Heuristics are efficient cognitive processes that ignore information. In contrast to the widely held view that less processing reduces accuracy, the study of heuristics shows that less information, computation, and time can in fact improve accuracy. We review the major progress made so far: (a) the discovery of less‐is‐more effects; (b) the study of the ecological rationality of heuristics, which examines in which environments a given strategy succeeds or fails, and why; (c) an advancement from vague labels to computational models of heuristics; (d) the development of a systematic theory of heuristics that identifies their building blocks and the evolved capacities they exploit, and views the cognitive system as relying on an “adaptive toolbox;” and (e) the development of an empirical methodology that accounts for individual differences, conducts competitive tests, and has provided evidence for people’s adaptive use of heuristics. Homo heuristicus has a biased mind and ignores part of the available information, yet a biased mind can handle uncertainty more efficiently and robustly than an unbiased mind relying on more resource‐intensive and general‐purpose processing strategies.

As far as we can know, animals have always relied on heuristics to solve adaptive problems, and so have humans. To measure the area of a candidate nest cavity, a narrow crack in a rock, an ant has no yardstick but a rule of thumb: Run around on an irregular path for a fixed period while laying down a pheromone trail, and then leave. Return, move around on a different irregular path, and estimate the size of the cavity by the frequency of encountering the old trail. This heuristic is remarkably precise: Nests half the area of others yielded reencounter frequencies 1.96 times greater (Mugford, Mallon, & Franks, 2001). To choose a mate, a peahen similarly uses a heuristic: Rather than investigating all peacocks posing and displaying in a lek eager to get her attention or weighting and adding all male features to calculate the one with the highest expected utility, she investigates only three or four, and chooses the one with the largest number of eyespots (Petrie & Halliday, 1994). Many of these evolved rules of thumb are amazingly simple and efficient (for an overview, see Hutchinson & Gigerenzer, 2005). The Old Testament says that God created humans in his image and let them dominate all animals, from whom they fundamentally differ (Genesis 1:26). It might not be entirely accidental that in cognitive science some form of omniscience (knowledge of all relevant probabilities and utilities, for instance) and omnipotence (the ability to compute complex functions in a split second) has shaped models of human cognition. Yet humans and animals have common ancestors, related sensory and motor processes, and even share common cognitive heuristics. Consider how a baseball outfielder catches a ball. The view of cognition favoring omniscience and omnipotence suggests that complex problems are solved with complex mental algorithms: “he behaves as if he had solved a set of differential equations in predicting the trajectory of the ball… At some subconscious level, something functionally equivalent to the mathematical calculations is going on” (Dawkins, 1989, p. 96). Dawkins carefully inserts “as if” to indicate that he is not quite sure whether brains actually perform these computations. And there is indeed no evidence that brains do. Instead, experiments have shown that players rely on several heuristics. The gaze heuristic is the simplest one and works if the ball is already high up in the air: Fix your gaze on the ball, start running, and adjust your running speed so that the angle of gaze remains constant (see Gigerenzer, 2007). A player who relies on the gaze heuristic can ignore all causal variables necessary to compute the trajectory of the ball––the initial distance, velocity, angle, air resistance, speed and direction of wind, and spin, among others. By paying attention to only one variable, the player will end up where the ball comes down without computing the exact spot. The same heuristic is also used by animal species for catching prey and for intercepting potential mates. In pursuit and predation, bats, birds, and dragonflies maintain a constant optical angle between themselves and their prey, as do dogs when catching a Frisbee (Shaffer, Krauchunas, Eddy, & McBeath, 2004). The term heuristic is of Greek origin, meaning “serving to find out or discover.” The mathematician George Polya distinguished heuristics from analytic methods; for instance, heuristics are indispensable for finding a proof, whereas analysis is required to check a proof’s validity. In the 1950s, Herbert Simon (1955, 1991), who studied with Polya in Stanford, first proposed that people satisfice rather than maximize. Maximization means optimization, the process of finding the best solution for a problem, whereas satisficing (a Northumbrian word for “satisfying”) means finding a good‐enough solution. Simon used his term satisficing both as a generic term for everything that is not optimizing as well as for a specific heuristic: In order to select a good alternative (e.g., a house or a spouse) from a series of options encountered sequentially, a person sets an aspiration level, chooses the first one that meets the aspiration, and then terminates search. The aspiration level can be fixed or adjusted following experience (Selten, 2001). For Simon, humans rely on heuristics not simply because their cognitive limitations prevent them from optimizing but also because of the task environment. For instance, chess has an optimal solution, but no computer or mind, be it Deep Blue or Kasparov, can find this optimal sequence of moves, because the sequence is computationally intractable to discover and verify. Most problems of interest are computationally intractable, and this is why engineers and artificial intelligence (AI) researchers often rely on heuristics to make computers smart. In the 1970s, the term heuristic acquired a different connotation, undergoing a shift from being regarded as a method that makes computers smart to one that explains why people are not smart. Daniel Kahneman, Amos Tversky, and their collaborators published a series of experiments in which people’s reasoning was interpreted as exhibiting fallacies. “Heuristics and biases” became one phrase. It was repeatedly emphasized that heuristics are sometimes good and sometimes bad, but virtually every experiment was designed to show that people violate a law of logic, probability, or some other standard of rationality. On the positive side, this influential research drew psychologists’ attention to cognitive heuristics and helped to create two new fields: behavioral economics, and behavioral law and economics. On the negative side, heuristics became seen as something best to avoid, and consequently, this research was disconnected from the study of heuristics in AI and behavioral biology. Another negative and substantial consequence was that computational models of heuristics, such as lexicographic rules (Fishburn, 1974) and elimination‐by‐aspects (Tversky, 1972), became replaced by one‐word labels: availability, representativeness, and anchoring. These were seen as the mind’s substitutes for rational cognitive procedures. By the end of the 20th century, the use of heuristics became associated with shoddy mental software, generating three widespread misconceptions: 1 Heuristics are always second‐best.

2 We use heuristics only because of our cognitive limitations.

3 More information, more computation, and more time would always be better. These three beliefs are based on the so‐called accuracy‐effort trade‐off, which is considered a general law of cognition: If you invest less effort, the cost is lower accuracy. Effort refers to searching for more information, performing more computation, or taking more time; in fact, these typically go together. Heuristics allow for fast and frugal decisions; thus, it is commonly assumed that they are second‐best approximations of more complex “optimal” computations and serve the purpose of trading off accuracy for effort. If information were free and humans had eternal time, so the argument goes, more information and computation would always be better. For instance, Tversky (1972, p. 98) concluded that elimination‐by‐aspects “cannot be defended as a rational procedure of choice.” More outspokenly, two eminent decision theorists, Keeney and Raiffa (1993), asserted that reliance on lexicographic heuristics “is more widely adopted in practice than it deserves to be,” and they stressed that “it is our belief that, leaving aside ‘administrative ease,’ it is rarely appropriate” and “will rarely pass a test of reasonableness” (pp. 77–78). They did not, however, put their intuition to a test. A few years later, our research team conducted such tests, with surprising results. Contrary to the belief in a general accuracy‐effort trade‐off, less information and computation can actually lead to higher accuracy, and in these situations the mind does not need to make trade‐offs. Here, a less‐is‐more effect holds. That simple heuristics can be more accurate than complex procedures is one of the major discoveries of the last decades (Gigerenzer, 2008). Heuristics achieve this accuracy by successfully exploiting evolved mental abilities and environmental structures. Since this initial finding, a systematic science of heuristics has emerged, which we review in this article, together with the reactions it has provoked. Beginning with the standard explanation of why people rely on heuristics and the common assumption of a general accuracy‐effort trade‐off, we introduce less‐is‐more phenomena that contradict it. We then present the ecological rationality of heuristics as an alternative explanation and show how less‐is‐more phenomena emerge from the bias–variance dilemma that cognitive systems face in uncertain worlds. In the following sections, we make a case against the widespread use of vague labels instead of models of heuristics, review some of the progress made in the development of a systematic theory of the adaptive toolbox, and end with a discussion of proper methodology.

4. Unpacking the adaptive toolbox 4.1. The building blocks of heuristics Although examples of rules of thumb in biology are not rare, they tend to be curiosities, partly because biology lacks a systematic theory of heuristics. Similarly, within cognitive science, there has been no such theory (although see Payne et al., 1993). The next step in progress we deal with is the beginning of a systematic study of heuristics and their building blocks. Research into the adaptive toolbox attempts to formulate such a theory by identifying the heuristics that humans and other animals use, the building blocks of heuristics that can be used to generate new ones, and the evolved capacities that these building blocks exploit (Gigerenzer & Selten, 2001). The gaze heuristic introduced earlier has three building blocks. As pointed out, it only works when the ball is already high in the air, but it fails if the ball is at the beginning of its trajectory. To adjust to this new situation, a player does not need a new heuristic, but only to adapt the third building block. Instead of 1 Fix your gaze on the ball,

2 start running, and

3 adjust your running speed so that the angle of gaze remains constant, the adapted heuristic is: 1 Fix your gaze on the ball,

2 start running, and

3 adjust your running speed so that the image of the ball rises at a constant rate. One can intuitively see its logic. If the player sees the ball rising from the point at which it was hit with accelerating speed, the player should run backward, because the ball will hit the ground behind the player’s position. If, however, the ball rises with decreasing speed, the player needs to run toward the ball instead. Just as there is a class of such tracking heuristics, there is a class of one‐good‐reason heuristics, of which take‐the‐best is one member. These heuristics also have three building blocks: search rules, stopping rules, and decision rules. Take‐the‐best is not a useful heuristic in every situation; more generally, no single strategy is always the best one––otherwise, the mind would resemble a mechanic with only one tool at hand. Consider the first building block of take‐the‐best: Search rule: Search through cues in order of their validity. This search rule can be followed if the cues are retrieved from memory, but situations exist in which the order of cues is dictated from outside. Consider a red deer stag in rutting season that wants to enter the territory of a harem holder: In a fight with the rival over the females, which male is likely to win? For the stag, this question is a matter of genetic survival. Typically, the first cue is roaring. If the harem holder roars more impressively, the challenger may already give up and walk away. Otherwise, the next contest is initiated, parallel walking. It allows the competitors to assess each other’s physical fitness and, potentially, confidence at a closer distance. If this contest also fails to produce a clear winner, the third contest is started: head‐butting, the riskiest activity, as it can result in dangerous injuries (Clutton‐Brock & Albon, 1979). This step‐by‐step heuristic is like take‐the‐best, but the search rule differs. The order of cues is not determined by (whatever the stag believes to be) the most valid cue, but by the cue that is first accessible. Sound can be encountered first in a forest environment where vision is restricted, visual stimuli next, and the most valid cue, head‐butting, is last because it requires close contact. Thus, for the male deer, the adapted search rule is: Search rule: Search through cues in order of their environmental accessibility. The other building blocks remain the same. Consider now a situation where search by validity is not constrained. However, the task is new and the individual does not have the experience to come up with a good order. In this case, one can prove that it is of advantage to adjust the stopping rule and consequently, the decision rule (Karelaia, 2006): Stopping rule: Stop as soon as two cues are found that point to the same object. Decision rule: Infer that this object has the higher criterion value.

This stopping rule, termed a confirmation rule, works well in situations where (a) the decision maker knows little about the validity of the cues, and (b) the costs of cues are rather low (Karelaia, 2006). It is remarkably robust and insensitive to knowledge about cue ordering, and there is experimental evidence that a substantial proportion of people rely on this stopping rule as long as the problem is new (Gigerenzer, Dieckmann, & Gaissmaier, in press). By adapting the building blocks of heuristics, organisms can react to new tasks and changing environments.

4.2. How does the mind select heuristics? Table 2 shows 10 heuristics in the adaptive toolbox of humans. But how does the mind select a heuristic that is reasonable for the task at hand? Although far from a complete understanding of this mostly unconscious process, we know there are at least three selection principles. The first is that memory constrains the choice set of heuristics and thereby creates specific cognitive niches for different heuristics (Marewski & Schooler, unpublished data). Consider the choice between the first three heuristics in Table 2: the recognition heuristic, the fluency heuristic, and take‐the‐best. Assume it is 2003, and a visitor has been invited to the third round of the Wimbledon Gentlemen’s tennis tournament and encouraged to place a bet on who will win. The two players are Andy Roddick and Tommy Robredo. First, assume that the visitor is fairly ignorant about tennis and has heard of Roddick but not of Robredo. This state of memory restricts the choice set to the recognition heuristic: If you have heard of one player but not the other, predict that the recognized player will win the game. As it happened, Roddick won the match. In fact, this correct inference is not an exception: This simple heuristic predicted the matches of Wimbledon 2003 and 2005 with equal or higher accuracy than the ATP rankings and the seeding of the Wimbledon experts did (Scheibehenne & Bröder, 2007; Serwe & Frings, 2006). Now assume that the visitor has heard of both players but recalls nothing else about them. That state of memory limits the choice set to the fluency heuristic: If you have heard of both players, but the name of one came faster to your mind than the other, predict that this player will win the game. Finally, assume that the visitor is more knowledgeable and can recall various facts about both players. That again eliminates the recognition heuristic and leaves a choice between the fluency heuristic and take‐the‐best. According to the experimental evidence, the majority of subjects switch to knowledge‐based heuristics such as take‐the‐best when the values of both alternatives on relevant cues can be recalled (Marewski, Gaissmaier, Schooler, Goldstein, & Gigerenzer, unpublished data), consistent with an analysis of the relative ecological rationality of the two heuristics in this situation. The general point is that memory “selects” heuristics in a way that makes it easier and faster to apply a heuristic when it is likely to yield accurate decisions. In the extreme case where the visitor has not heard of any of the players, none of the heuristics can be used. In this event, the visitor can resort to social heuristics, such as imitate the majority: Bet on the player on whom most others bet (Table 2). The second known selection principle, after memory, is feedback. Strategy selection theory (Rieskamp & Otto, 2006) provides a quantitative model that can be understood as a reinforcement theory where the unit of reinforcement is not a behavior, but a heuristic. This model allows predictions about the probability that a person selects one strategy within a defined set of strategies. The third selection principle relies on the structure of the environment, as analyzed in the study of ecological rationality. For instance, the recognition heuristic is likely to lead to fast and accurate judgments if the recognition validity is high, that is, a strong correlation between recognition and the criterion exists, as is the case for tennis and other sports tournaments. There is experimental evidence that people tend to rely on this heuristic if the recognition validity is high but less so if the recognition validity α is low or at chance level (α = .5). For instance, name recognition of Swiss cities is a valid predictor of their population (α = .86), but not for their distance from the center of Switzerland, the city of Interlaken (α = .51). Pohl (2006) reported that 89% of participants relied on the recognition heuristic in judgments of population, but only 54% in judgments of distance to Interlaken. Thus, the use of the recognition heuristic involves two processes: first, recognition in order to see whether the heuristic can be applied, and second, evaluation in order to judge whether it should be applied. Using functional magnetic resonance imaging (fMRI), Volz et al. (2006) reported specific neural activity that corresponded to these two processes. Similarly, the take‐the‐best heuristic is more accurate when the weights of cues vary widely, but less so when they are about equal. Rieskamp and Otto (2006) and Bröder (2003) reported that people adaptively select take‐the‐best when the environment has this property.

6. Homo heuristicus In this article, we presented a vision of human nature based on an adaptive toolbox of heuristics rather than on traits, attitudes, preferences, and similar internal explanations. We reviewed the progress made in developing a science of heuristics, beginning with the discovery of less‐is‐more effects that contradict the prevailing explanation in terms of accuracy‐effort trade‐offs. Instead, we argue that the answer to the question, “Why heuristics?” lies in their ecological rationality, that is, in the environmental structures to which a given heuristic is adapted. Using the bias–variance dilemma, we showed how the ecological rationality of heuristics can be formally studied, focusing on uncertain criteria and small samples that constitute environmental structures which fast and frugal heuristics can exploit. Homo heuristicus can rely on heuristics because they are accurate, not because they require less effort at the cost of some accuracy. We hope to have raised our readers’ curiosity about the emerging science of heuristics and also hope that they might be inspired to solve some of the open questions, such as whether there is a system of building blocks of heuristics, similar to the elements in chemistry, and how a vocabulary for describing relevant environmental structures can be found. Let us end this article about the rationality of mortals from God’s point of view. How would a grand planner design a human mind? Consider three design perspectives. Design 1 would give the mind perfect memory. This would be ideal in a world that is absolutely certain and predictable, where what was observed in the past will also be observed in the future. This mind could remember, for instance, every day’s temperature and thus could perfectly predict the future. In this world, perfect memory guarantees zero bias and zero variance, as every event has been observed and perfectly memorized. In fact, evolution has created something very close. A prominent example is a Russian named Shereshevsky, whom Luria (1968) studied for over three decades without finding the limits of his astounding memory. But this memory came at a price. For instance, Shereshevsky would read a page and recall it word for word, both forwards and backwards, but when he was asked to summarize the gist of what he read, he was more or less at a loss. Gist, abstraction, and other ways of going beyond the information given were not what this perfect memory buried in detail could deliver. Design 2 accounts for the fact that the world is not absolutely predictable and fully observable, and therefore, a perfect memory would be a waste of energy. Instead, the goal is a mind that can make intelligent inferences from limited samples. The ideal is to have an infinitely flexible system of abstract representations to ensure zero bias, so that whatever structure the world has, it can be reproduced perfectly. As the content of the samples of observations in this world will vary, the induced representations are likely to be different, and this creates variance. Such a mind works best with large samples of observations and in a world that is relatively stable. Yet because this mind has no bias and must choose from an infinite space of representations, it is likely to require resource‐intensive cognitive processing. This kind of design suggests general‐purpose processing strategies such as exemplar models and neural networks as models of cognition (see Fig. 2). Design 3 aims at a mind that can make inferences quickly from a few observations, and it exploits the fact that bias can be adaptive and can help to reduce the estimation error (Figs. 1 and 2). This design relies on several inference tools rather than a single universal tool. Each has a bias that can be offset by a greater reduction in variance. This design works well in a world where inferences have to be made from small samples, and where the future may change in unforeseen ways (Bookstaber & Langsam, 1985). Unlike in the previous cases, the creator of Design 3 need not assume omniscience, that is, knowledge of all relevant options, consequences, and probabilities both now and in the future. This corresponds to the world in which many experts live, such as the business managers using the hiatus heuristic and the Nobel laureate relying on 1/N. After all, to build a mind with zero bias assumes that one knows the true state of the world and the representations needed to model it. Zero bias is neither possible nor always desirable for a real mind. Adopting the perspective of Design 3, the study of simple heuristics shows not only how a mind can make accurate inferences about an uncertain world efficiently but also how this efficiency is crucial to adapting the mind to its environment. Viewing humans as Homo heuristicus challenges widely held beliefs about the nature of cognitive processing and explains why less processing can result in better inferences.

Acknowledgments We are grateful to Julian Marewski, Shabnam Mousavi, Lael Schooler, and three anonymous reviewers for their helpful comments.

Appendix Appendix 1: Environments used in the bias–variance analysis m binary cues to an integer criterion. The two classes of environment considered here are both parameterized by m. The first class of environment comprises binary environments, each of which has 2m objects defined by b m (i) maps integers onto their binary representations, coded using the binary cues (for example, b 4 (3) = (0,0,1,1)). Binary environments have noncompensatory weights, and the cues are uncorrelated. For example, H binary (3) defines the following environment: An environment is a collection of objects. Each object relatesbinary cues to an integer criterion. The two classes of environment considered here are both parameterized by. The first class of environment comprises, each of which hasobjects defined bywhere the function) maps integers onto their binary representations, coded using the binary cues (for example,(3) = (0,0,1,1)). Binary environments have noncompensatory weights, and the cues are uncorrelated. For example,(3) defines the following environment: Object Cue 1 Cue 2 Cue 3 Criterion A 0 0 0 0 B 0 0 1 1 C 0 1 0 2 D 0 1 1 3 E 1 0 0 4 F 1 0 1 5 G 1 1 0 6 H 1 1 1 7 Guttman environments, each of which has m objects given by The second class of environment comprises, each of which hasobjects given by For example, H Guttman (5) defines the following environment: Object Cue 1 Cue 2 Cue 3 Cue 4 Cue 5 Criterion A 0 0 0 0 1 0 B 0 0 0 1 1 1 C 0 0 1 1 1 2 D 0 1 1 1 1 3 E 1 1 1 1 1 4 In Guttman environments, all cues have validity 1.0 and are highly correlated with both other cues and the criterion. Binary and Guttman environments provide useful insights because they (a) elicit drastically different relative performances between take‐the‐best and alternative strategies that assess conditional dependencies between cues, and (b) are governed by a known underlying function, which allows us to perform a bias–variance decomposition of the error incurred by the different strategies.