key theoretical addition to understanding social stereotyping and prejudice. Behav Brain Sci . 2014;37(5):483-4. doi:10.1017/S0140525X1300366X

del Campo C, Pauser S, Steiner E, et al.  Decision making styles and the use of heuristics in decision making .  J Bus Econ.  2016;86:389–412. doi:10.1007/s11573-016-0811-y

Marewski JN, Gigerenzer G. Heuristic decision making in medicine .  Dialogues Clin Neurosci . 2012;14(1):77-89. doi:10.31887/DCNS.2012.14.1/jmarewski

Zheng Y, Yang Z, Jin C, Qi Y, Liu X. The influence of emotion on fairness-related decision making: A critical review of theories and evidence .  Front Psychol . 2017;8:1592. doi:10.3389/fpsyg.2017.01592

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Heuristic Problem Solving: A comprehensive guide with 5 Examples

What are heuristics, advantages of using heuristic problem solving, disadvantages of using heuristic problem solving, heuristic problem solving examples, frequently asked questions.

• Speed: Heuristics are designed to find solutions quickly, saving time in problem solving tasks. Rather than spending a lot of time analyzing every possible solution, heuristics help to narrow down the options and focus on the most promising ones.
• Flexibility: Heuristics are not rigid, step-by-step procedures. They allow for flexibility and creativity in problem solving, leading to innovative solutions. They encourage thinking outside the box and can generate unexpected and valuable ideas.
• Simplicity: Heuristics are often easy to understand and apply, making them accessible to anyone regardless of their expertise or background. They don’t require specialized knowledge or training, which means they can be used in various contexts and by different people.
• Cost-effective: Because heuristics are simple and efficient, they can save time, money, and effort in finding solutions. They also don’t require expensive software or equipment, making them a cost-effective approach to problem solving.
• Real-world applicability: Heuristics are often based on practical experience and knowledge, making them relevant to real-world situations. They can help solve complex, messy, or ill-defined problems where other problem solving methods may not be practical.
• Potential for errors: Heuristic problem solving relies on generalizations and assumptions, which may lead to errors or incorrect conclusions. This is especially true if the heuristic is not based on a solid understanding of the problem or the underlying principles.
• Limited scope: Heuristic problem solving may only consider a limited number of potential solutions and may not identify the most optimal or effective solution.
• Lack of creativity: Heuristic problem solving may rely on pre-existing solutions or approaches, limiting creativity and innovation in problem-solving.
• Over-reliance: Heuristic problem solving may lead to over-reliance on a specific approach or heuristic, which can be problematic if the heuristic is flawed or ineffective.
• Lack of transparency: Heuristic problem solving may not be transparent or explainable, as the decision-making process may not be explicitly articulated or understood.
• Trial and error: This heuristic involves trying different solutions to a problem and learning from mistakes until a successful solution is found. A software developer encountering a bug in their code may try other solutions and test each one until they find the one that solves the issue.
• Working backward: This heuristic involves starting at the goal and then figuring out what steps are needed to reach that goal. For example, a project manager may begin by setting a project deadline and then work backward to determine the necessary steps and deadlines for each team member to ensure the project is completed on time.
• Breaking a problem into smaller parts: This heuristic involves breaking down a complex problem into smaller, more manageable pieces that can be tackled individually. For example, an HR manager tasked with implementing a new employee benefits program may break the project into smaller parts, such as researching options, getting quotes from vendors, and communicating the unique benefits to employees.
• Using analogies: This heuristic involves finding similarities between a current problem and a similar problem that has been solved before and using the solution to the previous issue to help solve the current one. For example, a salesperson struggling to close a deal may use an analogy to a successful sales pitch they made to help guide their approach to the current pitch.
• Simplifying the problem: This heuristic involves simplifying a complex problem by ignoring details that are not necessary for solving it. This allows the problem solver to focus on the most critical aspects of the problem. For example, a customer service representative dealing with a complex issue may simplify it by breaking it down into smaller components and addressing them individually rather than simultaneously trying to solve the entire problem.

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Why do we take mental shortcuts?

What are heuristics.

Heuristics are mental shortcuts that can facilitate problem-solving and probability judgments. These strategies are generalizations, or rules-of-thumb, that reduce cognitive load. They can be effective for making immediate judgments, however, they often result in irrational or inaccurate conclusions.

Where this bias occurs

We use heuristics in all sorts of situations. One type of heuristic, the availability heuristic , often happens when we’re attempting to judge the frequency with which a certain event occurs. Say, for example, someone asked you whether more tornadoes occur in Kansas or Nebraska. Most of us can easily call to mind an example of a tornado in Kansas: the tornado that whisked Dorothy Gale off to Oz in Frank L. Baum’s The Wizard of Oz . Although it’s fictional, this example comes to us easily. On the other hand, most people have a lot of trouble calling to mind an example of a tornado in Nebraska. This leads us to believe that tornadoes are more common in Kansas than in Nebraska. However, the states actually report similar levels. 1

Individual effects

The thing about heuristics is that they aren’t always wrong. As generalizations, there are many situations where they can yield accurate predictions or result in good decision-making. However, even if the outcome is favorable, it was not achieved through logical means. When we use heuristics, we risk ignoring important information and overvaluing what is less relevant. There’s no guarantee that using  heuristics will work out and, even if it does, we’ll be making the decision for the wrong reason. Instead of basing it on reason, our behavior is resulting from a mental shortcut with no real rationale to support it.

Systemic effects

Heuristics become more concerning when applied to politics, academia, and economics. We may all resort to heuristics from time to time, something that is true even of members of important institutions who are tasked with making large, influential decisions. It is necessary for these figures to have a comprehensive understanding of the biases and heuristics that can affect our behavior, so as to promote accuracy on their part.

How it affects product

Heuristics can be useful in product design. Specifically, because heuristics are intuitive to us, they can be applied to create a more user-friendly experience and one that is more valuable to the customer. For example, color psychology is a phenomenon explaining how our experiences with different colors and color families can prime certain emotions or behaviors. Taking advantage of the representativeness heuristic, one could choose to use passive colors (blue or green) or more active colors (red, yellow, orange) depending on the goals of the application or product. 18 For example, if a developer is trying to evoke a feeling of calm for their app that provides guided meditations, they may choose to make the primary colors of the program light blues and greens. Colors like red and orange are more emotionally energizing and may be useful in settings like gyms or crossfit programs. 

By integrating heuristics into products we can enhance the user experience. If an application, device, or item includes features that make it feel intuitive, easy to navigate and familiar, customers will be more inclined to continue to use it and recommend it to others. Appealing to those mental shortcuts we can minimize the chances of user error or frustration with a product that is overly complicated.

Heuristics and AI

Artificial intelligence and machine learning tools already use the power of heuristics to inform its output. In a nutshell, simple AI tools operate based on a set of built in rules and sometimes heuristics! These are encoded within the system thus aiding in decision-making and the presentation of learning material. Heuristic algorithms can be used to solve advanced computational problems, providing efficient and approximate solutions.  Like in humans, the use of heuristics can result in error, and thus must be used with caution. However, machine learning tools and AI can be useful in supporting human decision-making, especially when clouded by emotion, bias or irrationality due to our own susceptibility to heuristics. 

Why it happens

In their paper “Judgment Under Uncertainty: Heuristics and Biases” 2 , Daniel Kahneman and Amos Tversky identified three different kinds of heuristics: availability, representativeness, as well as anchoring and adjustment. Each type of heuristic is used for the purpose of reducing the mental effort needed to make a decision, but they occur in different contexts.

Availability heuristic

The availability heuristic, as defined by Kahneman and Tversky, is the mental shortcut used for making frequency or probability judgments based on “the ease with which instances or occurrences can be brought to mind”. 3 This was touched upon in the previous example, judging the frequency with which tornadoes occur in Kansas relative to Nebraska. 3

The availability heuristic occurs because certain memories come to mind more easily than others. In Kahneman and Tversky’s example participants were asked if more words in the English language start with the letter K or have K as the third letter  Interestingly, most participants responded with the former when in actuality, it is the latter that is true. The idea being that it is much more difficult to think of words that have K as the third letter than it is to think of words that start with K. 4 In this case,  words that begin with K are more readily available to us than words with the K as the third letter.

Representativeness heuristic

Individuals tend to classify events into categories, which, as illustrated by Kahneman and Tversky, can result in our use of the representativeness heuristic. When we use this heuristic, we categorize events or objects based on how they relate to instances we are already familiar with.  Essentially, we have built our own categories, which we use to make predictions about novel situations or people. 5 For example, if someone we meet in one of our university lectures looks and acts like what we believe to be a stereotypical medical student, we may judge the probability that they are studying medicine as highly likely, even without any hard evidence to support that assumption.

The representativeness heuristic is associated with prototype theory. 6 This prominent theory in cognitive science, the prototype theory explains object and identity recognition. It suggests that we categorize different objects and identities in our memory. For example, we may have a category for chairs, a category for fish, a category for books, and so on. Prototype theory posits that we develop prototypical examples for these categories by averaging every example of a given category we encounter. As such, our prototype of a chair should be the most average example of a chair possible, based on our experience with that object. This process aids in object identification because we compare every object we encounter against the prototypes stored in our memory. The more the object resembles the prototype, the more confident we are that it belongs in that category. 

Prototype theory may give rise to the representativeness heuristic as it is in situations when a particular object or event is viewed as similar to the prototype stored in our memory, which leads us to classify the object or event into the category represented by that prototype. To go back to the previous example, if your peer closely resembles your prototypical example of a med student, you may place them into that category based on the prototype theory of object and identity recognition. This, however, causes you to commit the representativeness heuristic.

Anchoring and adjustment heuristic

Another heuristic put forth by Kahneman and Tversky in their initial paper is the anchoring and adjustment heuristic. 7 This heuristic describes how, when estimating a certain value, we tend to give an initial value, then adjust it by increasing or decreasing our estimation. However, we often get stuck on that initial value – which is referred to as anchoring – this results in us making insufficient adjustments. Thus, the adjusted value is biased in favor of the initial value we have anchored to.

In an example of the anchoring and adjustment heuristic, Kahneman and Tversky gave participants questions such as “estimate the number of African countries in the United Nations (UN).” A wheel labeled with numbers from 0-100 was spun, and participants were asked to say whether or not the number the wheel landed on was higher or lower than their answer to the question. Then, participants were asked to estimate the number of African countries in the UN, independent from the number they had spun. Regardless, Kahneman and Tversky found that participants tended to anchor onto the random number obtained by spinning the wheel. The results showed that  when the number obtained by spinning the wheel was 10, the median estimate given by participants was 25, while, when the number obtained from the wheel was 65, participants’ median estimate was 45.8.

A 2006 study by Epley and Gilovich, “The Anchoring and Adjustment Heuristic: Why the Adjustments are Insufficient” 9 investigated the causes of this heuristic. They illustrated that anchoring often occurs because the new information that we anchor to is more accessible than other information Furthermore, they provided empirical evidence to demonstrate that our adjustments tend to be insufficient because they require significant mental effort, which we are not always motivated to dedicate to the task. They also found that providing incentives for accuracy led participants to make more sufficient adjustments. So, this particular heuristic generally occurs when there is no real incentive to provide an accurate response.

Quick and easy

Though different in their explanations, these three types of heuristics allow us to respond automatically without much effortful thought. They provide an immediate response and do not use up much of our mental energy, which allows us to dedicate mental resources to other matters that may be more pressing. In that way, heuristics are efficient, which is a big reason why we continue to use them. That being said, we should be mindful of how much we rely on them because there is no guarantee of their accuracy.

Why it is important

As illustrated by Tversky and Kahneman, using heuristics can cause us to engage in various cognitive biases and commit certain fallacies. 10 As a result, we may make poor decisions, as well as inaccurate judgments and predictions. Awareness of heuristics can aid us in avoiding them, which will ultimately lead us to engage in more adaptive behaviors.

How to avoid it

Heuristics arise from automatic System 1 thinking. It is a common misconception that errors in judgment can be avoided by relying exclusively on System 2 thinking. However, as pointed out by Kahneman, neither System 2 nor System 1 are infallible. 11   While System 1 can result in relying on heuristics leading to certain biases, System 2 can give rise to other biases, such as the confirmation bias . 12 In truth, Systems 1 and 2 complement each other, and using them together can lead to more rational decision-making. That is, we shouldn’t make judgments automatically, without a second thought, but we shouldn’t overthink things to the point where we’re looking for specific evidence to support our stance. Thus, heuristics can be avoided by making judgments more effortfully, but in doing so, we should attempt not to overanalyze the situation.

How it all started

The first three heuristics – availability, representativeness, as well as anchoring and adjustment – were identified by Tverksy and Kahneman in their 1974 paper, “Judgment Under Uncertainty: Heuristics and Biases”. 13 In addition to presenting these heuristics and their relevant experiments, they listed the respective biases each can lead to.

For instance, upon defining the availability heuristic, they demonstrated how it may lead to illusory correlation , which is the erroneous belief that two events frequently co-occur. Kahneman and Tversky made the connection by illustrating how the availability heuristic can cause us to over- or under-estimate the frequency with which certain events occur. This may result in drawing correlations between variables when in reality there are none.  

Referring to our tendency to overestimate our accuracy making probability judgments, Kahneman and Tversky also discussed how the illusion of validity is facilitated by the representativeness heuristic. The more representative an object or event is, the more confident we feel in predicting certain outcomes. The illusion of validity, as it works with the representativeness heuristic, can be demonstrated by our assumptions of others based on past experiences. If you have only ever had good experiences with people from Canada, you will be inclined to judge most Canadians as pleasant. In reality, your small sample size cannot account for the whole population. Representativeness is not the only factor in determining the probability of an outcome or event, meaning we should not be as confident in our predictive abilities.

Example 1 – Advertising

Those in the field of advertising should have a working understanding of heuristics as consumers often rely on these shortcuts when making decisions about purchases. One heuristic that frequently comes into play in the realm of advertising is the scarcity heuristic . When assessing the value of something, we often fall back on this heuristic, leading us to believe that the rarity or exclusiveness of an object contributes to its value.

A 2011 study by Praveen Aggarwal, Sung Yul Jun, and Jong Ho Huh evaluated the impact of “scarcity messages” on consumer behavior. They found that both “limited quantity” and “limited time” advertisements influence consumers’ intentions to purchase, but “limited quantity” messages are more effective. This explains why people get so excited over the one-day-only Black Friday sales, and why the countdowns of units available on home shopping television frequently lead to impulse buys. 14

Knowledge of the scarcity heuristic can help businesses thrive, as “limited quantity” messages make potential consumers competitive and increase their intentions to purchase. 15 This marketing technique can be a useful tool for bolstering sales and bringing attention to your business.

Example 2 – Stereotypes

One of the downfalls of heuristics is that they have the potential to lead to stereotyping, which is often harmful. Kahneman and Tversky illustrated how the representativeness heuristic might result in the propagation of stereotypes. The researchers presented participants with a personality sketch of a fictional man named Steve followed by a list of possible occupations. Participants were tasked with ranking the likelihood of each occupation being Steve’s. Since the personality sketch described Steve as shy, helpful, introverted, and organized, participants tended to indicate that it was probable that he was a  librarian. 16 In this particular case the stereotype is less harmful than many others, however it accurately illustrates the link between heuristics and stereotypes.

Published in 1989, Patricia Devine’s paper “Stereotypes and Prejudice: Their Automatic and Controlled Components” illustrates how, even among people who are low in prejudice, rejecting stereotypes requires a certain level of motivation and cognitive capacity. 17 We typically use heuristics in order to avoid exerting too much mental energy, specifically when we are not sufficiently motivated to dedicate mental resources to the task at hand. Thus, when we lack the mental capacity to make a judgment or decision effortfully, we may rely upon automatic heuristic responses and, in doing so, risk propagating stereotypes.

Stereotypes are an example of how heuristics can go wrong. Broad generalizations do not always apply, and their continued use can have serious consequences. This underscores the importance of effortful judgment and decision-making, as opposed to automatic.

Heuristics are mental shortcuts that allow us to make quick judgment calls based on generalizations or rules of thumb.

Heuristics, in general, occur because they are efficient ways of responding when we are faced with problems or decisions. They come about automatically, allowing us to allocate our mental energy elsewhere. Specific heuristics occur in different contexts; the availability heuristic happens because we remember certain memories better than others, the representativeness heuristic can be explained by prototype theory, and the anchoring and adjustment heuristic occurs due to lack of incentive to put in the effort required for sufficient adjustment.

The scarcity heuristic, which refers to how we value items more when they are limited, can be used to the advantage of businesses looking to increase sales. Research has shown that advertising objects as “limited quantity” increases consumers' competitiveness and their intentions to buy the item.

While heuristics can be useful, we should exert caution, as they are generalizations that may lead us to propagate stereotypes ranging from inaccurate to harmful.

Putting more effort into decision-making instead of making decisions automatically can help us avoid heuristics. Doing so requires more mental resources, but it will lead to more rational choices.

Related TDL articles

What are heuristics.

This interview with The Decision Lab’s Managing Director Sekoul Krastev delves into the history of heuristics, their applications in the real world, and their consequences, both positive and negative.

10 Decision-Making Errors that Hold Us Back at Work

In this article, Dr. Melina Moleskis examines the common decision-making errors that occur in the workplace. Everything from taking in feedback provided by customers to cracking the problems of on-the-fly decision-making, Dr. Moleskis delivers workable solutions that anyone can implement. 

Case studies

From insight to impact: our success stories, is there a problem we can help with.

• Gilovich, T., Keltner, D., Chen. S, and Nisbett, R. (2015).  Social Psychology  (4th edition). W.W. Norton and Co. Inc.
• Tversky, A. and Kahneman, D. (1974). Judgment Under Uncertainty: Heuristics and Biases.  Science . 185(4157), 1124-1131.
• Mervis, C. B., & Rosch, E. (1981). Categorization of natural objects.  Annual Review of Psychology ,  32 (1), 89–115. https://doi.org/10.1146/annurev.ps.32.020181.000513
• Epley, N., & Gilovich, T. (2006). The anchoring-and-adjustment heuristic.  Psychological Science -Cambridge- ,  17 (4), 311–318.
• System 1 and System 2 Thinking.  The Marketing Society.  https://www.marketingsociety.com/think-piece/system-1-and-system-2-thinking
• Aggarwal, P., Jun, S. Y., & Huh, J. H. (2011). Scarcity messages.  Journal of Advertising ,  40 (3), 19–30.
• Devine, P. G. (1989). Stereotypes and prejudice: their automatic and controlled components.  Journal of Personality and Social Psychology ,  56 (1), 5–18. https://doi.org/10.1037/0022-3514.56.1.5
• Kuo, L., Chang, T., &amp; Lai, C.-C. (2022). Research on product design modeling image and color psychological test. Displays, 71, 102108. https://doi.org/10.1016/j.displa.2021.102108

About the Authors

Dan is a Co-Founder and Managing Director at The Decision Lab. He is a bestselling author of Intention - a book he wrote with Wiley on the mindful application of behavioral science in organizations. Dan has a background in organizational decision making, with a BComm in Decision & Information Systems from McGill University. He has worked on enterprise-level behavioral architecture at TD Securities and BMO Capital Markets, where he advised management on the implementation of systems processing billions of dollars per week. Driven by an appetite for the latest in technology, Dan created a course on business intelligence and lectured at McGill University, and has applied behavioral science to topics such as augmented and virtual reality.

Dr. Sekoul Krastev

Sekoul is a Co-Founder and Managing Director at The Decision Lab. He is a bestselling author of Intention - a book he wrote with Wiley on the mindful application of behavioral science in organizations. A decision scientist with a PhD in Decision Neuroscience from McGill University, Sekoul's work has been featured in peer-reviewed journals and has been presented at conferences around the world. Sekoul previously advised management on innovation and engagement strategy at The Boston Consulting Group as well as on online media strategy at Google. He has a deep interest in the applications of behavioral science to new technology and has published on these topics in places such as the Huffington Post and Strategy & Business.

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Types of Heuristics in Psychology

Categories Cognition

When you are trying to solve a problem or make a decision, you don’t always have time to examine every possible answer or possibility. Sometimes, you have to rely on the information you already have to make the best guess or estimate in a limited amount of time.

This is an example of using heuristics, or mental ‘rules of thumb,’ that help you make choices quickly and easily. 

There are many different ways to solve problems, but some take more time than others. Heuristics can be thought of as mental shortcuts that often help us make educated guesses.

Definition : A heuristic in psychology refers to a mental shortcut or rule of thumb that helps individuals make decisions or solve problems more efficiently. It is a cognitive strategy that allows us to simplify complex information and make judgments quickly. 

Table of Contents

3 Key Types of Heuristics

There are several different types of heuristics that we commonly use in our everyday lives. 

Availability Heuristic

This heuristic involves making judgments based on the ease with which examples or instances come to mind. For example, if we can easily recall instances of successful outcomes from a particular option, we are more likely to choose it. 

Representativeness Heuristic

This heuristic involves making judgments based on how well an object or event matches a particular prototype or stereotype. For example, if someone fits our mental image of a successful entrepreneur, we may assume they are more likely to be successful. 

Anchoring and Adjustment Heuristic

The anchoring and adjustment heuristic heuristic involves starting with an initial anchor or reference point and then adjusting our judgment based on additional information. For example, when negotiating a price, we may start with a high anchor and then adjust downward based on the seller’s counteroffer. 

Why We Use Different Types of Heuristics

We don’t always have the time–or the resources–to consider every possible option for every decision we make. People make hundreds of decisions each day. If we had to meticulously use trial and error or other methods to make each choice, we’d never get anything done.

Heuristics are often used when we don’t have the time or resources to gather all the necessary information for a decision.

Of course, heuristics aren’t perfect. They can also be biased and may lead to inaccurate decisions. Despite their limitations, heuristics are valuable because they allow us to make decisions quickly and with minimal effort. 

There are different types of heuristics that individuals use in various situations. Some common types include availability heuristics, representativeness heuristics, and anchoring and adjustment heuristics. 

Each type of heuristic has its own set of characteristics and biases. Understanding heuristics is important because they can contribute to cognitive biases, which are systematic errors in thinking. By recognizing these biases, we can become more aware of our decision-making processes and make more informed choices. 

How Were These Types of Heuristics Discovered? 

While we may like to believe that our choices are rooted in rationality and logic, psychologists have shown that there are certain patterns that tend to dictate how we solve the problems we face. During the 1970s, [sychologists Amos Tversky and Daniel Kahneman conducted groundbreaking studies on how people make judgments in the face of uncertainty.

Their work challenged the traditional view that humans always make rational choices based on complete information. 

Tversky and Kahneman suggested that heuristics are mental shortcuts that individuals use to simplify complex problems and make judgments quickly. They identified several common heuristics, such as the availability heuristic, which involves making judgments based on how easily examples come to mind, and the representativeness heuristic, which involves making judgments based on how closely something resembles a typical example. 

This research provided valuable insights into the limitations and biases associated with heuristics. They showed that heuristics can lead to systematic errors in thinking known as cognitive biases . 

How We Use Different Types of Heuristics to Make Decisions?

Heuristics are an inextricable part of our daily lives, even though we are rarely aware of them. In decisions both large and small, we use heuristics to help narrow down our choices and determine which option is right for us, often based on very limited information. 

For example, the availability heuristic helps us make decisions based on the ease with which examples come to mind. If we can easily recall instances of successful outcomes from a particular option, we are more likely to choose it. 

Heuristics also aid in problem-solving by providing shortcuts to finding solutions. Instead of exhaustively analyzing every possible solution, heuristics allow us to quickly identify potential options based on past experiences or general rules of thumb. This can save time and mental effort, especially when we need to act quickly.

Advertisers often employ heuristics to create persuasive messages that appeal to consumers’ cognitive biases. By framing information in a certain way or using social proof, they can influence our decision-making and encourage specific actions. 

Examples of Types of Heuristics 

There are examples of heuristics all around us. Examining some of these examples can help give greater insight into how they shape our thinking and influence our choices. 

• For example, imagine that you are going to be flying to another country for vacation. In the weeks before your flight, you find yourself recalling numerous news stories of plane crashes. Because these examples spring to mind so readily, you may overestimate the likelihood that a plane crash will occur. This is an example of the availability heuristic.
• Or imagine you deciding who to vote for in an upcoming election. You might look at the candidates and pick one based on your expectations about good leadership traits. Basing your decision on how well the candidate fits your expectations rather than on their voting record or policy platform is an example of the representativeness heuristic.
• Or imagine that you are thinking about buying a new house. You look at the list price, and then use that number as an ‘anchor’ to base your offer on. It may not necessarily indicate what the house is worth or what other similar houses are going for, but you’re still likely to use that initial number as a reference point for all future negotiations. 

These examples highlight how heuristics can simplify decision-making but also demonstrate their potential limitations. By recognizing these heuristics in action, we can become more aware of their influence and make more informed choices. 

Heuristics vs. Other Decision-Making Strategies 

Heuristics are just one of the many strategies people utilize to make decisions. We may be more likely to rely on heuristics when:

• When need to make decisions quickly
• When we don’t have the cognitive resources to use other strategies
• When we have relevant past experience

It is important to note that heuristics and other decision-making strategies are not mutually exclusive. In fact, individuals often use a combination of heuristics and other strategies depending on the context and the specific decision at hand. 

Understanding the differences between heuristics and other decision-making strategies can help individuals become more aware of their decision-making processes and make more informed choices. By recognizing the strengths and limitations of each approach, individuals can develop a more balanced and effective decision-making toolkit.

Using Different Types of Heuristics to Make Better Decisions

Using various types of heuristics can be a valuable tool for making better decisions. By understanding how heuristics work and being aware of their potential biases, individuals can harness the power of heuristics to improve their decision-making processes. 

• Recognize when they are appropriate . Heuristics are particularly useful when time is limited or when there is a lack of information. Mental shortcuts can help individuals make quick and efficient decisions in these cases. 
• Combine them with other decision-making strategies . While heuristics provide shortcuts, they are not foolproof and can lead to cognitive biases. By incorporating other strategies such as weighing pros and cons or conducting research, individuals can mitigate the potential biases associated with heuristics. 
• Be aware of the specific heuristics being used and their potential limitations . Different types of heuristics, such as availability heuristics or representativeness heuristics, have their own biases and may not always lead to accurate judgments. 

By understanding these biases, individuals can make more informed decisions and avoid common pitfalls. In conclusion, heuristics can be a powerful tool for making better decisions. Recognizing when to use them, combining them with other strategies, and being aware of their limitations can help you make better decisions.

Bobadilla-Suarez, S., & Love, B. C. (2018). Fast or frugal, but not both: Decision heuristics under time pressure . Journal of Experimental Psychology: Learning, Memory, and Cognition , 44(1), 24–33. https://doi.org/10.1037/xlm0000419

Lindström, B., Jangard, S., Selbing, I., & Olsson, A. (2018). The role of a “common is moral” heuristic in the stability and change of moral norms . Journal of Experimental Psychology: General , 147(2), 228–242. https://doi.org/10.1037/xge0000365

Heuristics: The Psychology of Mental Shortcuts

• Archaeology
• Ph.D., Materials Science and Engineering, Northwestern University
• B.A., Chemistry, Johns Hopkins University
• B.A., Cognitive Science, Johns Hopkins University

Heuristics (also called “mental shortcuts” or “rules of thumb") are efficient mental processes that help humans solve problems and learn new concepts. These processes make problems less complex by ignoring some of the information that’s coming into the brain, either consciously or unconsciously. Today, heuristics have become an influential concept in the areas of judgment and decision-making.

Key Takeaways: Heuristics

• Heuristics are efficient mental processes (or "mental shortcuts") that help humans solve problems or learn a new concept.
• In the 1970s, researchers Amos Tversky and Daniel Kahneman identified three key heuristics: representativeness, anchoring and adjustment, and availability.
• The work of Tversky and Kahneman led to the development of the heuristics and biases research program.

History and Origins

Gestalt psychologists postulated that humans solve problems and perceive objects based on heuristics. In the early 20th century, the psychologist Max Wertheimer identified laws by which humans group objects together into patterns (e.g. a cluster of dots in the shape of a rectangle).

The heuristics most commonly studied today are those that deal with decision-making. In the 1950s, economist and political scientist Herbert Simon published his A Behavioral Model of Rational Choice , which focused on the concept of on bounded rationality : the idea that people must make decisions with limited time, mental resources, and information.

In 1974, psychologists Amos Tversky and Daniel Kahneman pinpointed specific mental processes used to simplify decision-making. They showed that humans rely on a limited set of heuristics when making decisions with information about which they are uncertain—for example, when deciding whether to exchange money for a trip overseas now or a week from today. Tversky and Kahneman also showed that, although heuristics are useful, they can lead to errors in thinking that are both predictable and unpredictable.

In the 1990s, research on heuristics, as exemplified by the work of Gerd Gigerenzer’s research group, focused on how factors in the environment impact thinking–particularly, that the strategies the mind uses are influenced by the environment–rather than the idea that the mind uses mental shortcuts to save time and effort.

Significant Psychological Heuristics

Tversky and Kahneman’s 1974 work, Judgment under Uncertainty: Heuristics and Biases , introduced three key characteristics: representativeness, anchoring and adjustment, and availability. 

The  representativeness  heuristic allows people to judge the likelihood that an object belongs in a general category or class based on how similar the object is to members of that category.

To explain the representativeness heuristic, Tversky and Kahneman provided the example of an individual named Steve, who is “very shy and withdrawn, invariably helpful, but with little interest in people or reality. A meek and tidy soul, he has a need for order and structure, and a passion for detail.” What is the probability that Steve works in a specific occupation (e.g. librarian or doctor)? The researchers concluded that, when asked to judge this probability, individuals would make their judgment based on how similar Steve seemed to the stereotype of the given occupation.

The anchoring and adjustment heuristic allows people to estimate a number by starting at an initial value (the “anchor”) and adjusting that value up or down. However, different initial values lead to different estimates, which are in turn influenced by the initial value.

To demonstrate the anchoring and adjustment heuristic, Tversky and Kahneman asked participants to estimate the percentage of African countries in the UN. They found that, if participants were given an initial estimate as part of the question (for example, is the real percentage higher or lower than 65%?), their answers were rather close to the initial value, thus seeming to be "anchored" to the first value they heard.

The availability heuristic allows people to assess how often an event occurs or how likely it will occur, based on how easily that event can be brought to mind. For example, someone might estimate the percentage of middle-aged people at risk of a heart attack by thinking of the people they know who have had heart attacks.

Tversky and Kahneman's findings led to the development of the heuristics and biases research program. Subsequent works by researchers have introduced a number of other heuristics.

The Usefulness of Heuristics

There are several theories for the usefulness of heuristics. The  accuracy-effort trade-off   theory  states that humans and animals use heuristics because processing every piece of information that comes into the brain takes time and effort. With heuristics, the brain can make faster and more efficient decisions, albeit at the cost of accuracy. 

Some suggest that this theory works because not every decision is worth spending the time necessary to reach the best possible conclusion, and thus people use mental shortcuts to save time and energy. Another interpretation of this theory is that the brain simply does not have the capacity to process everything, and so we  must  use mental shortcuts.

Another explanation for the usefulness of heuristics is the  ecological rationality theory. This theory states that some heuristics are best used in specific environments, such as uncertainty and redundancy. Thus, heuristics are particularly relevant and useful in specific situations, rather than at all times.

• Gigerenzer, G., and Gaissmeier, W. “Heuristic decision making.” Annual Review of Psychology , vol. 62, 2011, pp. 451-482.
• Hertwig, R., and Pachur, T. “Heuristics, history of.” In International Encyclopedia of the Social & Behavioral Sciences, 2 Edition nd , Elsevier, 2007.
• “Heuristics representativeness.” Cognitive Consonance.
• Simon. H. A. “A behavioral model of rational choice.” The Quarterly Journal of Economics , vol. 69, no. 1, 1955, pp. 99-118.
• Tversky, A., and Kahneman, D. “Judgment under uncertainty: Heuristics and biases.” Science , vol. 185, no. 4157, pp. 1124-1131.
• What Is Cognitive Bias? Definition and Examples
• What Is a Schema in Psychology? Definition and Examples
• What Is Theory of Mind in Psychology?
• What Is Positive Psychology?
• Why Being a Perfectionist Can Be Harmful
• What Is Mindfulness in Psychology?
• Psychodynamic Theory: Approaches and Proponents
• What Is Behaviorism in Psychology?
• Understanding the Triarchic Theory of Intelligence
• An Introduction to Rogerian Therapy
• How Psychology Defines and Explains Deviant Behavior
• Information Processing Theory: Definition and Examples
• The Life of Carl Jung, Founder of Analytical Psychology
• Understanding Sexual Orientation From a Psychological Perspective
• What Is the Elaboration Likelihood Model in Psychology?
• Introduction to Evolutionary Psychology

7.3 Problem-Solving

Learning objectives.

By the end of this section, you will be able to:

• Describe problem solving strategies
• Define algorithm and heuristic
• Explain some common roadblocks to effective problem solving

   People face problems every day—usually, multiple problems throughout the day. Sometimes these problems are straightforward: To double a recipe for pizza dough, for example, all that is required is that each ingredient in the recipe be doubled. Sometimes, however, the problems we encounter are more complex. For example, say you have a work deadline, and you must mail a printed copy of a report to your supervisor by the end of the business day. The report is time-sensitive and must be sent overnight. You finished the report last night, but your printer will not work today. What should you do? First, you need to identify the problem and then apply a strategy for solving the problem.

The study of human and animal problem solving processes has provided much insight toward the understanding of our conscious experience and led to advancements in computer science and artificial intelligence. Essentially much of cognitive science today represents studies of how we consciously and unconsciously make decisions and solve problems. For instance, when encountered with a large amount of information, how do we go about making decisions about the most efficient way of sorting and analyzing all the information in order to find what you are looking for as in visual search paradigms in cognitive psychology. Or in a situation where a piece of machinery is not working properly, how do we go about organizing how to address the issue and understand what the cause of the problem might be. How do we sort the procedures that will be needed and focus attention on what is important in order to solve problems efficiently. Within this section we will discuss some of these issues and examine processes related to human, animal and computer problem solving.

PROBLEM-SOLVING STRATEGIES

   When people are presented with a problem—whether it is a complex mathematical problem or a broken printer, how do you solve it? Before finding a solution to the problem, the problem must first be clearly identified. After that, one of many problem solving strategies can be applied, hopefully resulting in a solution.

Problems themselves can be classified into two different categories known as ill-defined and well-defined problems (Schacter, 2009). Ill-defined problems represent issues that do not have clear goals, solution paths, or expected solutions whereas well-defined problems have specific goals, clearly defined solutions, and clear expected solutions. Problem solving often incorporates pragmatics (logical reasoning) and semantics (interpretation of meanings behind the problem), and also in many cases require abstract thinking and creativity in order to find novel solutions. Within psychology, problem solving refers to a motivational drive for reading a definite “goal” from a present situation or condition that is either not moving toward that goal, is distant from it, or requires more complex logical analysis for finding a missing description of conditions or steps toward that goal. Processes relating to problem solving include problem finding also known as problem analysis, problem shaping where the organization of the problem occurs, generating alternative strategies, implementation of attempted solutions, and verification of the selected solution. Various methods of studying problem solving exist within the field of psychology including introspection, behavior analysis and behaviorism, simulation, computer modeling, and experimentation.

A problem-solving strategy is a plan of action used to find a solution. Different strategies have different action plans associated with them (table below). For example, a well-known strategy is trial and error. The old adage, “If at first you don’t succeed, try, try again” describes trial and error. In terms of your broken printer, you could try checking the ink levels, and if that doesn’t work, you could check to make sure the paper tray isn’t jammed. Or maybe the printer isn’t actually connected to your laptop. When using trial and error, you would continue to try different solutions until you solved your problem. Although trial and error is not typically one of the most time-efficient strategies, it is a commonly used one.

   Another type of strategy is an algorithm. An algorithm is a problem-solving formula that provides you with step-by-step instructions used to achieve a desired outcome (Kahneman, 2011). You can think of an algorithm as a recipe with highly detailed instructions that produce the same result every time they are performed. Algorithms are used frequently in our everyday lives, especially in computer science. When you run a search on the Internet, search engines like Google use algorithms to decide which entries will appear first in your list of results. Facebook also uses algorithms to decide which posts to display on your newsfeed. Can you identify other situations in which algorithms are used?

A heuristic is another type of problem solving strategy. While an algorithm must be followed exactly to produce a correct result, a heuristic is a general problem-solving framework (Tversky & Kahneman, 1974). You can think of these as mental shortcuts that are used to solve problems. A “rule of thumb” is an example of a heuristic. Such a rule saves the person time and energy when making a decision, but despite its time-saving characteristics, it is not always the best method for making a rational decision. Different types of heuristics are used in different types of situations, but the impulse to use a heuristic occurs when one of five conditions is met (Pratkanis, 1989):

• When one is faced with too much information
• When the time to make a decision is limited
• When the decision to be made is unimportant
• When there is access to very little information to use in making the decision
• When an appropriate heuristic happens to come to mind in the same moment

Working backwards is a useful heuristic in which you begin solving the problem by focusing on the end result. Consider this example: You live in Washington, D.C. and have been invited to a wedding at 4 PM on Saturday in Philadelphia. Knowing that Interstate 95 tends to back up any day of the week, you need to plan your route and time your departure accordingly. If you want to be at the wedding service by 3:30 PM, and it takes 2.5 hours to get to Philadelphia without traffic, what time should you leave your house? You use the working backwards heuristic to plan the events of your day on a regular basis, probably without even thinking about it.

Another useful heuristic is the practice of accomplishing a large goal or task by breaking it into a series of smaller steps. Students often use this common method to complete a large research project or long essay for school. For example, students typically brainstorm, develop a thesis or main topic, research the chosen topic, organize their information into an outline, write a rough draft, revise and edit the rough draft, develop a final draft, organize the references list, and proofread their work before turning in the project. The large task becomes less overwhelming when it is broken down into a series of small steps.

Further problem solving strategies have been identified (listed below) that incorporate flexible and creative thinking in order to reach solutions efficiently.

Additional Problem Solving Strategies :

• Abstraction – refers to solving the problem within a model of the situation before applying it to reality.
• Analogy – is using a solution that solves a similar problem.
• Brainstorming – refers to collecting an analyzing a large amount of solutions, especially within a group of people, to combine the solutions and developing them until an optimal solution is reached.
• Divide and conquer – breaking down large complex problems into smaller more manageable problems.
• Hypothesis testing – method used in experimentation where an assumption about what would happen in response to manipulating an independent variable is made, and analysis of the affects of the manipulation are made and compared to the original hypothesis.
• Lateral thinking – approaching problems indirectly and creatively by viewing the problem in a new and unusual light.
• Means-ends analysis – choosing and analyzing an action at a series of smaller steps to move closer to the goal.
• Method of focal objects – putting seemingly non-matching characteristics of different procedures together to make something new that will get you closer to the goal.
• Morphological analysis – analyzing the outputs of and interactions of many pieces that together make up a whole system.
• Proof – trying to prove that a problem cannot be solved. Where the proof fails becomes the starting point or solving the problem.
• Reduction – adapting the problem to be as similar problems where a solution exists.
• Research – using existing knowledge or solutions to similar problems to solve the problem.
• Root cause analysis – trying to identify the cause of the problem.

The strategies listed above outline a short summary of methods we use in working toward solutions and also demonstrate how the mind works when being faced with barriers preventing goals to be reached.

One example of means-end analysis can be found by using the Tower of Hanoi paradigm . This paradigm can be modeled as a word problems as demonstrated by the Missionary-Cannibal Problem :

Missionary-Cannibal Problem

Three missionaries and three cannibals are on one side of a river and need to cross to the other side. The only means of crossing is a boat, and the boat can only hold two people at a time. Your goal is to devise a set of moves that will transport all six of the people across the river, being in mind the following constraint: The number of cannibals can never exceed the number of missionaries in any location. Remember that someone will have to also row that boat back across each time.

Hint : At one point in your solution, you will have to send more people back to the original side than you just sent to the destination.

The actual Tower of Hanoi problem consists of three rods sitting vertically on a base with a number of disks of different sizes that can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top making a conical shape. The objective of the puzzle is to move the entire stack to another rod obeying the following rules:

• 1. Only one disk can be moved at a time.
• 2. Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod.
• 3. No disc may be placed on top of a smaller disk.

  Figure 7.02. Steps for solving the Tower of Hanoi in the minimum number of moves when there are 3 disks.

Figure 7.03. Graphical representation of nodes (circles) and moves (lines) of Tower of Hanoi.

The Tower of Hanoi is a frequently used psychological technique to study problem solving and procedure analysis. A variation of the Tower of Hanoi known as the Tower of London has been developed which has been an important tool in the neuropsychological diagnosis of executive function disorders and their treatment.

GESTALT PSYCHOLOGY AND PROBLEM SOLVING

As you may recall from the sensation and perception chapter, Gestalt psychology describes whole patterns, forms and configurations of perception and cognition such as closure, good continuation, and figure-ground. In addition to patterns of perception, Wolfgang Kohler, a German Gestalt psychologist traveled to the Spanish island of Tenerife in order to study animals behavior and problem solving in the anthropoid ape.

As an interesting side note to Kohler’s studies of chimp problem solving, Dr. Ronald Ley, professor of psychology at State University of New York provides evidence in his book A Whisper of Espionage  (1990) suggesting that while collecting data for what would later be his book  The Mentality of Apes (1925) on Tenerife in the Canary Islands between 1914 and 1920, Kohler was additionally an active spy for the German government alerting Germany to ships that were sailing around the Canary Islands. Ley suggests his investigations in England, Germany and elsewhere in Europe confirm that Kohler had served in the German military by building, maintaining and operating a concealed radio that contributed to Germany’s war effort acting as a strategic outpost in the Canary Islands that could monitor naval military activity approaching the north African coast.

While trapped on the island over the course of World War 1, Kohler applied Gestalt principles to animal perception in order to understand how they solve problems. He recognized that the apes on the islands also perceive relations between stimuli and the environment in Gestalt patterns and understand these patterns as wholes as opposed to pieces that make up a whole. Kohler based his theories of animal intelligence on the ability to understand relations between stimuli, and spent much of his time while trapped on the island investigation what he described as  insight , the sudden perception of useful or proper relations. In order to study insight in animals, Kohler would present problems to chimpanzee’s by hanging some banana’s or some kind of food so it was suspended higher than the apes could reach. Within the room, Kohler would arrange a variety of boxes, sticks or other tools the chimpanzees could use by combining in patterns or organizing in a way that would allow them to obtain the food (Kohler & Winter, 1925).

While viewing the chimpanzee’s, Kohler noticed one chimp that was more efficient at solving problems than some of the others. The chimp, named Sultan, was able to use long poles to reach through bars and organize objects in specific patterns to obtain food or other desirables that were originally out of reach. In order to study insight within these chimps, Kohler would remove objects from the room to systematically make the food more difficult to obtain. As the story goes, after removing many of the objects Sultan was used to using to obtain the food, he sat down ad sulked for a while, and then suddenly got up going over to two poles lying on the ground. Without hesitation Sultan put one pole inside the end of the other creating a longer pole that he could use to obtain the food demonstrating an ideal example of what Kohler described as insight. In another situation, Sultan discovered how to stand on a box to reach a banana that was suspended from the rafters illustrating Sultan’s perception of relations and the importance of insight in problem solving.

Grande (another chimp in the group studied by Kohler) builds a three-box structure to reach the bananas, while Sultan watches from the ground.  Insight , sometimes referred to as an “Ah-ha” experience, was the term Kohler used for the sudden perception of useful relations among objects during problem solving (Kohler, 1927; Radvansky & Ashcraft, 2013).

Solving puzzles.

   Problem-solving abilities can improve with practice. Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills. Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9×9 grid. The simple sudoku below (see figure) is a 4×4 grid. To solve the puzzle, fill in the empty boxes with a single digit: 1, 2, 3, or 4. Here are the rules: The numbers must total 10 in each bolded box, each row, and each column; however, each digit can only appear once in a bolded box, row, and column. Time yourself as you solve this puzzle and compare your time with a classmate.

How long did it take you to solve this sudoku puzzle? (You can see the answer at the end of this section.)

   Here is another popular type of puzzle (figure below) that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:

Did you figure it out? (The answer is at the end of this section.) Once you understand how to crack this puzzle, you won’t forget.

   Take a look at the “Puzzling Scales” logic puzzle below (figure below). Sam Loyd, a well-known puzzle master, created and refined countless puzzles throughout his lifetime (Cyclopedia of Puzzles, n.d.).

What steps did you take to solve this puzzle? You can read the solution at the end of this section.

Pitfalls to problem solving.

   Not all problems are successfully solved, however. What challenges stop us from successfully solving a problem? Albert Einstein once said, “Insanity is doing the same thing over and over again and expecting a different result.” Imagine a person in a room that has four doorways. One doorway that has always been open in the past is now locked. The person, accustomed to exiting the room by that particular doorway, keeps trying to get out through the same doorway even though the other three doorways are open. The person is stuck—but she just needs to go to another doorway, instead of trying to get out through the locked doorway. A mental set is where you persist in approaching a problem in a way that has worked in the past but is clearly not working now.

Functional fixedness is a type of mental set where you cannot perceive an object being used for something other than what it was designed for. During the Apollo 13 mission to the moon, NASA engineers at Mission Control had to overcome functional fixedness to save the lives of the astronauts aboard the spacecraft. An explosion in a module of the spacecraft damaged multiple systems. The astronauts were in danger of being poisoned by rising levels of carbon dioxide because of problems with the carbon dioxide filters. The engineers found a way for the astronauts to use spare plastic bags, tape, and air hoses to create a makeshift air filter, which saved the lives of the astronauts.

   Researchers have investigated whether functional fixedness is affected by culture. In one experiment, individuals from the Shuar group in Ecuador were asked to use an object for a purpose other than that for which the object was originally intended. For example, the participants were told a story about a bear and a rabbit that were separated by a river and asked to select among various objects, including a spoon, a cup, erasers, and so on, to help the animals. The spoon was the only object long enough to span the imaginary river, but if the spoon was presented in a way that reflected its normal usage, it took participants longer to choose the spoon to solve the problem. (German & Barrett, 2005). The researchers wanted to know if exposure to highly specialized tools, as occurs with individuals in industrialized nations, affects their ability to transcend functional fixedness. It was determined that functional fixedness is experienced in both industrialized and nonindustrialized cultures (German & Barrett, 2005).

In order to make good decisions, we use our knowledge and our reasoning. Often, this knowledge and reasoning is sound and solid. Sometimes, however, we are swayed by biases or by others manipulating a situation. For example, let’s say you and three friends wanted to rent a house and had a combined target budget of $1,600. The realtor shows you only very run-down houses for $1,600 and then shows you a very nice house for $2,000. Might you ask each person to pay more in rent to get the $2,000 home? Why would the realtor show you the run-down houses and the nice house? The realtor may be challenging your anchoring bias. An anchoring bias occurs when you focus on one piece of information when making a decision or solving a problem. In this case, you’re so focused on the amount of money you are willing to spend that you may not recognize what kinds of houses are available at that price point.

The confirmation bias is the tendency to focus on information that confirms your existing beliefs. For example, if you think that your professor is not very nice, you notice all of the instances of rude behavior exhibited by the professor while ignoring the countless pleasant interactions he is involved in on a daily basis. Hindsight bias leads you to believe that the event you just experienced was predictable, even though it really wasn’t. In other words, you knew all along that things would turn out the way they did. Representative bias describes a faulty way of thinking, in which you unintentionally stereotype someone or something; for example, you may assume that your professors spend their free time reading books and engaging in intellectual conversation, because the idea of them spending their time playing volleyball or visiting an amusement park does not fit in with your stereotypes of professors.

Finally, the availability heuristic is a heuristic in which you make a decision based on an example, information, or recent experience that is that readily available to you, even though it may not be the best example to inform your decision . Biases tend to “preserve that which is already established—to maintain our preexisting knowledge, beliefs, attitudes, and hypotheses” (Aronson, 1995; Kahneman, 2011). These biases are summarized in the table below.

Were you able to determine how many marbles are needed to balance the scales in the figure below? You need nine. Were you able to solve the problems in the figures above? Here are the answers.

   Many different strategies exist for solving problems. Typical strategies include trial and error, applying algorithms, and using heuristics. To solve a large, complicated problem, it often helps to break the problem into smaller steps that can be accomplished individually, leading to an overall solution. Roadblocks to problem solving include a mental set, functional fixedness, and various biases that can cloud decision making skills.

References:

Openstax Psychology text by Kathryn Dumper, William Jenkins, Arlene Lacombe, Marilyn Lovett and Marion Perlmutter licensed under CC BY v4.0. https://openstax.org/details/books/psychology

Review Questions:

1. A specific formula for solving a problem is called ________.

a. an algorithm

b. a heuristic

c. a mental set

d. trial and error

2. Solving the Tower of Hanoi problem tends to utilize a  ________ strategy of problem solving.

a. divide and conquer

b. means-end analysis

d. experiment

3. A mental shortcut in the form of a general problem-solving framework is called ________.

4. Which type of bias involves becoming fixated on a single trait of a problem?

a. anchoring bias

b. confirmation bias

c. representative bias

d. availability bias

5. Which type of bias involves relying on a false stereotype to make a decision?

6. Wolfgang Kohler analyzed behavior of chimpanzees by applying Gestalt principles to describe ________.

a. social adjustment

b. student load payment options

c. emotional learning

d. insight learning

7. ________ is a type of mental set where you cannot perceive an object being used for something other than what it was designed for.

a. functional fixedness

c. working memory

Critical Thinking Questions:

1. What is functional fixedness and how can overcoming it help you solve problems?

2. How does an algorithm save you time and energy when solving a problem?

Personal Application Question:

1. Which type of bias do you recognize in your own decision making processes? How has this bias affected how you’ve made decisions in the past and how can you use your awareness of it to improve your decisions making skills in the future?

anchoring bias

availability heuristic

confirmation bias

functional fixedness

hindsight bias

problem-solving strategy

representative bias

trial and error

working backwards

Answers to Exercises

algorithm:  problem-solving strategy characterized by a specific set of instructions

anchoring bias:  faulty heuristic in which you fixate on a single aspect of a problem to find a solution

availability heuristic:  faulty heuristic in which you make a decision based on information readily available to you

confirmation bias:  faulty heuristic in which you focus on information that confirms your beliefs

functional fixedness:  inability to see an object as useful for any other use other than the one for which it was intended

heuristic:  mental shortcut that saves time when solving a problem

hindsight bias:  belief that the event just experienced was predictable, even though it really wasn’t

mental set:  continually using an old solution to a problem without results

problem-solving strategy:  method for solving problems

representative bias:  faulty heuristic in which you stereotype someone or something without a valid basis for your judgment

trial and error:  problem-solving strategy in which multiple solutions are attempted until the correct one is found

working backwards:  heuristic in which you begin to solve a problem by focusing on the end result

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Some Helpful Problem-Solving Heuristics

A  heuristic  is a thinking strategy, something that can be used to tease out further information about a problem and thus help you figure out what to do when you don’t know what to do. Here are 25 heuristics that can be useful in solving problems. They help you monitor your thought processes, to step back and watch yourself at work, and thus keep your cool in a challenging situation.

• Ask somebody else  how to do the problem. This strategy is probably the most used world-wide, though it is not one we encourage our students to use, at least not initially.
• Guess and try  (guess, check, and revise). Your first guess might be right! But incorrect guesses can often suggest a direction toward a solution. (N.B. A spreadsheet is a powerful aid in guessing and trying. Set up the relationships and plug in a number to see if you get what you want. If you don’t, it is easy to try another number. And another.)
• Restate the problem  using words that make sense to you. One way to do this is to explain the problem to someone else. Often this is all it takes for the light to dawn.
• Organize information  into a table or chart. Having it laid out clearly in front of you frees up your mind for thinking. And perhaps you can use the organized data to generate more information.
• Draw a picture  of the problem. Translate problem information into pictures, diagrams, sketches, glyphs, arrows, or some other kind of representation.
• Make a model  of the problem. The model might be a physical or mental model, perhaps using a computer. You might vary the problem information to see whether and how the model may be affected.
• Look for patterns , any kind of patterns: number patterns, verbal patterns, spatial/visual patterns, patterns in time, patterns in sound. (Some people define mathematics as the science of patterns.)
• Act out the problem , if it is stated in a narrative form. Acting it out can have the same effect as drawing a picture. What’s more, acting out the problem might disclose incorrect assumptions you are making.
• Invent notation . Name things in the problem (known or unknown) using words or symbols, including relationships between problem components.
• Write equations . An equation is simply the same thing named two different ways.
• Check all possibilities  in a systematic way. A table or chart may help you to be systematic.
• Work backwards  from the end condition to the beginning condition. Working backwards is particularly helpful when letting a variable (letter) represent an unknown.
• Identify subgoals  in the problem. Break up the problem into a sequence of smaller problems (“If I knew this, then I could get that”).
• Simplify the problem . Use easier or smaller numbers, or look at extreme cases (e.g., use the minimum or maximum value of one of the varying quantities).
• Restate the problem again . After working on the problem for a time, back off a bit and put it into your own words in still a different way, since now you know more about it.
• Change your point of view . Use your imagination to change the way you are looking at the problem. Turn it upside down, or pull it inside out.
• Check for hidden assumptions  you may be making (you might be making the problem harder than it really is). These assumptions are often found by changing the given numbers or conditions and looking to see what happens.
• Identify needed and given information clearly . You may not need to find everything you think you need to find, for instance.
• Make up your own technique . It is your mind, after all; use mental actions that make sense to you. The key is to do something that engages you with the problem.
• Try combinations of the above heuristics .

These heuristics can be readily pointed out to students as they engage problems in the classroom. However, real-world problems are often confronted many times over or on increasingly complex levels. For those kinds of problems, George Polya, the father of modern problem-solving heuristics, identified a fifth class (E) of looking-back heuristics. We include these here for completeness, but also with the teaching caveat that solutions often improve and insights grow deeper after the initial pressure to produce a solution has been resolved. Subsequent considerations of a problem situation are invariably deeper than the first attempt.

• Check your solution . Substitute your answer or results back into the problem. Are all of the conditions satisfied?
• Find another solution . There may be more than one answer. Make sure you have them all.
• Solve the problem a different way . Your first solution will seldom be the best solution. Now that the pressure is off, you may readily find other ways to solve the problem.
• Solve a related problem . Steve Brown and Marion Walter in their book,  The Art of Problem Posing , suggest the “What if not?” technique. What if the train goes at a different speed? What if there are 8 children, instead of 9? What if . . .? Fascinating discoveries can be made in this way, leading to:
• Generalize the solution . Can you glean from your solution how it can be made to fit a whole class of related situations? Can you prove your result?

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You Already Use Heuristics Every Day. Here's What They Are

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Between balancing professional obligations with personal responsibilities and getting through the everyday tasks that keep you alive, your brain can get more than a little overwhelmed . Thankfully, it has a strategy to stay afloat: relying on heuristics.

Heuristics are those little mental shortcuts that all of us use to solve problems and make quick, efficient judgment calls. You might also call them rules-of-thumb; heuristics help cut down on your decision-making time and help you move from one task to the other without having to stop too long to plan your next step. While heuristics are essential for freeing up your limited cognitive resources , they can also lead to trouble causing us to miss important facts or develop unfair biases.

Different Types of Heuristics

• The Availability Heuristic
• The Representative Heuristic
• The Fundamental Attribution Error

Whether you know it or not, you're likely using a variety of heuristics every day. Psychologists Amos Tversky and Daniel Kahneman are credited with first exploring the science of heuristics in the 1970s, and through their work, they identified several different types of mental shortcuts that most humans use. Since their initial findings, researchers have continued to explore the field of heuristics and identify new ways we as humans take advantage of an array of mental shortcuts. Here are three of the big ones:

1. The Availability Heuristic

The availability heuristic comes into play any time you make a judgment about something based on your memories of related instances or available information that's specific to that scenario. If you're pressed for time and have to make a quick decision, the availability heuristic may help you quickly arrive at a conclusion. In other cases, it can lead you astray. For example, when asked about the probability of plane crashes, homicides and shark attacks, people tend to overestimate the odds of each just because these events are so memorable — that's the availability heuristic at play.

The availability heuristic may also be responsible for social media's negative effect on your mood : If all you see in your feed is pictures of people partying in Ibiza, you're likely to assume you're the only one not having the time of your life. But that may not be true — you're just jumping to that conclusion based on the evidence that's available (you're probably not seeing as many boring photo ops from other people's couches).

2. The Representative Heuristic

When you categorize objects (or other people) based on how similar they are to existing prototypes, you're calling on the representative heuristic. For example, if you assume a potential dating app suitor would make a better accountant than a CEO because he describes himself as "quiet," you're using the representative heuristic.

If you presume another guy is more likely a massage therapist than a software engineer because he says he's into essential oils and yoga, you're making that assumption because those qualities sound more representative of the former than the latter (when in reality, probability dictates that he's more likely to be a software engineer, considering there are more than 3 million of them in the United States alone).

3. The Fundamental Attribution Error

Also known as correspondence bias or over-attribution effect, the fundamental attribution error describes the tendency to attribute a person's behavior to their personality or character rather than the situation they're in.

"I believe the fundamental attribution error is one of the most interesting heuristics, because it reveals the disparity in how humans think of themselves versus other people," Kate Gapinski, Ph.D., clinical psychologist and adjunct professor at the University of San Francisco, says via email. "We tend to attribute the behavior of others as being driven by internal, stable characteristics such as character and personality, while we often attribute our own behavior as stemming from external circumstances."

According to Gapinski, a clear current example of the fundamental attribution error in action has to do with media reports of violence against people who refuse to wear face masks during the pandemic.

"These attacks, presumably committed by people who believe masks are essential for public safety, may be driven by an interpretation that those not wearing them are fundamentally selfish, inconsiderate and reckless toward others and thus deserve to be punished," Gapinski says. "Ironically, it's quite likely that the aggressors of these events have themselves forgotten or chosen not to wear a mask at some point. However, the fundamental attribution error predicts that we will tend to blame the situation rather than personal traits like character for our own mistakes (e.g., 'I was running late after a poor night's sleep, so no wonder I forgot')."

Heuristics are more than rules-of-thumb; they can be used to make life-saving decisions in professions like medicine and aviation. In situations of uncertainty, professionals use something called " fast-and-frugal heuristics ," simple strategies that actually ignore part of the available information. These types of strategies are crucial in high-stress situations because they're simple to execute and they reduce the amount of computation our brains have to do to get to an answer.

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What are the 3 types of heuristics.

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What are heuristics and how do they help us make decisions?

Heuristics are simple rules of thumb that our brains use to make decisions. When you choose a work outfit that looks professional instead of sweatpants, you’re making a decision based on past information. That's not intuition; it’s heuristics. Instead of weighing all the information available to make a data-backed choice, heuristics enable us to move quickly into action—mostly without us even realizing it. In this article, you’ll learn what heuristics are, their common types, and how we use them in different scenarios.

Green means go. Most of us accept this as common knowledge, but it’s actually an example of a micro-decision—in this case, your brain is deciding to go when you see the color green.

You make countless of these subconscious decisions every day. Many things that you might think just come naturally to you are actually caused by heuristics—mental shortcuts that allow you to quickly process information and take action. Heuristics help you make smaller, almost unnoticeable decisions using past information, without much rational input from your brain.

Heuristics are helpful for getting things done more quickly, but they can also lead to biases and irrational choices if you’re not aware of them. Luckily, you can use heuristics to your advantage once you recognize them, and make better decisions in the workplace.

What is a heuristic?

Heuristics are mental shortcuts that your brain uses to make decisions. When we make rational choices, our brains weigh all the information, pros and cons, and any relevant data. But it’s not possible to do this for every single decision we make on a day-to-day basis. For the smaller ones, your brain uses heuristics to infer information and take almost-immediate action.

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How heuristics work

For example, if you’re making a larger decision about whether to accept a new job or stay with your current one, your brain will process this information slowly. For decisions like this, you collect data by referencing sources—chatting with mentors, reading company reviews, and comparing salaries. Then, you use that information to make your decision. Meanwhile, your brain is also using heuristics to help you speed along that track. In this example, you might use something called the “availability heuristic” to reference things you’ve recently seen about the new job. The availability heuristic makes it more likely that you’ll remember a news story about the company’s higher stock prices. Without realizing it, this can make you think the new job will be more lucrative.

On the flip side, you can recognize that the new job has had some great press recently, but that might be just a great PR team at work. Instead of “buying in” to what the availability heuristic is trying to tell you—that positive news means it’s the right job—you can acknowledge that this is a bias at work. In this case, comparing compensation and work-life balance between the two companies is a much more effective way to choose which job is right for you.

History of heuristics

The term "heuristics," originating from the Greek word meaning “to discover,” has ancient roots, but much of today's understanding comes from twentieth-century social scientists. Herbert Simon's research into "bounded rationality" highlighted the use of heuristics in decision-making, particularly under constraints like limited time and information.

Daniel Kahneman was one of the first researchers to study heuristics in his behavioral economics work in the 1970’s, along with fellow psychologist Amos Tversky. They theorized that many of the decisions and judgments we make aren’t rational—meaning we don’t move through a series of decision-making steps to come to a solution. Instead, the human brain uses mental shortcuts to form seemingly irrational, “fast and frugal” decisions—quick choices that don’t require a lot of mental energy.

Kahneman’s work showed that heuristics lead to systematic errors (or biases), which act as the driving force for our decisions. He was able to apply this research to economic theory, leading to the formation of behavioral economics and a Nobel Prize for Kahneman in 2002.

In the years since, the study of heuristics has grown in popularity with economists and in cognitive psychology. Gerd Gigerenzer’s research , for example, challenges the idea that heuristics lead to errors or flawed thinking. He argues that heuristics are actually indicators that human beings are able to make decisions more effectively without following the traditional rules of logic. His research seems to indicate that heuristics lead us to the right answer most of the time.

Types of heuristics

Heuristics are everywhere, whether we notice them or not. There are hundreds of heuristics at play in the human brain, and they interact with one another constantly. To understand how these heuristics can help you, start by learning some of the more common types of heuristics.

Recognition heuristic

The recognition heuristic uses what we already know (or recognize) as a criterion for decisions. The concept is simple: When faced with two choices, you’re more likely to choose the item you recognize versus the one you don’t.

This is the very base-level concept behind branding your business, and we see it in all well-known companies. Businesses develop a brand messaging strategy in the hopes that when you’re faced with buying their product or buying someone else's, you recognize their product, have a positive association with it, and choose that one. For example, if you’re going to grab a soda and there are two different cans in the fridge, one a Coca-Cola, and the other a soda you’ve never heard of, you are more likely to choose the Coca-Cola simply because you know the name.

Familiarity heuristic

The familiarity heuristic is a mental shortcut where individuals prefer options or information that is familiar to them. This heuristic is based on the notion that familiar items are seen as safer or superior. It differs from the recognition heuristic, which relies solely on whether an item is recognized. The familiarity heuristic involves a deeper sense of comfort and understanding, as opposed to just recognizing something.

An example of this heuristic is seen in investment decisions. Investors might favor well-known companies over lesser-known ones, influenced more by brand familiarity than by an objective assessment of the investment's potential. This tendency showcases how the familiarity heuristic can lead to suboptimal choices, as it prioritizes comfort and recognition over a thorough evaluation of all available options.

Availability heuristic

The availability heuristic is a cognitive bias where people judge the frequency or likelihood of events based on how easily similar instances come to mind. This mental shortcut depends on the most immediate examples that pop into one's mind when considering a topic or decision. The ease of recalling these instances often leads to a distorted perception of their actual frequency, as recent, dramatic, or emotionally charged memories tend to be more memorable.

A notable example of the availability heuristic is the public's reaction to shark attacks. When the media reports on shark attacks, these incidents become highly memorable due to their dramatic nature, leading people to overestimate the risk of such events. This heightened perception is despite statistical evidence showing the rarity of shark attacks. The result is an exaggerated fear and a skewed perception of the actual danger of swimming in the ocean.

Representativeness heuristic

The representativeness heuristic is when we try to assign an object to a specific category or idea based on past experiences. Oftentimes, this comes up when we meet people—our first impression. We expect certain things (such as clothing and credentials) to indicate that a person behaves or lives a certain way.

Without proper awareness, this heuristic can lead to discrimination in the workplace. For example, representativeness heuristics might lead us to believe that a job candidate from an Ivy League school is more qualified than one from a state university, even if their qualifications show us otherwise. This is because we expect Ivy League graduates to act a certain way, such as by being more hard-working or intelligent. Of course, in our rational brains, we know this isn’t the case. That’s why it’s important to be aware of this heuristic, so you can use logical thinking to combat potential biases.

Anchoring and adjustment heuristic

Used in finance for economic forecasting, anchoring and adjustment is when you start with an initial piece of information (the anchor) and continue adjusting until you reach an acceptable decision. The challenge is that sometimes the anchor ends up not being a good enough value to begin with. In other words, you choose the anchor based on unknown biases and then make further decisions based on this faulty assumption.

Anchoring and adjustment are often used in pricing, especially with SaaS companies. For example, a displayed, three-tiered pricing model shows you how much you get for each price point. The layout is designed to make it look like you won’t get much for the lower price, and you don’t necessarily need the highest price, so you choose the mid-level option (the original target). The anchors are the low price (suggesting there’s not much value here) and the high price (which shows that you’re getting a "discount" if you choose another option). Thanks to those two anchors, you feel like you’re getting a lot of value, no matter what you spend.

Affect heuristic

You know the advice; think with your heart. That’s the affect heuristic in action, where you make a decision based on what you’re feeling. Emotions are important ways to understand the world around us, but using them to make decisions is irrational and can impact your work.

For example, let’s say you’re about to ask your boss for a promotion. As a product marketer, you’ve made a huge impact on the company by helping to build a community of enthusiastic, loyal customers. But the day before you have your performance review , you find out that a small project you led for a new product feature failed. You decide to skip the conversation asking for a raise and instead double down on how you can improve.

In this example, you’re using the affect heuristic to base your entire performance on the failure of one small project—even though the rest of your performance (building that profitable community) is much more impactful than a new product feature. If you weighed the options rationally, you would see that asking for a raise is still a logical choice. But instead, the fear of asking for a raise after a failure felt like too big a trade-off.

Satisficing

Satisficing is when you accept an available option that’s satisfactory (i.e., just fine) instead of trying to find the best possible solution. In other words, you’re settling. This creates a “bounded rationality,” where you’re constrained by the choices that are good-enough, instead of pushing past the limits to discover more. This isn’t always negative—for lower-impact scenarios, it might not make sense to invest time and energy into finding the optimal choice. But there are also times when this heuristic kicks in and you end up settling for less than what’s possible.

For example, let’s say you’re a project manager planning the budget for the next fiscal year. Instead of looking at previous spend and revenue, you satisfice and base the budget off projections, assuming that will be good enough. But without factoring in historical data, your budget isn’t going to be as equipped to manage hiccups or unexpected changes. In this case, you can mitigate satisficing with a logically-based data review that, while longer, will produce a more accurate and thoughtful budget plan.

Trial and error heuristic

The trial and error heuristic is a problem-solving method where solutions are found through repeated experimentation. It's used when a clear path to the solution isn't known, relying on iterative learning from failures and adjustments.

For example, a chef might experiment with various ingredient combinations and techniques to perfect a new recipe. Each attempt informs the next, demonstrating how trial and error facilitates discovery in situations without formal guidelines.

Pros and cons of heuristics

Heuristics are effective at helping you get more done quickly, but they also have downsides. Psychologists don’t necessarily agree on whether heuristics and biases are positive or negative. But the argument seems to boil down to these two pros and cons:

Heuristics pros:

Simple heuristics reduce cognitive load, allowing you to accomplish more in less time with fast and frugal decisions. For example, the satisficing heuristic helps you find a "good enough" choice. So if you’re making a complex decision between whether to cut costs or invest in employee well-being , you can use satisficing to find a solution that’s a compromise. The result might not be perfect, but it allows you to take action and get started—you can always adjust later on.

Heuristics cons:

Heuristics create biases. While these cognitive biases enable us to make rapid-fire decisions, they can also lead to rigid, unhelpful beliefs. For example, confirmation bias makes it more likely that you’ll seek out other opinions that agree with your own. This makes it harder to keep an open mind, hear from the other side, and ultimately change your mind—which doesn’t help you build the flexibility and adaptability so important for succeeding in the workplace.

Heuristics and psychology

Heuristics play a pivotal role in psychology, especially in understanding how people make decisions within their cognitive limitations. These mental shortcuts allow for quicker decisions, often necessary in a fast-paced world, but they can sometimes lead to errors in judgment.

The study of heuristics bridges various aspects of psychology, from cognitive processes to behavioral outcomes, and highlights the balance between efficient decision-making and the potential for bias.

Stereotypes and heuristic thinking

Stereotypes are a form of heuristic where individuals make assumptions based on group characteristics, a process analyzed in both English and American psychology.

While these generalizations can lead to rapid conclusions and rational decisions under certain circumstances, they can also oversimplify complex human behaviors and contribute to prejudiced attitudes. Understanding stereotypes as a heuristic offers insight into the cognitive limitations of the human mind and their impact on social perceptions and interactions.

How heuristics lead to bias

Because heuristics rely on shortcuts and stereotypes, they can often lead to bias. This is especially true in scenarios where cognitive limitations restrict the processing of all relevant information. So how do you combat bias? If you acknowledge your biases, you can usually undo them and maybe even use them to your advantage. There are ways you can hack heuristics, so that they work for you (not against you):

Be aware. Heuristics often operate like a knee-jerk reaction—they’re automatic. The more aware you are, the more you can identify and acknowledge the heuristic at play. From there, you can decide if it’s useful for the current situation, or if a logical decision-making process is best.

Flip the script. When you notice a negative bias, turn it around. For example, confirmation bias is when we look for things to be as we expect. So if we expect our boss to assign us more work than our colleagues, we might always experience our work tasks as unfair. Instead, turn this around by repeating that your boss has your team’s best interests at heart, and you know everyone is working hard. This will re-train your confirmation bias to look for all the ways that your boss is treating you just like everyone else.

Practice mindfulness. Mindfulness helps to build self-awareness, so you know when heuristics are impacting your decisions. For example, when we tap into the empathy gap heuristic, we’re unable to empathize with someone else or a specific situation. However, if we’re mindful, we can be aware of how we’re feeling before we engage. This helps us to see that the judgment stems from our own emotions and probably has nothing to do with the other person.

Examples of heuristics in business

This is all well and good in theory, but how do heuristic decision-making and thought processes show up in the real world? One reason researchers have invested so much time and energy into learning about heuristics is so that they can use them, like in these scenarios:

How heuristics are used in marketing

Effective marketing does so much for a business—it attracts new customers, makes a brand a household name, and converts interest into sales, to name a few. One way marketing teams are able to accomplish all this is by applying heuristics.

Let’s use ambiguity aversion as an example. Ambiguity aversion means you're less likely to choose an item you don’t know. Marketing teams combat this by working to become familiar to their customers. This could include the social media team engaging in a more empathetic or conversational way, or employing technology like chat-bots to show that there’s always someone available to help. Making the business feel more approachable helps the customer feel like they know the brand personally—which lessens ambiguity aversion.

How heuristics are used in business strategy

Have you ever noticed how your CEO seems to know things before they happen? Or that the CFO listens more than they speak? These are indications that they understand people in a deeper way, and are able to engage with their employees and predict outcomes because of it. C-suite level executives are often experts in behavioral science, even if they didn’t study it. They tend to get what makes people tick, and know how to communicate based on these biases. In short, they use heuristics for higher-level decision-making processes and execution. 

This includes business strategy . For example, a startup CEO might be aware of their representativeness bias towards investors—they always look for the person in the room with the  fancy suit or car. But after years in the field, they know logically that this isn’t always true—plenty of their investors have shown up in shorts and sandals. Now, because they’re aware of their bias, they can build it into their investment strategy. Instead of only attending expensive, luxury events, they also attend conferences with like-minded individuals and network among peers. This approach can lead them to a greater variety of investors and more potential opportunities.

Heuristics vs algorithms

Heuristics and algorithms are both used by the brain to reduce the mental effort of decision-making, but they operate a bit differently. Algorithms act as guidelines for specific scenarios. They have a structured process designed to solve that specific problem. Heuristics, on the other hand, are general rules of thumb that help the brain process information and may or may not reach a solution.

For example, let's say you’re cooking a well-loved family recipe. You know the steps inside and out, and you no longer need to reference the instructions. If you’re following a recipe step-by-step, you’re using an algorithm. If, however, you decide on a whim to sub in some of your fresh garden vegetables because you think it will taste better, you’re using a heuristic.

How to use heuristics to make better decisions

Heuristics can help us make decisions quickly and with less cognitive strain. While they can be efficient, they sometimes lead to errors in judgment. Understanding how to use heuristics effectively can improve decision-making, especially in complex or uncertain situations.

Take time to think

Rushing often leads to reliance on automatic heuristics, which might not always be suitable. To make better decisions, slow down your thinking process. Take a step back, breathe, and allow yourself a moment of distraction. This pause can provide a fresh perspective and help you notice details or angles you might have missed initially.

Clarify your objectives

When making a decision, it's important to understand the ultimate goal. Our automatic decision-making processes tend to favor immediate benefits, sometimes overlooking long-term impacts or the needs of others involved. Consider the broader implications of your decision. Who else is affected? Is there a common objective that benefits all parties? Such considerations can lead to more holistic and effective decisions.

Manage your emotional influences

Emotions significantly influence our decision-making, often without our awareness. Fast decisions are particularly prone to emotional biases. Acknowledge your feelings, but also separate them from the facts at hand. Are you making a decision based on solid information or emotional reactions? Distinguishing between the two can lead to more rational and balanced choices.

Beware of binary thinking

All-or-nothing thinking is a common heuristic trap, where we see decisions as black or white with no middle ground. However, real-life decisions often have multiple paths and possibilities. It's important to recognize this complexity. There might be compromises or alternative options that weren't initially considered. By acknowledging the spectrum of possibilities, you can make more nuanced and effective decisions.

Heuristic FAQs

What is heuristic thinking.

Heuristic thinking refers to a method of problem-solving, learning, or discovery that employs a practical approach—often termed a "rule of thumb"—to make decisions quickly. Heuristic thinking is a type of cognition that humans use subconsciously to make decisions and judgments with limited time.

What is a heuristic evaluation?

A heuristic evaluation is a usability inspection method used in the fields of user interface (UI) and user experience (UX) design. It involves evaluators examining the interface and judging its compliance with recognized usability principles, known as heuristics. These heuristics serve as guidelines to identify usability problems in a design, making the evaluation process more systematic and comprehensive.

What are computer heuristics?

Computer heuristics are algorithms used to solve complex problems or make decisions where an exhaustive search is impractical. In fields like artificial intelligence and cybersecurity, these heuristic methods allow for efficient problem-solving and decision-making, often based on trial and error or rule-of-thumb strategies.

What are heuristics in psychology?

In psychology, heuristics are quick mental rules for making decisions. They are important in social psychology for understanding how we think and decide. Figures like Kahneman and Tversky, particularly in their work "Judgment Under Uncertainty: Heuristics and Biases," have influenced the study of heuristics in psychology.

Learn heuristics, de-mystify your brain

Your brain doesn’t actually work in mysterious ways. In reality, researchers know why we do a lot of the things we do. Heuristics help us to understand the choices we make that don’t make much sense. Once you understand heuristics, you can also learn to use them to your advantage—both in business, and in life. 

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What are heuristics? Representative vs. availability heuristics

One topic that many of my psychology tutoring students get confused about is the topic of heuristics, which comes up when they study judgment and decision-making.

What is a heuristic?

A heuristic is a rule-of-thumb. It is a shortcut to solving a problem when you’re too lazy or overwhelmed or otherwise unable to solve it the proper way.

Here’s an example. Let’s say someone asked you: “Hey! How long is the gestational period of the African elephant?”

The proper response to this strange question would be to say, “Hmm, I don’t know. Hold on one second, let me check.” At this point, you would pull out your smartphone and Google until you stumble upon the Wikipedia page for gestational periods of various mammals. But what if you didn’t have your phone on you, or you didn’t feel like taking it out of your bag? Then you might say, “Hmm, well, the gestational period for humans is about 9 months, but elephants are bigger, so I’m gonna say…15 months?” (The correct answer is 645 days, or about 21 months).

So you would be wrong, but hey, it’s a weird question anyway, and you were kind of close. [If $10,000 or your reputation were on the line, then you’d probably take the time to Google.] This is the heuristic approach to answering the question because you used some information you already knew to make an educated guess (but still a guess!) to answer the question.

Heuristics come in all flavors, but two main types are the representativeness heuristic and the availability heuristic. Students often get these confused, but I’m going to see if I can clear up how they’re different with the use of some examples.

The Availability Heuristic

The availability heuristic is when you make a judgment about something based on how available examples are in your mind. So, this heuristic has a lot to do with your memory of specific instances and what you’ve been exposed to. Some examples:

• Judging the population of cities (when cities are more available in your mind, like New York or Berlin, you will overestimate their populations).
• Judging the frequency of deaths from different causes (morbid, I know). People tend to overestimate the number of deaths from, say, airplane crashes, but underestimate the number of deaths from, say, asthma. This is because people hear about deaths from airplane crashes in the news, so they can bring to mind a fair number of examples of this, but they can’t bring to mind examples of people dying from asthma. This is why reading the news can actually be misleading, since rare instances can be covered to the point of seeming commonplace.
• One of my favorite examples: “Are there more words that begin with “r” or that have “r” as their third letter?” To answer this question, you can’t help but bring specific words to mind. Words that begin with “r” are easy to think of; words that have “r” as their third letter are harder to think of, so many people answer this question with “words that begin with ‘r’” when in fact, that’s the wrong answer.

The Representative Heuristic

On to representativeness . These decisions tend to be based on how similar an example is to something else (or how typical or representative the particular case in question is). In this way, representativeness is basically stereotyping. While availability has more to do with memory of specific instances, representativeness has more to do with memory of a prototype, stereotype or average. Let me try to make this clear with some examples:

• “Linda the bank teller” – this is one of the most famous examples. It comes from the work of Kahneman and Tversky. In this problem, you are told a little bit about Linda, and then asked what her profession is likely to be. Linda is described as an avid protester who went to an all girls’ college. She is an environmentalist, politically liberal, etc. (I’m making up these details, but the information that subjects got in this study is quite similar). Basically, she’s described in such a way that you can’t help but think that she must be a feminist, because the prototype/stereotype that you have in your head is that women who are like Linda are feminists. So when people are asked if Linda is more likely to be a bank teller (working for The Man!) or a feminist bank teller, most people say the latter, even though that doesn’t make any sense, in terms of probability. In this case, people use a shortcut that involved a stereotype to answer the question, and they ignored actual likelihoods.
• “Tom W.” – another classic example. Even when you know that people are way more likely to be psychology majors than engineering majors, people still say that Tom W. is likely to be an engineer, when he was originally described as a nerd . You know - someone who plays video games, likes building things, doesn’t have the highest social IQ. We think engineers tend to be like that, and that people like that tend to be engineers, so we’ll ignore the facts and go with a stereotype.

I can see why representativeness and availability seem similar, because when you use these heuristics, you are always using information that you had in the past to make a guess. But representativeness is less about particular examples, and more about stereotypes (which are probably formed on the basis of examples, but it’s often unclear where the stereotype even originated!). Availability is about particular examples and how readily they come to mind. This is why we tend to use availability when judging the number of things, because counting examples that come to mind is one way to answer that kind of question.

Heuristics on AP or GRE Psychology Tests 

I hope that was helpful, or at least fun! Another psychology tutor tip I have for you, if you’re preparing for the AP Psych or GRE Psych tests, is that these tests tend to use examples that you probably have come across in your review already. So if you memorize which examples go with which heuristics, that’s another way to answer those questions correctly. Obviously, trying to abstract the underlying principles behind the two heuristics is a lot better, but if you’re studying to the test, definitely memorize the famous examples.

For more information about heuristics, biases and decision-making, check out Nobel Laureate Daniel Kahneman’s book Thinking Fast and Slow.

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8.2 Problem-Solving: Heuristics and Algorithms

Learning objectives.

• Describe the differences between heuristics and algorithms in information processing.

When faced with a problem to solve, should you go with intuition or with more measured, logical reasoning? Obviously, we use both of these approaches. Some of the decisions we make are rapid, emotional, and automatic. Daniel Kahneman (2011) calls this “fast” thinking. By definition, fast thinking saves time. For example, you may quickly decide to buy something because it is on sale; your fast brain has perceived a bargain, and you go for it quickly. On the other hand, “slow” thinking requires more effort; applying this in the same scenario might cause us not to buy the item because we have reasoned that we don’t really need it, that it is still too expensive, and so on. Using slow and fast thinking does not guarantee good decision-making if they are employed at the wrong time. Sometimes it is not clear which is called for, because many decisions have a level of uncertainty built into them. In this section, we will explore some of the applications of these tendencies to think fast or slow.

We will look further into our thought processes, more specifically, into some of the problem-solving strategies that we use. Heuristics are information-processing strategies that are useful in many cases but may lead to errors when misapplied. A heuristic is a principle with broad application, essentially an educated guess about something. We use heuristics all the time, for example, when deciding what groceries to buy from the supermarket, when looking for a library book, when choosing the best route to drive through town to avoid traffic congestion, and so on. Heuristics can be thought of as aids to decision making; they allow us to reach a solution without a lot of cognitive effort or time.

The benefit of heuristics in helping us reach decisions fairly easily is also the potential downfall: the solution provided by the use of heuristics is not necessarily the best one. Let’s consider some of the most frequently applied, and misapplied, heuristics in the table below.

In many cases, we base our judgments on information that seems to represent, or match, what we expect will happen, while ignoring other potentially more relevant statistical information. When we do so, we are using the representativeness heuristic . Consider, for instance, the data presented in the table below. Let’s say that you went to a hospital, and you checked the records of the babies that were born on that given day. Which pattern of births do you think you are most likely to find?

Most people think that list B is more likely, probably because list B looks more random, and matches — or is “representative of” — our ideas about randomness, but statisticians know that any pattern of four girls and four boys is mathematically equally likely. Whether a boy or girl is born first has no bearing on what sex will be born second; these are independent events, each with a 50:50 chance of being a boy or a girl. The problem is that we have a schema of what randomness should be like, which does not always match what is mathematically the case. Similarly, people who see a flipped coin come up “heads” five times in a row will frequently predict, and perhaps even wager money, that “tails” will be next. This behaviour is known as the gambler’s fallacy . Mathematically, the gambler’s fallacy is an error: the likelihood of any single coin flip being “tails” is always 50%, regardless of how many times it has come up “heads” in the past.

The representativeness heuristic may explain why we judge people on the basis of appearance. Suppose you meet your new next-door neighbour, who drives a loud motorcycle, has many tattoos, wears leather, and has long hair. Later, you try to guess their occupation. What comes to mind most readily? Are they a teacher? Insurance salesman? IT specialist? Librarian? Drug dealer? The representativeness heuristic will lead you to compare your neighbour to the prototypes you have for these occupations and choose the one that they seem to represent the best. Thus, your judgment is affected by how much your neibour seems to resemble each of these groups. Sometimes these judgments are accurate, but they often fail because they do not account for base rates , which is the actual frequency with which these groups exist. In this case, the group with the lowest base rate is probably drug dealer.

Our judgments can also be influenced by how easy it is to retrieve a memory. The tendency to make judgments of the frequency or likelihood that an event occurs on the basis of the ease with which it can be retrieved from memory is known as the availability heuristic (MacLeod & Campbell, 1992; Tversky & Kahneman, 1973). Imagine, for instance, that I asked you to indicate whether there are more words in the English language that begin with the letter “R” or that have the letter “R” as the third letter. You would probably answer this question by trying to think of words that have each of the characteristics, thinking of all the words you know that begin with “R” and all that have “R” in the third position. Because it is much easier to retrieve words by their first letter than by their third, we may incorrectly guess that there are more words that begin with “R,” even though there are in fact more words that have “R” as the third letter.

The availability heuristic may explain why we tend to overestimate the likelihood of crimes or disasters; those that are reported widely in the news are more readily imaginable, and therefore, we tend to overestimate how often they occur. Things that we find easy to imagine, or to remember from watching the news, are estimated to occur frequently. Anything that gets a lot of news coverage is easy to imagine. Availability bias does not just affect our thinking. It can change behaviour. For example, homicides are usually widely reported in the news, leading people to make inaccurate assumptions about the frequency of murder. In Canada, the murder rate has dropped steadily since the 1970s (Statistics Canada, 2018), but this information tends not to be reported, leading people to overestimate the probability of being affected by violent crime. In another example, doctors who recently treated patients suffering from a particular condition were more likely to diagnose the condition in subsequent patients because they overestimated the prevalence of the condition (Poses & Anthony, 1991).

The anchoring and adjustment heuristic is another example of how fast thinking can lead to a decision that might not be optimal. Anchoring and adjustment is easily seen when we are faced with buying something that does not have a fixed price. For example, if you are interested in a used car, and the asking price is $10,000, what price do you think you might offer? Using $10,000 as an anchor, you are likely to adjust your offer from there, and perhaps offer $9000 or $9500. Never mind that $10,000 may not be a reasonable anchoring price. Anchoring and adjustment does not just happen when we’re buying something. It can also be used in any situation that calls for judgment under uncertainty, such as sentencing decisions in criminal cases (Bennett, 2014), and it applies to groups as well as individuals (Rutledge, 1993).

In contrast to heuristics, which can be thought of as problem-solving strategies based on educated guesses, algorithms are problem-solving strategies that use rules. Algorithms are generally a logical set of steps that, if applied correctly, should be accurate. For example, you could make a cake using heuristics — relying on your previous baking experience and guessing at the number and amount of ingredients, baking time, and so on — or using an algorithm. The latter would require a recipe which would provide step-by-step instructions; the recipe is the algorithm. Unless you are an extremely accomplished baker, the algorithm should provide you with a better cake than using heuristics would. While heuristics offer a solution that might be correct, a correctly applied algorithm is guaranteed to provide a correct solution. Of course, not all problems can be solved by algorithms.

As with heuristics, the use of algorithmic processing interacts with behaviour and emotion. Understanding what strategy might provide the best solution requires knowledge and experience. As we will see in the next section, we are prone to a number of cognitive biases that persist despite knowledge and experience.

Key Takeaways

• We use a variety of shortcuts in our information processing, such as the representativeness, availability, and anchoring and adjustment heuristics. These help us to make fast judgments but may lead to errors.
• Algorithms are problem-solving strategies that are based on rules rather than guesses. Algorithms, if applied correctly, are far less likely to result in errors or incorrect solutions than heuristics. Algorithms are based on logic.

Bennett, M. W. (2014). Confronting cognitive ‘anchoring effect’ and ‘blind spot’ biases in federal sentencing: A modest solution for reforming and fundamental flaw. Journal of Criminal Law and Criminology , 104 (3), 489-534.

Kahneman, D. (2011). Thinking, fast and slow. New York, NY: Farrar, Straus and Giroux.

MacLeod, C., & Campbell, L. (1992). Memory accessibility and probability judgments: An experimental evaluation of the availability heuristic.  Journal of Personality and Social Psychology, 63 (6), 890–902.

Poses, R. M., & Anthony, M. (1991). Availability, wishful thinking, and physicians’ diagnostic judgments for patients with suspected bacteremia.  Medical Decision Making,  11 , 159-68.

Rutledge, R. W. (1993). The effects of group decisions and group-shifts on use of the anchoring and adjustment heuristic. Social Behavior and Personality, 21 (3), 215-226.

Statistics Canada. (2018). Ho micide in Canada, 2017 . Retrieved from https://www150.statcan.gc.ca/n1/en/daily-quotidien/181121/dq181121a-eng.pdf

Tversky, A., & Kahneman, D. (1973). Availability: A heuristic for judging frequency and probability.  Cognitive Psychology, 5 , 207–232.

Psychology - 1st Canadian Edition Copyright © 2020 by Sally Walters is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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What Are Heuristics?

Understanding heuristics.

• Pros and Cons
• Examples in Behavioral Economics

Heuristics and Psychology

The bottom line.

• Investing Basics

Heuristics: Definition, Pros & Cons, and Examples

James Chen, CMT is an expert trader, investment adviser, and global market strategist.

Heuristics are mental shortcuts that help people make quick decisions. They are rules or methods that help people use reason and past experience to solve problems efficiently. Commonly used to simplify problems and avoid cognitive overload, heuristics are part of how the human brain evolved and is wired, allowing individuals to quickly reach reasonable conclusions or solutions to complex problems. These solutions may not be optimal ones but are often sufficient given limited timeframes and calculative capacity.

These cognitive shortcuts feature prominently in behavioral economics .

Key Takeaways

• Heuristics are mental shortcuts for solving problems in a quick way that delivers a result that is sufficient enough to be useful given time constraints.
• Investors and financial professionals use a heuristic approach to speed up analysis and investment decisions.
• Heuristics can lead to poor decision-making based on a limited data set, but the speed of decisions can sometimes make up for the disadvantages.
• Behavioral economics has focused on heuristics as one limitation of human beings behaving like rational actors.
• Availability, anchoring, confirmation bias, and the hot hand fallacy are some examples of heuristics people use in their economic lives.

Investopedia / Danie Drankwalter

People employ heuristics naturally due to the evolution of the human brain. The brain can only process so much information at once and therefore must employ various shortcuts or practical rules of thumb . We would not get very far if we had to stop to think about every little detail or collect every piece of available information and integrate it into an analysis.

Heuristics therefore facilitate timely decisions that may not be the absolute best ones but are appropriate enough. Individuals are constantly using this sort of intelligent guesswork, trial and error, process of elimination, and past experience to solve problems or chart a course of action. In a world that is increasingly complex and overloaded with big data, heuristic methods make decision-making simpler and faster through shortcuts and good-enough calculations.

First identified in economics by the political scientist and organizational scholar Herbert Simon in his work on bounded rationality, heuristics have now become a cornerstone of behavioral economics.

Rather than subscribing to the idea that economic behavior was rational and based upon all available information to secure the best possible outcome for an individual ("optimizing"), Simon believed decision-making was about achieving outcomes that were "good enough" for the individual based on their limited information and balancing the interests of others. Simon called this " satisficing ," a portmanteau of the words "satisfy" and "suffice."

Advantages and Disadvantages of Using Heuristics

The main advantage to using heuristics is that they allow people to make good enough decisions without having all of the information and without having to undertake complex calculations.

Because humans cannot possibly obtain or process all the information needed to make fully rational decisions, they instead seek to use the information they do have to produce a satisfactory result, or one that is good enough. Heuristics allow people to go beyond their cognitive limits.

Heuristics are also advantageous when speed or timeliness matters—for example, deciding to enter a trade or making a snap judgment about some important decision. Heuristics are thus handy when there is no time to carefully weigh all options and their merits.

Disadvantages

There are also drawbacks to using heuristics. While they may be quick and dirty, they will likely not produce the optimal decision and can also be wrong entirely. Quick decisions without all the information can lead to errors in judgment, and miscalculations can lead to mistakes.

Moreover, heuristics leave us prone to biases that tend to lead us toward irrational economic behavior and sway our understanding of the world. Such heuristics have been identified and cataloged by the field of behavioral economics.

Quick & easy

Allows decision-making that goes beyond our cognitive capacity

Allows for snap judgments when time is limited

Often inaccurate

Can lead to systemic biases or errors in judgment

Example of Heuristics in Behavioral Economics

Representativeness.

A popular shortcut method in problem-solving identified in behavioral economics is called representativeness heuristics. Representativeness uses mental shortcuts to make decisions based on past events or traits that are representative of or similar to the current situation.

Say, for example, Fast Food ABC expanded its operations to India and its stock price soared. An analyst noted that India is a profitable venture for all fast-food chains. Therefore, when Fast Food XYZ announced its plan to explore the Indian market the following year, the analyst wasted no time in giving XYZ a "buy" recommendation.

Although their shortcut approach saved reviewing data for both companies, it may not have been the best decision. Fast Food XYZ may have food that is not appealing to Indian consumers, which research would have revealed.

Anchoring and Adjustment

Anchoring and adjustment is another prevalent heuristic approach. With anchoring and adjustment, a person begins with a specific target number or value—called the anchor—and subsequently adjusts that number until an acceptable value is reached over time. The major problem with this method is that if the value of the initial anchor is not the true value, then all subsequent adjustments will be systematically biased toward the anchor and away from the true value.

An example of anchoring and adjustment is a car salesman beginning negotiations with a very high price (that is arguably well above the  fair value ). Because the high price is an anchor, the final price will tend to be higher than if the car salesman had offered a fair or low price to start.

Availability (Recency) Heuristic

The availability (or recency) heuristic is an issue where people give too much weight to the probability of an event happening again if it recently has occurred. For instance, if a shark attack is reported in the news, those headlines make the event salient and can lead people to stay away from the water, even though shark attacks remain very rare.

Another example is the case of the " hot hand ," or the sense that following a string of successes, an individual is likely to continue being successful. Whether at the casino, in the markets, or playing basketball, the hot hand has been debunked. A string of recent good luck does not alter the overall probability of events occurring.

Confirmation Bias

Confirmation bias is a well-documented heuristic whereby people give more weight to information that fits with their existing worldviews or beliefs. At the same time, information that contradicts these beliefs is discounted or rejected.

Investors should be aware of their own tendency toward confirmation bias so that they can overcome poor decision-making, missing chances, and avoid falling prey to bubbles . Seeking out contrarian views and avoiding affirmative questions are two ways to counteract confirmation bias.

Hindsight Bias

Hindsight is always 20/20. However, the hindsight bias leads us to forget that we made incorrect predictions or estimates prior to them occurring. Rather, we become convinced that we had accurately predicted an event before it occurred, even when we did not. This can lead to overconfidence for making future predictions, or regret for not taking past opportunities.

Stereotypes

Stereotypes are a kind of heuristic that allows us to form opinions or judgments about people whom we have never met. In particular, stereotyping takes group-level characteristics about certain social groups—often ones that are racist, sexist, or otherwise discriminatory—and casts those characteristics onto all of the members in that group, regardless of their individual personalities, beliefs, skills, or behaviors.

By imposing oversimplified beliefs onto people, we can quickly judge potential interactions with them or individual outcomes of those people. However, these judgments are often plain wrong, derogatory, and perpetuate social divisions and exclusions.

Heuristics were first identified and taken seriously by scholars in the middle of the 20th century with the work of Herbert Simon, who asked why individuals and firms don't act like rational actors in the real world, even with market pressures punishing irrational decisions. Simon found that corporate managers do not usually optimize but instead rely on a set of heuristics or shortcuts to get the job done in a way that is good enough (to "satisfice").

Later, in the 1970s and '80s, psychologists Amos Tversky and Daniel Kahneman working at the Hebrew University in Jerusalem, built off of Herbert Simon's work and developed what is known as Prospect Theory . A cornerstone of behavioral economics, Prospect Theory catalogs several heuristics used subconsciously by people as they make financial evaluations.

One major finding is that people are loss-averse —that losses loom larger than gains (i.e., the pain of losing $50 is far more than the pleasure of receiving $50). Here, people adopt a heuristic to avoid realizing losses, sometimes spurring them to take excessive risks in order to do so—but often leading to even larger losses.

More recently, behavioral economists have tried to develop policy measures or "nudges" to help correct people's irrational use of heuristics in order to help them achieve more optimal outcomes—for instance, by having people enroll in a retirement savings plan by default instead of having to opt in.

What Are the Types of Heuristics?

To date, several heuristics have been identified by behavioral economics—or else developed to aid people in making otherwise complex decisions. In behavioral economics, representativeness, anchoring and adjustment, and availability (recency) are among the most widely cited. Heuristics may be categorized in many ways, such as cognitive versus emotional biases or errors in judgment versus errors in calculation.

What Is Heuristic Thinking?

Heuristic thinking uses mental shortcuts—often unconsciously—to quickly and efficiently make otherwise complex decisions or judgments. These can be in the form of a "rule of thumb" (e.g., saving 5% of your income in order to have a comfortable retirement) or cognitive processes that we are largely unaware of like the availability bias.

What Is Another Word for Heuristic?

Heuristic may also go by the following terms: rule of thumb; mental shortcut; educated guess; or satisfice.

How Does a Heuristic Differ From an Algorithm?

An algorithm is a step-by-step set of instructions that are followed to achieve some goal or outcome, often optimizing that outcome. They are formalized and can be expressed as a formula or "recipe." As such, they are reproducible in the sense that an algorithm will always provide the same output, given the same input.

A heuristic amounts to an educated guess or gut feeling. Rather than following a set of rules or instructions, a heuristic is a mental shortcut. Moreover, it often produces sub-optimal and even irrational outcomes that may differ even when given the same input.

What Are Computer Heuristics?

In computer science, a heuristic refers to a method of solving a problem that proves to be quicker or more efficient than traditional methods. This may involve using approximations rather than precise calculations or techniques that circumvent otherwise computationally intensive routines.

Heuristics are practical rules of thumb that manifest as mental shortcuts in judgment and decision-making. Without heuristics, our brains would not be able to function given the complexity of the world, the amount of data to process, and the calculative abilities required to form an optimal decision. Instead, heuristics allow us to make quick, good-enough choices.

However, these choices may also be subject to inaccuracies and systemic biases, such as those identified by behavioral economics.

Simon, Herbert. " Herbert Simon, Innovation, and Heuristics ." Mind & Society, vol. 17, 2019, pp. 97-109.

Kahneman, Daniel, and Tversky, Amos. " Prospect Theory: An Analysis of Decision Under Risk ." The Econometric Society, vol. 47, no. 2, 1979, pp. 263-292.

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Understanding Heuristics in Problem Solving and Decision Making

Heuristics are mental shortcuts or rules of thumb that simplify decision making and problem-solving processes. They are strategies derived from previous experiences with similar problems that help individuals make quick, efficient judgments. The term "heuristic" comes from the Greek word "heuriskein," which means "to discover" or "to find." Heuristics play a crucial role in both everyday life and expert systems, allowing for satisfactory solutions when an exhaustive search is impractical.

Types of Heuristics

There are several types of heuristics commonly identified in cognitive psychology and behavioral economics, including but not limited to:

• Availability Heuristic: This involves estimating the likelihood of events based on their availability in memory. If something can be recalled easily, it is thought to be more common or likely.
• Representativeness Heuristic: This heuristic involves judging the probability of an event by finding a ‘representative’ or similar event and assuming the probabilities will be similar.
• Anchoring and Adjustment Heuristic: This is the process of making decisions based on adjustments to a previously existing value or starting point, known as the anchor.
• Affect Heuristic: Decisions are made based on the emotions associated with the outcomes or aspects of the decision, rather than a logical assessment.

Heuristics are not perfect and can lead to cognitive biases or systematic errors in thinking. However, they are valuable in that they allow for rapid decision-making, which can be particularly beneficial in fast-paced or emergency situations.

Heuristics in Problem Solving

In problem-solving, heuristics help in creating a simplified model of the world that makes it easier to generate solutions. They reduce the cognitive load by focusing on the most relevant aspects of the problem. For example, a common heuristic in problem-solving is "divide and conquer," where a complex problem is broken down into smaller, more manageable parts.

Heuristics in Decision Making

Heuristics also play a significant role in decision making, especially under conditions of uncertainty. They help individuals make quick decisions without having to analyze extensive information. For instance, a consumer might choose a product based on brand recognition (availability heuristic) rather than comparing all available alternatives.

Advantages and Disadvantages of Heuristics

The primary advantage of heuristics is their efficiency. They allow individuals to make decisions quickly, which is essential in many real-world situations where time is of the essence. However, the use of heuristics can also lead to biases and errors. For example, the availability heuristic can cause people to overestimate the likelihood of dramatic or recently reported events, such as plane crashes or shark attacks.

Heuristics in Artificial Intelligence

In artificial intelligence (AI), heuristics are used to design algorithms that can solve problems more efficiently. In AI, a heuristic function can estimate how close a state in a search space is to a goal state. This is particularly useful in games like chess, where the heuristic might be a function that evaluates who is ahead in a given board position.

Heuristics are an essential aspect of human cognition, aiding in rapid decision-making and problem-solving. While they can sometimes lead to errors or biases, their benefits in terms of speed and efficiency are undeniable. Understanding heuristics is crucial not only for cognitive psychology and AI but also for improving decision-making processes in various fields, including business, medicine, and public policy.

Kahneman, D., Slovic, P., & Tversky, A. (1982). Judgment under Uncertainty: Heuristics and Biases. Cambridge University Press.

Simon, H. A. (1956). Rational choice and the structure of the environment. Psychological Review, 63(2), 129–138.

Newell, A., & Simon, H. A. (1972). Human Problem Solving. Prentice-Hall.

Russell, S. J., & Norvig, P. (2009). Artificial Intelligence: A Modern Approach. Prentice Hall.

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Reviewed by Psychology Today Staff

A heuristic is a mental shortcut that allows an individual to make a decision, pass judgment, or solve a problem quickly and with minimal mental effort. While heuristics can reduce the burden of decision-making and free up limited cognitive resources, they can also be costly when they lead individuals to miss critical information or act on unjust biases.

• Understanding Heuristics
• Different Heuristics
• Problems with Heuristics

As humans move throughout the world, they must process large amounts of information and make many choices with limited amounts of time. When information is missing, or an immediate decision is necessary, heuristics act as “rules of thumb” that guide behavior down the most efficient pathway.

Heuristics are not unique to humans; animals use heuristics that, though less complex, also serve to simplify decision-making and reduce cognitive load.

Generally, yes. Navigating day-to-day life requires everyone to make countless small decisions within a limited timeframe. Heuristics can help individuals save time and mental energy, freeing up cognitive resources for more complex planning and problem-solving endeavors.

The human brain and all its processes—including heuristics— developed over millions of years of evolution . Since mental shortcuts save both cognitive energy and time, they likely provided an advantage to those who relied on them.

Heuristics that were helpful to early humans may not be universally beneficial today . The familiarity heuristic, for example—in which the familiar is preferred over the unknown—could steer early humans toward foods or people that were safe, but may trigger anxiety or unfair biases in modern times.

The study of heuristics was developed by renowned psychologists Daniel Kahneman and Amos Tversky. Starting in the 1970s, Kahneman and Tversky identified several different kinds of heuristics, most notably the availability heuristic and the anchoring heuristic.

Since then, researchers have continued their work and identified many different kinds of heuristics, including:

Familiarity heuristic

Fundamental attribution error

Representativeness heuristic

Satisficing

The anchoring heuristic, or anchoring bias , occurs when someone relies more heavily on the first piece of information learned when making a choice, even if it's not the most relevant. In such cases, anchoring is likely to steer individuals wrong .

The availability heuristic describes the mental shortcut in which someone estimates whether something is likely to occur based on how readily examples come to mind . People tend to overestimate the probability of plane crashes, homicides, and shark attacks, for instance, because examples of such events are easily remembered.

People who make use of the representativeness heuristic categorize objects (or other people) based on how similar they are to known entities —assuming someone described as "quiet" is more likely to be a librarian than a politician, for instance. 

Satisficing is a decision-making strategy in which the first option that satisfies certain criteria is selected , even if other, better options may exist.

Heuristics, while useful, are imperfect; if relied on too heavily, they can result in incorrect judgments or cognitive biases. Some are more likely to steer people wrong than others.

Assuming, for example, that child abductions are common because they’re frequently reported on the news—an example of the availability heuristic—may trigger unnecessary fear or overprotective parenting practices. Understanding commonly unhelpful heuristics, and identifying situations where they could affect behavior, may help individuals avoid such mental pitfalls.

Sometimes called the attribution effect or correspondence bias, the term describes a tendency to attribute others’ behavior primarily to internal factors—like personality or character— while attributing one’s own behavior more to external or situational factors .

If one person steps on the foot of another in a crowded elevator, the victim may attribute it to carelessness. If, on the other hand, they themselves step on another’s foot, they may be more likely to attribute the mistake to being jostled by someone else .

Listen to your gut, but don’t rely on it . Think through major problems methodically—by making a list of pros and cons, for instance, or consulting with people you trust. Make extra time to think through tasks where snap decisions could cause significant problems, such as catching an important flight.

Many apps claim to use nudges but instead use simple reminders that are just re-labeled as nudges. The terminology matters—true nudges use more potent behavioral science.

When you make a mistake for the third time, it's probably about you, not the situation.

The myth of the perfect question, the "fit" fallacy, and more.

Your plans should not be set based on the wisdom shared by successful people. They should be based on your context, your strengths, and your creative inspiration from that wisdom.

Discover how the anchoring effect, a subtle cognitive bias, shapes our decisions across life's domains.

Artificial intelligence already plays a role in deciding who’s getting hired. The way to improve AI is very similar to how we fight human biases.

Think you are avoiding the motherhood penalty by not having children? Think again. Simply being a woman of childbearing age can trigger discrimination.

Psychological experiments on human judgment under uncertainty showed that people often stray from presumptions about rational economic agents.

Are experts more confident in what they know than what they don't? Yes, but it's not so clear-cut.

Psychology, like other disciplines, uses the scientific method to acquire knowledge and uncover truths—but we still ask experts for information and rely on intuition. Here's why.

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An efficient tour construction heuristic for generating the candidate set of the traveling salesman problem with large sizes.

1. Introduction

2. from clustering to tour construction: an innovative approach to tsp, 2.1. clustering techniques: theory and principles, 2.2. our novel tour construction heuristic.

• Splitting the problem into subproblems with fuzzy clustering ( k subproblems);
• Solving each subproblem with Helsgaun’s Lin–Kernighan heuristic;
• Splitting the tours found at step 2 into two paths ( 2k paths in total);
• Connecting the paths into a solution for the entire problem with Helsgaun’s Lin–Kernighan heuristic;
• Post-optimization of randomly selected segments of the solution found at step 4 with Helsgaun’s Lin–Kernighan heuristic.
• The first cluster center is chosen uniformly at random from the vertices;
• All other cluster centers are chosen as follows: select 100 vertices uniformly at random and choose the one that is the furthest away from the cluster centers that have already been determined. This method aims to ensure that the new cluster centers are as far apart as possible from the existing ones, which can help in achieving a more diverse and well-distributed set of cluster centers.
• Determining the closest and second-closest clusters to each cluster based on the distances of the clusters’ centers;
• Determining the two splitting points by finding the closest vertices to the closest and second-closest clusters;
• Deleting for each splitting point one of the two edges in which the splitting point appears.

3.1. Parameter Tuning and Its Impact on Heuristic Performance

3.1.1. effect of cluster numbers on solution quality and runtime, 3.1.2. impact of basic moves in the lin–kernighan heuristic, 3.1.3. fuzzy clustering vs. traditional clustering, 3.1.4. effects of the fuzziness parameter, 3.1.5. post-optimization impact, 3.2. comparison with the popmusic heuristic, 3.2.1. evaluation on benchmark instances, 3.2.2. time complexity analysis, 3.2.3. tour improvement performance, 3.3. discussion, 4. conclusions, author contributions, data availability statement, conflicts of interest.

• Applegate, D.L.; Bixby, R.E.; Chvátal, V.; Cook, W.J.; Espinoza, D.; Goycoolea, M.; Helsgaun, K. Certification of an optimal tour through 85,900 cities. Oper. Res. Lett. 2009 , 37 , 11–15. [ Google Scholar ] [ CrossRef ]
• Helsgaun, K. An effective implementation of the Lin-Kernighan traveling salesman heuristic. Eur. J. Oper. Res. 2000 , 126 , 106–130. [ Google Scholar ] [ CrossRef ]
• Moscato, P. On Evolution, Search, Optimization, Genetic Algorithms and Martial Arts—Towards Memetic Algorithms. In Technical Report Caltech Concurrent Computation Program, Report 826 ; California Institute of Technology: Pasadena, CA, USA, 1989. [ Google Scholar ]
• Kóczy, L.T.; Földesi, P.; Tüű-Szabó, B. Enhanced discrete bacterial memetic evolutionary algorithm—An efficacious metaheuristic for the traveling salesman optimization. Inf. Sci. 2018 , 460–461 , 389–400. [ Google Scholar ] [ CrossRef ]
• Nguyen, H.D.; Yoshihara, I.; Yamamori, K.; Yasunaga, M. Implementation of an effective hybrid GA for large-scale traveling salesman problems. IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 2007 , 37 , 92–99. [ Google Scholar ] [ CrossRef ] [ PubMed ]
• Skinderowicz, R. Improving Ant Colony Optimization efficiency for solving large TSP instances. Appl. Soft Comput. 2022 , 120 , 108653. [ Google Scholar ] [ CrossRef ]
• Singh, S.P.; Kumar, N.; Dhiman, G.; Vimal, S.; Viriyasitavat, W. AI-Powered Metaheuristic Algorithms: Enhancing Detection and Defense for Consumer Technology. IEEE Consum. Electron. Mag. 2024 , 1–8. [ Google Scholar ] [ CrossRef ]
• Jauhar, S.K.; Pant, M. Genetic algorithms in supply chain management: A critical analysis of the literature. Sādhanā 2016 , 41 , 993–1017. [ Google Scholar ] [ CrossRef ]
• Balaji, A.N.; Jawahar, N. A simulated annealing algorithm for a two-stage fixed charge distribution problem of a supply chain. Int. J. Oper. Res. 2010 , 7 , 192–215. [ Google Scholar ] [ CrossRef ]
• Bentley, J.L. Multidimensional binary search trees used for associative searching. Commun. ACM 1975 , 18 , 509–517. [ Google Scholar ] [ CrossRef ]
• Padberg, M.W.; Rinaldi, G. Optimization of a 532-city symmetric traveling salesman problem by branch and cut. Oper. Res. Lett. 1987 , 6 , 1–7. [ Google Scholar ] [ CrossRef ]
• Applegate, D.L.; Bixby, R.E.; Chvátal, V.; Cook, W.J. The Traveling Salesman Problem: A Computational Study , 1st ed.; Princeton University Press: Princeton, NJ, USA, 2007; pp. 469–489. [ Google Scholar ]
• Blazinskas, A.; Misevicius, A. Generating High Quality Candidate Sets by Tour Merging for the Traveling Salesman Problem. In Information and Software Technologies. ICIST 2012 Communications in Computer and Information Science ; Skersys, T., Butleris, R., Butkiene, R., Eds.; Springer: Berlin/Heidelberg, Germany, 2012; Volume 319. [ Google Scholar ]
• Ali, I.J.; Tüű-Szabó, B.; Kóczy, L.T. Effect of the initial population construction on the DBMEA algorithm searching for the optimal solution of the traveling salesman problem. Infocommun. J. 2022 , 14 , 72–78. [ Google Scholar ]
• Taillard, E.D.; Voss, S. Popmusic—Partial Optimization Metaheuristic under Special Intensification Conditions. In Essays and Surveys in Metaheuristics ; Operations Research/Computer Science Interfaces Series; Springer: Boston, MA, USA, 2002; Volume 15. [ Google Scholar ]
• Taillard, E.D. Heuristic methods for large centroid clustering problems. J. Heuristics 2003 , 9 , 51–73. [ Google Scholar ] [ CrossRef ]
• Queiroga, E.; Sadykov, R.; Uchoa, E. A POPMUSIC matheuristic for the capacitated vehicle routing problem. Comput. Oper. Res. 2021 , 136 , 105475. [ Google Scholar ] [ CrossRef ]
• Alvim, A.C.F.; Taillard, E.D. POPMUSIC for the point feature label placement problem. Eur. J. Oper. Res. 2009 , 192 , 396–413. [ Google Scholar ] [ CrossRef ]
• Taillard, E.D.; Helsgaun, K. POPMUSIC for the travelling salesman problem. Eur. J. Oper. Res. 2019 , 272 , 420–429. [ Google Scholar ] [ CrossRef ]
• Taillard, E.D. A linearithmic heuristic for the travelling salesman problem. Eur. J. Oper. Res. 2022 , 297 , 442–450. [ Google Scholar ] [ CrossRef ]
• Dunn, J.C. A fuzzy relative ISODATA process and its use in detecting compact well-separated clusters. J. Cybern. 1974 , 3 , 32–57. [ Google Scholar ] [ CrossRef ]
• Bezdek, J.C. Pattern Recognition with Fuzzy Objective Function Algorithms ; Springer: New York, NY, USA, 1981. [ Google Scholar ]
• Suganya, R.; Shanthi, R. Fuzzy c-means algorithm—A review. Int. J. Sci. Res. Publ. 2012 , 2 , 1. [ Google Scholar ]
• Kim, W.D.; Lee, K.H.; Lee, D. A novel initialization scheme for the fuzzy c-means algorithm for color clustering. Pattern Recognit. Lett. 2004 , 25 , 227–237. [ Google Scholar ] [ CrossRef ]
• Yu, X.C.; He, H.; Hu, D.; Zhou, W. Land cover classification of remote sensing imagery based on interval-valued data fuzzy c-means algorithm. Sci. China Earth Sci. 2014 , 57 , 1306–1313. [ Google Scholar ] [ CrossRef ]
• Chuang, K.-S.; Tzeng, H.-L.; Chen, S.; Wu, J.; Chen, T.J. Fuzzy c-means clustering with spatial information for image segmentation. Comput. Med. Imaging Graph. 2006 , 30 , 9–15. [ Google Scholar ] [ CrossRef ] [ PubMed ]
• Reinelt, G. Improving Solutions. The Traveling Salesman: Computational Solutions for TSP Applications ; Springer: Berlin/Heidelberg, Germany, 1994; pp. 100–132. [ Google Scholar ]
• Lin, S.; Kernighan, B.W. An effective heuristic algorithm for the traveling-salesman problem. Oper. Res. 1973 , 21 , 498–516. [ Google Scholar ] [ CrossRef ]

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Tüű-Szabó, B.; Földesi, P.; Kóczy, L.T. An Efficient Tour Construction Heuristic for Generating the Candidate Set of the Traveling Salesman Problem with Large Sizes. Mathematics 2024 , 12 , 2960. https://doi.org/10.3390/math12192960

Tüű-Szabó B, Földesi P, Kóczy LT. An Efficient Tour Construction Heuristic for Generating the Candidate Set of the Traveling Salesman Problem with Large Sizes. Mathematics . 2024; 12(19):2960. https://doi.org/10.3390/math12192960

Tüű-Szabó, Boldizsár, Péter Földesi, and László T. Kóczy. 2024. "An Efficient Tour Construction Heuristic for Generating the Candidate Set of the Traveling Salesman Problem with Large Sizes" Mathematics 12, no. 19: 2960. https://doi.org/10.3390/math12192960

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A stable higher-order numerical method for solving a system of third-order singular Emden-Fowler type equations

• Original Research
• Published: 24 September 2024

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• Nirupam Sahoo 1 &
• Randhir Singh   ORCID: orcid.org/0000-0003-0283-3754 1  

This paper proposes a new higher-order numerical method based on a difference scheme with uniform steps to solve a strongly nonlinear system of third-order singular Emden-Fowler-type equations. These problems are challenging to solve because of their singularity or strong nonlinearity. To handle the singularity of the problem, we approximate the derivatives at the endpoints and develop a new difference scheme. This scheme provides a system of nonlinear equations solved by an iterative method. Also, we mathematically establish the method’s stability, consistency, and convergence analysis using a matrix analysis approach. We also verify the presented technique’s efficiency, accuracy and applicability by solving different examples from the literature. We also show that the theoretical order of the technique is consistent with the numerical convergence rates. Additionally, our method easily achieves higher-order accuracy with minimal grid points, unlike most methods that typically require modifying the equation into an equivalent integral equation or using L’Hospital’s rule to remove singularities, resulting in lower-order accuracy approaches.

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Boubaker, K., Van Gorder, R.A.: Application of the BPES to Lane-Emden equations governing polytropic and isothermal gas spheres. New Astron. 17 (6), 565–569 (2012)

Article   Google Scholar  

Flesch, U.: The distribution of heat sources in the human head: a theoretical consideration. J. Theor. Biol. 54 (2), 285–287 (1975)

Lin, S.: Oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics. J. Theor. Biol. 60 (2), 449–457 (1976)

Ramos, J.I.: Linearization methods in classical and quantum mechanics. Comput. Phys. Commun. 153 (2), 199–208 (2003)

Article   MathSciNet   Google Scholar  

Dehghan, M., Shakeri, F.: Solution of an integro-differential equation arising in oscillating magnetic fields using He’s homotopy perturbation method. Progress Electromag. Res. 78 , 361–376 (2008)

Wazwaz, A.-M., Rach, R., Bougoffa, L., Duan, J.-S.: Solving the Lane-Emden-Fowler type equations of higher orders by the Adomian decomposition method. Comput. Model. Eng. Sci. 100 (6), 507–529 (2014)

MathSciNet   Google Scholar  

Shahni, J., Singh, R., Cattani, C.: Bernoulli collocation method for the third-order Lane-Emden-Fowler boundary value problem. Appl. Numer. Math. 186 (1), 100–103 (2023)

Lane, H.J.: On the theoretical temperature of the sun, under the hypothesis of a gaseous mass maintaining its volume by its internal heat, and depending on the laws of gases as known to terrestrial experiment. Am. J. Sci. 148 , 57–74 (1870)

Emden, R.: Gaskugeln: Anwendungen der mechanischen Wärmetheorie auf kosmologische und meteorologische Probleme, B. Teubner., (1907)

Chawla, M., Katti, C.: Finite difference methods and their convergence for a class of singular two point boundary value problems. Numer. Math. 39 (3), 341–350 (1982)

Desaix, M., Anderson, D., Lisak, M.: Variational approach to the Thomas-Fermi equation. Eur. J. Phys. 25 (6), 699 (2004)

Kanth, A.R.: Cubic spline polynomial for non-linear singular two-point boundary value problems. Appl. Math. Comput. 189 (2), 2017–2022 (2007)

Lakestani, M., Dehghan, M.: Four techniques based on the b-spline expansion and the collocation approach for the numerical solution of the Lane-Emden equation. Math. Methods Appl. Sci. 36 (16), 2243–2253 (2013)

Singh, R., Kumar, J.: An efficient numerical technique for the solution of nonlinear singular boundary value problems. Comput. Phys. Commun. 185 (4), 1282–1289 (2014)

Zhou, F., Xu, X.: Numerical solutions for the linear and nonlinear singular boundary value problems using laguerre wavelets. Adv. Difference Equ. 2016 (1), 17 (2016)

Parand, K., Yousefi, H., Delkhosh, M., Ghaderi, A.: A novel numerical technique to obtain an accurate solution to the thomas-fermi equation. Eur. Phys. J. Plus 131 (7), 228 (2016)

Verma, A.K., Tiwari, D.: Higher resolution methods based on quasilinearization and Haar wavelets on Lane-Emden equations. Int. J. Wavelets Multiresol. Inf. Process. 17 (03), 1950005 (2019)

Singh, R., Guleria, V., Singh, M.: Haar wavelet quasilinearization method for numerical solution of Emden-Fowler type equations. Math. Comput. Simul. 174 , 123–133 (2020)

Shahni, J., Singh, R.: Numerical solution of system of emden-fowler type equations by bernstein collocation method. J. Math. Chem. 59 (4), 1117–1138 (2021)

Shahni, J., Singh, R.: Laguerre wavelet method for solving Thomas-Fermi type equations. Eng. Comput. 38 (4), 2925–2935 (2022)

Shahni, J., Singh, R.: A fast numerical algorithm based on Chebyshev-wavelet technique for solving Thomas-Fermi type equation. Eng. Comput. 38 (Suppl 4), 3409–3422 (2022)

Shahni, J., Singh, R.: Numerical simulation of Emden-Fowler integral equation with Green’s function type kernel by Gegenbauer-wavelet, Taylor-wavelet and Laguerre-wavelet collocation methods. Math. Comput. Simul. 194 (2022), 430–444 (2021)

Alam, M.P., Begum, T., Khan, A.: A high-order numerical algorithm for solving Lane-Emden equations with various types of boundary conditions. Comput. Appl. Math. 40 (6), 1–28 (2021)

Sahoo, N., Singh, R.: A new efficient semi-numerical method with a convergence control parameter for Lane-Emden-Fowler boundary value problem. J. Comput. Sci. 70 , 102041 (2023)

Chan, C., Hon, Y.: A constructive solution for a generalized Thomas-Fermi theory of ionized atoms. Q. Appl. Math. 45 (3), 591–599 (1987)

Kim, W., Chun, C.: A modified Adomian decomposition method for solving higher-order singular boundary value problems. Zeitschrift für Naturforschung A 65 (12), 1093–1100 (2010)

Wazwaz, A.M.: Solving two Emden-Fowler type equations of third order by the variational iteration method. Appl. Math. Inf. Sci. 9 (5), 2429 (2015)

Dezhbord, A., Lotfi, T., Mahdiani, K.: A numerical approach for solving the high-order nonlinear singular emden-fowler type equations. Adv. Difference Equ. 2018 , 1–17 (2018)

Guirao, J.L., Sabir, Z., Saeed, T.: Design and numerical solutions of a novel third-order nonlinear Emden-Fowler delay differential model. Math. Probl. Eng. 2020 , 1–9 (2020)

Sabir, Z., Raja, M.A.Z., Umar, M., Shoaib, M.: Design of neuro-swarming-based heuristics to solve the third-order nonlinear multi-singular Emden-Fowler equation. Eur. Phys. J. Plus 135 (5), 410 (2020)

Ali, K. K., Mehanna, M., Wazwaz, A.-M., Shaalan, M.: Solve third order Lane-Emden-Fowler equation by Adomian decomposition method and quartic trigonometric B-spline method, Partial Diff. Equ. Appl. Math. 100676 (2024)

Izadi, M., Roul, P.: A new approach based on shifted Vieta-Fibonacci-quasilinearization technique and its convergence analysis for nonlinear third-order Emden-Fowler equation with multi-singularity. Commun. Nonlinear Sci. Numer. Simul. 117 , 106912 (2023)

Singh, R., Singh, M.: An optimal decomposition method for analytical and numerical solution of third-order Emden-Fowler type equations. J. Comput. Sci. 63 , 101790 (2022)

Shahni, J., Singh, R.: Numerical results of Emden-Fowler boundary value problems with derivative dependence using the bernstein collocation method. Eng. Comput. 38 (Suppl 1), 371–380 (2022)

Hajimohammadi, Z., Shekarpaz, S., Parand, K.: The novel learning solutions to nonlinear differential models on a semi-infinite domain. Eng. Comput. 39 (3), 2169–2186 (2023)

Parand, K., Aghaei, A., Kiani, S., Zadeh, T. I., Khosravi, Z.: A neural network approach for solving nonlinear differential equations of Lane–Emden type, Eng. Comput. 1–17 (2023)

Modanli, M., Murad, M.A.S., Abdulazeez, S.T.: A new computational method-based integral transform for solving time-fractional equation arises in electromagnetic waves. Z. Angew. Math. Phys. 74 (5), 186 (2023)

Abu Arqub, O., Abo-Hammour, Z., Momani, S., Shawagfeh, N.: Solving Singular Two-Point Boundary Value Problems Using Continuous Genetic Algorithm. In: Abstract and applied analysis, Vol. 2012, Wiley Online Library, p. 205391 (2012)

Rabah, A.B., Momani, S., Arqub, O.A.: The B-spline collocation method for solving conformable initial value problems of non-singular and singular types. Alex. Eng. J. 61 (2), 963–974 (2022)

Abu Arqub, O.: Reproducing Kernel algorithm for the analytical-numerical solutions of nonlinear systems of singular periodic boundary value problems. Math. Probl. Eng. 2015 (1), 518406 (2015)

Abu Arqub, O.: Computational algorithm for solving singular Fredholm time-fractional partial integrodifferential equations with error estimates. J. Appl. Math. Comput. 59 (1), 227–243 (2019)

Hasan, Y.Q., Zhu, L.M.: A note on the use of modified Adomian decomposition method for solving singular boundary value problems of higher-order ordinary differential equations. Commun. Nonlinear Sci. Numer. Simul. 14 (8), 3261–3265 (2009)

Hasan, Y.Q., Zhu, L.M.: Solving singular boundary value problems of higher-order ordinary differential equations by modified Adomian decomposition method. Commun. Nonlinear Sci. Numer. Simul. 14 (6), 2592–2596 (2009)

Singh, N., Kumar, M.: Adomian decomposition method for solving higher order boundary value problems. Math. Theory Model. 2 (1), 11–22 (2011)

Google Scholar  

Aruna, K., Kanth, A.R.: A novel approach for a class of higher order nonlinear singular boundary value problems. Int. J. Pure Appl. Math. 84 (4), 321–329 (2013)

Iqbal, M.K., Abbas, M., Wasim, I.: New cubic B-spline approximation for solving third order Emden-Flower type equations. Appl. Math. Comput. 331 , 319–333 (2018)

Shah, A., Yuan, L., Khan, A.: Upwind compact finite difference scheme for time-accurate solution of the incompressible Navier-Stokes equations. Appl. Math. Comput. 215 (9), 3201–3213 (2010)

Düring, B., Fournié, M., Jüngel, A.: High order compact finite difference schemes for a nonlinear Black-Scholes equation. Int. J. Theor. Appl. Finance 6 (07), 767–789 (2003)

Zhao, J., Davison, M., Corless, R.M.: Compact finite difference method for American option pricing. J. Comput. Appl. Math. 206 (1), 306–321 (2007)

Mathale, D., Dlamini, P., Khumalo, M.: Compact finite difference relaxation method for chaotic and hyperchaotic initial value systems. Comput. Appl. Math. 37 , 5187–5202 (2018)

Lele, S.K.: Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103 (1), 16–42 (1992)

Roul, P., Goura, V.P., Agarwal, R.: A compact finite difference method for a general class of nonlinear singular boundary value problems with Neumann and Robin boundary conditions. Appl. Math. Comput. 350 , 283–304 (2019)

Roul, P., Kumari, T.: A novel approach based on mixed exponential compact finite difference and oha methods for solving a class of nonlinear singular boundary value problems. Int. J. Comput. Math. 100 (3), 572–590 (2023)

Abdulazeez, S.T., Modanli, M.: Solutions of fractional order pseudo-hyperbolic telegraph partial differential equations using finite difference method. Alex. Eng. J. 61 (12), 12443–12451 (2022)

Tenekeci, M. E., Abdulazeez, S. T., Karadağ, K., Modanli, M.: Edge detection using the Prewitt operator with fractional order telegraph partial differential equations (PreFOTPDE), Multimedia Tools Appl. 1–17 (2024)

Sahoo, N., Singh, R., Ramos, H.: An innovative fourth-order numerical scheme with error analysis for Lane-Emden-Fowler type systems, Numer. Algorithms 1–29 (2024)

Abdulla, S.O., Abdulazeez, S.T., Modanli, M.: Comparison of third-order fractional partial differential equation based on the fractional operators using the explicit finite difference method. Alex. Eng. J. 70 , 37–44 (2023)

Malo, D.H., Masiha, R.Y., Murad, M.A.S., Abdulazeez, S.T.: A new computational method based on integral transform for solving linear and nonlinear fractional systems. Jurnal Matematika MANTIK 7 (1), 9–19 (2021)

Kirkpinar, S., Abdulazeez, S.T., Modanli, M.: Piecewise modeling of the transmission dynamics of contagious bovine pleuropneumonia depending on vaccination and antibiotic treatment. Fractals 30 (08), 2240217 (2022)

Verma, A.K., Singh, M.: Singular nonlinear three point BVPs arising in thermal explosion in a cylindrical reactor. J. Math. Chem. 53 (2), 670–684 (2015)

Godunov, S.K., Ryabenkii, V.S.: Difference Schemes: An Introduction to the Underlying Theory. Elsevier, London (1987)

Wazwaz, A.-M.: The variational iteration method for solving systems of third-order Emden-Fowler type equations. J. Math. Chem. 55 , 799–817 (2017)

Rufai, M.A., Ramos, H.: Numerical integration of third-order singular boundary-value problems of Emden-Fowler type using hybrid block techniques. Commun. Nonlinear Sci. Numer. Simul. 105 , 106069 (2022)

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Department of Mathematics, Birla Institute of Technology Mesra, Ranchi, 835215, India

Nirupam Sahoo & Randhir Singh

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N.S.: Contributed to formulation, Methodology, Visualization, Investigation, Programming, Writing - Original Draft. R.S.: Contributed to formulation, Methodology, Investigation, Writing- Review and Editing.

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Here, we present the system of nonlinear algebraic equations (at least 6 equations), solved by the Newton–Raphson method for Example 1:

for \(i=1\)

for \(i=2\)

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Sahoo, N., Singh, R. A stable higher-order numerical method for solving a system of third-order singular Emden-Fowler type equations. J. Appl. Math. Comput. (2024). https://doi.org/10.1007/s12190-024-02233-x

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Received : 06 May 2024

Revised : 20 August 2024

Accepted : 02 September 2024

Published : 24 September 2024

DOI : https://doi.org/10.1007/s12190-024-02233-x

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