Homo Heuristicus: Why Biased Minds Make Better Inferences

Polynomials of degree-1 and degree-2 lead to significant estimation bias because they lack the ability to capture the underlying cubic function h(x) and will therefore always differ from the underlying function.

“Polynomials of degree-1 and degree-2 lead to significant estimation bias because they lack the ability to capture the underlying cubic function h(x) and will therefore always differ from the underlying function.”

Higher degree polynomials suffer from increased variance due to their greater flexibility.

“The reason why this behavior is observed is that higher degree polynomials suffer from increased variance due to their greater flexibility.”

A degree-2 polynomial achieves a lower mean prediction error than a degree-10 polynomial.

“Finally, notice how a degree-2 polynomial achieves a lower mean prediction error than a degree-10 polynomial.”

Both high- and low-degree polynomials suffer from greater error than the best predicting polynomial model, which has degree-4.

“Both high-and low-degree polynomials suffer from greater error than the best predicting polynomial model, which has degree-4.”

The relationship between the degree of polynomial used and predictive accuracy is U-shaped.

“Here, the relationship between the degree of polynomial used and the resulting predictive accuracy is U-shaped.”

The higher the degree of the polynomial, the lower the error in fitting the observed data sample.

“The higher the degree of the polynomial, the lower the error in fitting the observed data sample.”

A degree-3 polynomial achieves the lowest mean prediction error on the problem with a degree-3 underlying function.

“As one would expect, a degree-3 polynomial achieves the lowest mean prediction error on this problem.”

All the models in Fig. 2 achieved a better fit to the data than take-the-best did.

“Indeed, all the models in Fig. 2 achieved a better fit to the data than take-the-best did.”

In the binary environment, take-the-best performs worse than its greedy counterpart.

“First, in the binary environment, take-the-best performs worse than its greedy counterpart.”

In the Guttman environment, take-the-best outperforms its greedy counterpart.

“Second, in the Guttman environment, take-the-best outperforms its greedy counterpart.”

Bias plays almost no role in explaining the difference in performance between the models.

“Bias plays almost no role in explaining the difference in performance between the models”

Both of these behaviors are driven by the variance component of error and the relative ability of the two strategies to keep variance within acceptable limits.

“Third, and perhaps most important, Fig. 5 reveals that both of these behaviors are driven by the variance component of error and the relative ability of the two strategies to keep variance within acceptable limits.”

A reanalysis of Richter and Späth (2006, Experiment 3) at the individual level reveals that even in the presence of conflicting information, the majority of participants still follow the recognition heuristic.

“of Richter and Spa ¨th (2006, Experiment 3) at the individual level reveals that even in the presence of conflicting information (bottom panel), the majority of participants still follow the recognition heuristic.”

• Also stated in: § 6. Homo heuristicus · plain

  “A reanalysis ofRichter and Spa ¨th (2006, Experiment 3) at the individual level reveals that even in the presence of conflicting information (bottom panel), the majority of participants still follow the recognition heuristic.”

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Less-is-more effects exist: more information or computation can decrease accuracy.

“Less-is-more effects: More information or computation can decrease accuracy; therefore, minds rely on simple heuristics in order to be more accurate than strategies that use more information and time.”

Less information, computation, and time can improve accuracy.

“less information, computation, and time can in fact improve accuracy.”

An analysis of 20 data sets showed that the result in Fig. 2 (take-the-best exceeding rivals under cross-validation) is the rule rather than the exception.

“An analysis of 20 data sets showed that the result in Fig. 2 is the rule rather than the exception (Brighton, 2006).”

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The accuracy-effort trade-off does not generally hold.

“Thus, the accuracy-effort trade-off does not generally hold; there are situations where one attains higher accuracy with less effort.”

In 20 studies where both tallying and multiple regression were tested by cross-validation, tallying achieved a higher predictive accuracy than multiple regression, averaged across all data sets.

“Averaged across all data sets, tallying achieved a higher predictive accuracy than multiple regression (Fig. 1).”

• cites Czerlinski, Gigerenzer, and Goldstein (1999)Not checked yet

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Baseball outfielders rely on the gaze heuristic: fix gaze on the ball, start running, and adjust running speed so that the angle of gaze remains constant.

“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).”

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The rationality of heuristics is ecological, not logical.

“The rationality of heuristics is therefore ecological, not logical.”

Nests half the area of others yielded reencounter frequencies 1.96 times greater.

“Nests half the area of others yielded reencounter frequencies 1.96 times greater (Mugford, Mallon, & Franks, 2001).”

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Chater et al.'s method of fitting the models on the learning sample and then testing these models on the entire sample (including the learning sample) favored those models that overfit the data, especially at high sample sizes.

“Yet, as Brighton (2006) showed in a reanalysis, Chater et al.'s method of fitting the models on the learning sample and then testing these models on the entire sample (including the learning sample) favored those models that overfit the data, especially at high sample sizes.”

• cites Brighton, 2006Not checked yet

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The answer to why and when heuristics are more accurate than strategies that use more information and computation is in the match between a heuristic and its environment.

“The answer is not in the heuristic alone, but in the match between a heuristic and its environment.”

The discovery of less-is-more effects forces us to reassess our normative ideals of rationality.

“Most important, it has become clear that the discovery of less-is-more effects forces us to reassess our normative ideals of rationality.”

The success of take-the-best seems to be due to the fact that it ignores dependencies between cues, which is adaptive when observations are sparse.

“In short, the success of take-the-best seems to be due to the fact that it ignores dependencies between cues in what turns out to be an adaptive processing policy when observations are sparse.”

Ants use a pheromone trail heuristic to measure the area of a candidate nest cavity.

“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.”

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The conditions under which the recognition heuristic leads to a less-is-more effect have been derived analytically.

“The conditions under which the recognition heuristic (discussed below) leads to a less-is-more effect have been derived analytically (Goldstein & Gigerenzer, 2002)”

• cites Goldstein & Gigerenzer, 2002Not checked yet

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The conditions under which tallying succeeds-low predictability of a criterion, small sample sizes relative to the number of available cues, and dependency between cues-are not infrequent in natural environments.

“Note that the conditions under which tallying succeeds-low predictability of a criterion, small sample sizes relative to the number of available cues, and dependency between cues--are not infrequent in natural environments.”

Ordering cues by conditional validity is a costly operation, which requires recomputing the predictive value of cues against multiple reference classes of observations.

“Ordering cues by conditional validity is a costly operation, which requires recomputing the predictive value of cues against multiple reference classes of observations.”

Peahens investigate only three or four peacocks and choose the one with the largest number of eyespots.

“she investigates only three or four, and chooses the one with the largest number of eyespots (Petrie & Halliday, 1994).”

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The existence of less-is-more effects shows that there is more to heuristics than the accuracy-effort trade-off: the mind can use less information and computation or take less time and nevertheless achieve better performance.

“The existence of these effects shows that there is more to heuristics than the accuracy-effort trade-off: The mind can use less information and computation or take less time and nevertheless achieve better performance.”

When one alters the search rule of take-the-best by ordering cues by conditional validity, performance drops to the level of the more resource-intensive algorithms.

“In fact, when one alters the search rule of take-the-best by carrying out the more resource-intensive process of ordering cues by conditional validity, performance drops to the level of the more resource-intensive algorithms (Fig. 2, bottom left).”

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Less-is-more effects challenge the classical definition of rational decision-making as the process of weighting and adding all information.

“Less-is-more effects are a second justification with normative consequences: They challenge the classical definition of rational decision-making as the process of weighting and adding all information.”

When accidental patterns are used to make predictions, these predictions are likely to be inaccurate.

“When accidental patterns are used to make predictions, these predictions are likely to be inaccurate.”

To control variance, one must abandon the ideal of general-purpose inductive inference and instead consider specialization.

“To control variance, one must abandon the ideal of general-purpose inductive inference and instead consider, to one degree or another, specialization (Geman et al., 1992).”

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We cannot remain agnostic and do both unless we are willing to make a bet on what patterns will actually occur.

“We cannot remain agnostic and do both unless we are willing to make a bet on what patterns will actually occur.”

Prediction error can be decomposed into the sum of three components: bias squared, variance, and noise.

“Total error ¼ ðbiasÞ 2 þ variance þ noise:”

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• cites Bishop, 1995 sourceNot checked yet

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• cites Hastie et al., 2001Not checked yet

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The conditions in which a beneficial degree of forgetting improves accuracy in inference have been derived analytically.

“as have the conditions in which a beneficial degree of forgetting improves accuracy in inference (Schooler & Hertwig, 2005).”

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To achieve low prediction error on a broad class of problems, a model must accommodate a rich class of patterns in order to ensure low bias.

“To achieve low prediction error on a broad class of problems, a model must accommodate a rich class of patterns in order to ensure low bias.”

General purpose models tend to be poor predictors of the future when data are sparse.

“This is why ''general purpose'' models tend to be poor predictors of the future when data are sparse (Geman et al., 1992).”

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Diversity in the class of patterns that the model can accommodate is likely to come at a price of an increase in variance.

“The price is an increase in variance, as the model will have a greater flexibility”

When analyzing the success of heuristics, we often find that they avoid overfitting the observations.

“As we have shown, when analyzing the success of heuristics, we often find that they avoid overfitting the observations.”

An algorithm's susceptibility to bias and variance will always depend on the underlying function and on how many observations of this function are available.

“An algorithm's susceptibility to bias and variance will always depend on the underlying function and on how many observations of this function are available.”

A heuristic's accuracy is always relative to the structure of the environment.

“Its accuracy is always relative to the structure of the environment.”

Studies on language acquisition indicate that there are sensitive phases in which a reduced memory and simpler input ('baby talk') speeds up language acquisition.

“Studies on language acquisition indicate that there are sensitive phases in which a reduced memory and simpler input (''baby talk'') speeds up language acquisition (Elman, 1993;Newport, 1990)”

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• cites Newport, 1990Not checked yet

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The more flexible the model, the more likely it is to capture not only the underlying pattern but unsystematic patterns such as noise.

“The more flexible the model, the more likely it is to capture not only the underlying pattern but unsystematic patterns such as noise.”

Human performance is often characterized as optimal in generalizing from few observations.

“cognitive science is increasingly stressing the senses in which the cognitive system performs remarkably well when generalizing from few observations, so much so that human performance is often characterized as optimal (e.g., Griffiths & Tenenbaum, 2006;Oaksford & Chater, 1998).”

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• cites Oaksford & Chater, 1998Not checked yet

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Experiments with experienced handball players indicate that they make better decisions with less time.

“experiments with experienced handball players indicate that they make better decisions with less time (Johnson & Raab, 2003)”

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An unbiased algorithm may suffer from high variance because the mean function may be precisely the underlying function, but the individual functions may suffer from excess variance and hence high error.

“Notice that an unbiased algorithm may suffer from high variance because the mean function may be precisely the underlying function, but the individual functions may suffer from excess variance and hence high error.”

A biased induction algorithm can predict more accurately than an unbiased one.

“there are many examples of how a biased induction algorithm can predict more accurately than an unbiased one (Hastie et al., 2001).”

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The ability of the cognitive system to make accurate predictions despite sparse exposure to the environment strongly indicates that the variance component of error is successfully being kept within acceptable limits.

“From the perspective of the bias-variance dilemma, the ability of the cognitive system to make accurate predictions despite sparse exposure to the environment strongly indicates that the variance component of error is successfully being kept within acceptable limits.”

Expert golfers (but not novices) do better when they have only 3 s to putt than when they can take all time they want.

“expert golfers (but not novices) do better when they have only 3 s to putt than when they can take all time they want (Beilock, Bertenthal, McCoy, & Carr, 2004;Beilock, Carr, MacMahon, & Starkes, 2002).”

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• cites Beilock, Carr, MacMahon, & Starkes, 2002Not checked yet

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A heuristic is not inherently good or bad, or accurate or inaccurate.

“This is why a heuristic is not inherently good or bad, or accurate or inaccurate, as is sometimes believed.”

A biased model can lead to more accurate predictions than an unbiased model.

“This is an example of how a biased model can lead to more accurate predictions than an unbiased model.”

The variance component of prediction error is essential to understanding why a less-is-more effect in heuristic inference can often be observed.

“The variance component of prediction error will prove essential to understanding why a less-is-more effect in heuristic inference can often be observed.”

Our cognitive systems are confronted with the bias-variance dilemma whenever they attempt to make inferences about the world.

“Our cognitive systems are confronted with the bias-variance dilemma whenever they attempt to make inferences about the world.”

The basic flaw in the original availability research was to introduce a label after data were observed, rather than formulate a heuristic as a computational model that allows predictions to be expressed in a testable way.

“The basic flaw in the original research was to introduce a label after data were observed, rather than formulate a heuristic as a computational model that allows predictions to be expressed in a testable way.”

• AssumptionRests on an assumption: The five consonants K, L, N, R, and V are an atypical sample because all five occur more often in the third position, whereas the majority of consonants occur more frequently in the first position.
• AssumptionRests on an assumption: There has been no successful replication of Tversky and Kahneman's (1973) availability study in the literature.

Sedlmeier, Hertwig, and Gigerenzer (1998) found that neither measure of availability could predict people's actual frequency judgments.

“The result was that neither measure of availability could predict people's actual frequency judgments.”

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The performance of the greedy version of take-the-best provides a good proxy for the behavior of a number of alternative models of inductive inference.

“Consequently, the performance of the greedy version of take-the-best provides a good proxy for the behavior of a number of alternative models of inductive inference.”

Very similar findings hold when the minimum description length principle is used as a model selection criterion.

“For example, very similar findings hold when the minimum description length principle is used as a model selection criterion (Brighton, 2006).”

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Within cognitive science, there has been no systematic theory of heuristics.

“Similarly, within cognitive science, there has been no such theory (although see Payne et al., 1993).”

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Model comparisons in natural environments show that this bet is often a good one.

“Model comparisons in natural environments show that this bet is often a good one.”

Noncompensatory environments are one example of a class of environments for which analytic results show that take-the-best is unbiased and likely to perform well.

“Noncompensatory environments are one example of a class of environments for which we have analytic results showing that take-the-best is unbiased and likely to perform well.”

Take-the-best bets on the fact that ignoring dependencies between cues is likely to result in low variance.

“In short, this comparison tells us that take-the-best bets on the fact that ignoring dependencies between cues is likely to result in low variance.”

The bet can also fail, even when take-the-best has zero bias.

“But as this comparison has revealed, the bet can also fail, even when takethe-best has zero bias.”

The bias-variance dilemma shows formally why a mind can be better off with an adaptive toolbox of biased, specialized heuristics.

“Put simply, the bias-variance dilemma shows formally why a mind can be better off with an adaptive toolbox of biased, specialized heuristics.”

Saying that a heuristic works because it avoids overfitting the data is only a shorthand explanation for what is often a more complex interaction between the heuristic, the environment, and the sample size.

“Saying that a heuristic works because it avoids overfitting the data is only a shorthand explanation for what is often a more complex interaction between the heuristic, the environment, and the sample size.”

A single, general-purpose tool with many adjustable parameters is likely to be unstable and to incur greater prediction error as a result of high variance.

“A single, general-purpose tool with many adjustable parameters is likely to be unstable and to incur greater prediction error as a result of high variance.”

The priority heuristic, a one-good-reason heuristic with no free parameters, has been shown to imply several major violations of expected utility theory simultaneously, including the Allais paradox and the fourfold pattern.

“The priority heuristic, a one-good-reason heuristic with no free parameters (Brandsta ¨tter, Gigerenzer, & Hertwig, 2008;Brandsta ¨tter et al., 2006) that has similar building blocks to take-the-best, has been shown to imply (not just have parameter sets that are consistent with) several of the major violations simultaneously, including the Allais paradox and the fourfold pattern (Katsikopoulos &”

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• cites Katsikopoulos & Gigerenzer, 2008Not checked yet

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The relative ability of two algorithms to avoid pathologies such as overfitting or excess complexity will always depend on the amount of data available.

“because the relative ability of two algorithms to avoid these pathologies will always depend on the amount of data available.”

In Sedlmeier et al. (1998), the two definitions of availability showed little correlation with one another.

“Moreover, the two definitions showed little correlation with one another.”

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There was no independent measure of availability in Tversky and Kahneman's (1973) study.

“there was no independent measure of availability in this study”

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The variance component of error is always an interaction between characteristics of the inference strategy, the structure of the environment, and the number of observations available.

“Secondly, the variance component of error is always an interaction between characteristics of the inference strategy, the structure of the environment, and the number of observations available.”

The performance of a heuristic in an environment is not reflected by a single number such as predictive accuracy, but by a learning curve revealing how bias and variance change as more observations become available.

“This is why the performance of heuristic in an environment is not reflected by a single number such as predictive accuracy, but by a learning curve revealing how bias and variance change as more observations become available (Perlich, Provost, & Simonoff, 2003).”

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Proving that another strategy achieves a better fit than take-the-best is something quite different to proving that the strategy also achieves a higher predictive accuracy.

“This result illustrates that proving that another strategy achieves a better fit than take-the-best is something quite different to proving that the strategy also achieves a higher predictive accuracy.”

In Tversky and Kahneman's (1973) study, two-thirds of participants judged the first position as being more likely for a majority of the five consonants.

“Two-thirds of participants judged the first position as being more likely for a majority of the five consonants.”

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If a heuristic like take-the-best is to outperform an alternative method, it must do so by incurring less variance.

“Consequently, if a heuristic like take-the-best is to outperform an alternative method, it must do so by incurring less variance.”

Analytic results detailing when take-the-best is unbiased will not necessarily point to the cases in which take-the-best performs well.

“This result illustrates that analytic results detailing when take-the-best is unbiased will not necessarily point to the cases in which take-the-best performs well.”

From the perspective of bias, take-the-best offers no advantage over the alternative methods considered, because practically all models of inductive inference are capable of reproducing any response pattern that take-the-best can.

“First, from the perspective of bias, take-the-best offers no advantage over the alternative methods we have considered, because practically all models of inductive inference are capable of reproducing any response pattern that take-the-best can.”

Adopting an alternative model selection criterion will not change the fact that the degree to which an algorithm is overly sensitive to the contents of the samples it learns from will depend on the size of the sample available.

“Adopting an alternative model selection criterion will not change the fact that the degree to which an algorithm is overly sensitive to the contents of the samples it learns from will depend on the size of the sample available.”

The less-is-more effect demonstrated in Fig. 2 can also be explained by the relative ability of the models to control variance.

“and the less-is-more effect we demonstrated in Fig. 2 can also be explained by the relative ability of the models to control variance.”

Because the learning curves of two strategies can cross, the superiority of one process over another will depend on the size of the training sample.

“Because the learning curves of two strategies-such as the pairs of curves in Fig. 2-can cross, the superiority of one process over another will depend on the size of the training sample.”

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.

“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.”

Payne et al. (1993) demonstrated that people tend to select heuristics in an adaptive way.

“The work by Payne et al. (1993) additionally demonstrated that people tend to select the heuristics in an adaptive way.”

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Rieskamp and Otto (2006) and Bröder (2003) reported that people adaptively select take-the-best when the environment has the property that cue weights vary widely.

“Rieskamp andOtto (2006) andBro ¨der (2003) reported that people adaptively select take-the-best when the environment has this property.”

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• cites Bro ¨der (2003)Not checked yet

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For the red deer stag, the step-by-step contest heuristic is like take-the-best, but the search rule differs: the order of cues is determined by the cue that is first accessible, not by the most valid cue.

“This step-by-step heuristic is like takethe-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.”

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Newell et al.'s results were disregarded by counting only subjects consistent with predictions in at least 90% of cases, so that only one-third (33%) behaved completely consistently with take-the-best's rules.

“Yet these results were disregarded by counting only those subjects who were consistent with the predictions in at least 90% of the cases, so that ''only one-third (33%) behaved in a manner completely consistent with TTB's search, stopping, and decision rules'' (p.82).”

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The recognition 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.

“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 & Bro ¨der, 2007;Serwe & Frings, 2006).”

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The confirmation stopping rule works well when the decision maker knows little about cue validity and cue costs are low.

“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).”

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For the male deer, the adapted search rule is to search through cues in order of their environmental accessibility.

“Thus, for the male deer, the adapted search rule is: Search rule: Search through cues in order of their environmental accessibility.”

In a new task where the individual lacks experience to order cues, it is advantageous to adjust the stopping rule and decision rule to stop as soon as two cues point to the same object and infer that object has higher criterion value.

“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.”

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By adapting the building blocks of heuristics, organisms can react to new tasks and changing environments.

“By adapting the building blocks of heuristics, organisms can react to new tasks and changing environments.”

Memory constrains the choice set of heuristics and thereby creates specific cognitive niches for different heuristics.

“The first is that memory constrains the choice set of heuristics and thereby creates specific cognitive niches for different heuristics (Marewski & Schooler, unpublished data).”

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Volz et al. (2006) reported specific neural activity that corresponded to the two processes of recognition and evaluation in the use of the recognition heuristic.

“Using functional magnetic resonance imaging (fMRI), Volz et al. (2006) reported specific neural activity that corresponded to these two processes.”

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Memory selects heuristics in a way that makes it easier and faster to apply a heuristic when it is likely to yield accurate decisions.

“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.”

To adjust to a ball at the beginning of its trajectory, a player does not need a new heuristic, but only to adapt the third building block.

“To adjust to this new situation, a player does not need a new heuristic, but only to adapt the third building block.”

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.

“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.”

• cites Marewski, Gaissmaier, Schooler, Goldstein, & Gigerenzer, unpublished dataNot checked yet

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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.

“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.”

It is not possible to assert that there is clear evidence for an alternative noncompensatory model that has not even been formulated and tested.

“Likewise, it is not possible to assert that there is clear evidence for an alternative noncompensatory model that has not even been formulated and tested.”

It is impossible to infer from means alone what proportion of individuals follow the recognition heuristic.

“It is impossible to infer from means alone what proportion of individuals follow the recognition heuristic.”

Evolution has created something very close to a perfect memory.

“In fact, evolution has created something very close.”

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To build a mind with zero bias assumes that one knows the true state of the world and the representations needed to model it.

“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.”

• AssumptionThe authors state this as an assumption: To build a mind with zero bias assumes that one knows the true state of the world and the representations needed to model it.

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.

“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.”

Design 3 works well in a world where inferences have to be made from small samples, and where the future may change in unforeseen ways.

“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).”

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Each inference tool has a bias that can be offset by a greater reduction in variance.

“Each has a bias that can be offset by a greater reduction in variance.”

Homo heuristicus can rely on heuristics because they are accurate, not because they require less effort at the cost of some accuracy.

“Homo heuristicus can rely on heuristics because they are accurate, not because they require less effort at the cost of some accuracy.”

Because a mind with no bias must choose from an infinite space of representations, it is likely to require resource-intensive cognitive processing.

“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.”

A mind with an infinitely flexible system of abstract representations works best with large samples of observations and in a relatively stable world.

“Such a mind works best with large samples of observations and in a world that is relatively stable.”

In virtually every task, there are individual differences in strategies.

“Individual-level tests are essential because in virtually every task we find individual differences in strategies.”

Because the world is not absolutely predictable and fully observable, a perfect memory would be a waste of energy.

“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.”

• AssumptionRests on an assumption: The world is not absolutely predictable and fully observable.