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Cited by 3,504Decision-Making and Behavioral EconomicsClinical Reasoning and Diagnostic SkillsCognitive Science and Education Research

Reasoning the fast and frugal way: Models of bounded rationality.

Open access
Gigerenzer, Gerd, Goldstein, Daniel G.·1996·Psychological Review
DOI 10.1037/0033-295x.103.4.650
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Abstract

Humans and animals make inferences about the world under limited time and knowledge. In contrast, many models of rational inference treat the mind as a Laplacean Demon, equipped with unlimited time, knowledge, and computational might. Following H. Simon's notion of satisfying, the authors have proposed a family of algorithms based on a simple psychological mechanism: one-reason decision making. These fast and frugal algorithms violate fundamental tenets of classical rationality: They neither look up nor integrate all information. By computer simulation, the authors held a competition between the satisfying "Take The Best" algorithm and various "rational" inference procedures (e.g., multiple regression). The Take The Best algorithm matched or outperformed all competitors in inferential speed and accuracy. This result in an existence proof that cognitive mechanisms capable of successful performance in the real world do not need to satisfy the classical norms of rational inference.

AI snapshot

Written from the paper’s full text.

TL;DR

The paper proposes fast and frugal satisficing algorithms, especially Take The Best, that make two-alternative inferences using one-reason decision making and limited search. In simulations on German city populations, Take The Best matched or outperformed “rational” integration algorithms in accuracy while searching far less information.

Key findings

  • Take The Best averaged .658 correct inferences across all limited-knowledge conditions, tied with weighted tallying (.658) and slightly above multiple regression (.657) and tallying (.656); it outperformed weighted linear (.623) and unit-weight linear (.621) models.
  • Take The Best searched an average of 5.9 cue values, less than a third of all available cue values; the Take The Last variant averaged 5.29 and the Minimalist variant 5.64.
  • The less-is-more effect appeared: maximum correct inferences were around 77% when individuals did not know all cue values, and learning more cities could eventually decrease accuracy.
  • The recognition principle was empirically supported: in a pilot study of 26 undergraduates, recognized German cities were larger than unrecognized ones in about 80% of comparisons, and participants followed the recognition principle in roughly 90% to 100% of cases in later tests.

Methods

  • Design: computer simulation competition between the satisficing Take The Best algorithm and five integration algorithms—tallying, weighted tallying, unit-weight linear model, weighted linear model, and multiple regression—on two-alternative city-population inference tasks.
  • Data/sample: the environment was all 83 German cities with more than 100,000 inhabitants after reunification, described by 9 binary ecological cues and 3,403 city pairs; limited knowledge was simulated across recognition of 0–83 cities and 0%, 10%, 20%, 50%, 75%, or 100% of cue values known, yielding 6 × 84 knowledge types with 500 simulated individuals each and about 858 million tests.
  • Analysis: performance was measured as proportion of correct inferences and amount of cue values searched; recognition validity was set to .8 from the pilot study, and multiple regression was given extra information, including actual city populations and missing-value substitutions.

Limitations

  • Stated: the authors cannot claim the integration algorithms are the best ones, nor know a priori which small variations will succeed; the key issue is the structure of environments in which particular algorithms thrive. They also state that for the simulation they assume the model is descriptively valid and do not provide further empirical evidence in this article.
  • Stated: Appendix transcription errors meant two starred minus values were in reality plus values; the authors say these should not have any noticeable effect on results and are irrelevant for the theoretical argument. They also note an earlier systematic testing order allowed Take The Last to exploit the sequence, so they reran the competition with randomly ordered city pairs.
  • Evident from the text: the simulations use one specific real-world environment—German city populations with 9 binary cues—so generalization to other inference tasks, cue structures, and domains is not established here; confidence judgments and social justification constraints are also explicitly not addressed in this article.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1037/0033-295x.103.4.650

Cites

83 of 83 references verified0 citation errors · 0 not checkable

Statistics

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Claims the paper makes

0 of 48 cited sources checked · 0 supported · 0 flagged

  • Findingown data

    In a computer simulation competition, the Take The Best algorithm matched or outperformed all competitor rational inference procedures (e.g., multiple regression) in inferential speed and accuracy.

    “By computer simulation, the authors held a competition between the satisficing”
    Quote in the paperSubstantial claim
  • Findingreasoning

    Using the 80% recognition validity half the time and guessing the other half, the organism scores 65% correct, which is the peak of the bottom curve.

    “Using the 80% effective recognition validity half of the time and guessing the other half of the time, the organism scores 65% correct, which is the peak of the bottom curve.”
    Quote in the paperSubstantial claim
  • Findingown data

    The maximum percentage of correct inferences by the Take The Best algorithm was around 77%.

    “The maximum percentage of correct inferences was around 77%.”
    Quote in the paperSubstantial claim
  • Findingnone given

    The redundancy of cues in the environment, as measured by pairwise correlations between cues, ranges between -.25 and .54, with an average absolute value of .19.

    “The redundancy of cues in the environment, as measured by pairwise correlations between cues, ranges between -.25 and .54,with an average absolute value of.19.”
    Quote in the paperNot a substantial claim
  • Findingown data

    The maximum Take The Best performance was not achieved when individuals knew all cue values of all cities, but rather when they knew less.

    “The striking result was that this maximum was not achieved when individuals knew all cue values of all cities, but rather when they knew less.”
    Quote in the paperSubstantial claim
  • May combine two claims. 43
  • Classified as probably not a substantial claim. 15
  • The quote only partly states this claim. 1

  • May combine two claims.

    Findingown data

    Take The Best drew as many correct inferences as any other algorithm, and more than some.

    “To our surprise, the Take The Best algorithm drew as many correct inferences as any of the other algorithms, and more than some.”
    • Also stated in: § Discussion · plain
      “The competition showed a surprising result: The Take The Best algorithm drew as many correct inferences about unknown features of a real-world environment as any of the integration algorithms, and more than some of them.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    All competitors do equally well with a complete lack of knowledge or with complete knowledge; they differ when knowledge is limited.

    “By looking at the lower-left and upper-right corners of Figure 6, one can see that all competitors do equally well with a complete lack of knowledge or with complete knowledge.They differ when knowledge is limited.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    Take The Best made as many correct inferences as weighted tallying and more than the other competitors.

    “The Take The Best algorithm made as many correct inferences as one of the competitors (weighted tallying) and more than the others.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingcitation

    Weighted tallying performed about as well as tallying, and the unit-weight linear model performed about as well as the weighted linear model.

    “Weighted tallying performed about as well as tallying, and the unit-weight linear model performed about as well as the weighted linear model--demonstrating that the previous finding that weights may be chosen in a fairly arbitrary manner, as long as they have the correct sign ( Dawes, 1979), is generalizable to tallying.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Dawes, 1979

      Not checked in the free run.

  • May combine two claims.

    Findingown data

    The average number of cue values searched across all simulated participants was 5.9, less than a third of all available cue values.

    “The average across all simulated participants was 5.9, which was less than a third of all available cue values.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingreasoning

    The PMM family of algorithms includes algorithms that do not violate transitivity, such as Take The Best, and algorithms that do, such as Minimalist.

    “The PMM family of algorithms includes algorithms that do not violate transitivity (such as the Take The Best algorithm), and others that do (e.g., the Minimalist algorithm).”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    Unlike integration algorithms, the curves for the variant algorithms are concave and the number of cues searched for is maximal when knowledge of cue values is lowest.

    “That is, unlike the integration algorithms, the curves are concave and the number of cues searched for is maximal when knowledge of cue values is lowest.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingnone given

    The Take The Last algorithm was faster but scored slightly less than the Minimalist algorithm.

    “The Take The Last algorithm was faster but scored slightly less than the Minimalist algorithm.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    In spite of intransitivities, the Minimalist algorithm's overall performance is only about 1 percentage point lower than that of the best transitive algorithms and a few percentage points better than some transitive algorithms.

    “Table 2 shows that in spite of these intransitivities, overall performance of the algorithm is only about 1 percentage point lower than that of the best transitive algorithms and a few percentage points better than some transitive algorithms.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingnone given

    The Take The Best algorithm does not need to estimate regression weights; it only needs to estimate a rank ordering of ecological validities.

    “The Take The Best algorithm does not need to estimate regression weights, it only needs to estimate a rank ordering of ecological validities.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The Take The Last algorithm exploited systematic testing and won the first round of the competition, outperforming other competitors by about 10 percentage points.

    “However, the Take The Last algorithm found out and won this first round of the competition, outperforming the other competitors by some 10 percentage points.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Findingnone given

    City populations are transitive.

    “and city populations are, in fact, transitive.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingnone given

    In the present environment, R^2 = .87, which is in the high range.

    “We have already seen that in the present environment, R z = .87,which is in the high rather than the moderate nr lnw range.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingreasoning

    Despite a high R^2 and only moderate-to-small correlation between cues, the satisficing algorithms performed quite successfully.

    “Thus, despite a high R 2 and only moderate-to-small correlation between cues, the satisficing algorithms performed quite successfully.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Findingnone given

    Regressing on the ranks of the cities does slightly better than regressing on the city populations.

    “An example: During the proof stage of this article we learned that regressing on the ranks of the cities does slightly better than regressing on the city populations.”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim.

    Premisecitation

    Simon argued that information-processing systems typically need to satisfice rather than optimize.

    “Simon (1956Simon ( , 1982) ) argued that information-processing systems typically need to satisfice rather than optimize.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Simon (1956, 1982)

      Not checked in the free run.

  • May combine two claims.

    Premisecitation

    PMM theory predicts when the hard-easy effect occurs, disappears, and inverts, and these predictions have been experimentally confirmed.

    “Similarly, the theory predicts when the hard-easy effect occurs, disappears, and invertswpredictions that have been experimentally confirmed by Hoffrage (1994) and by Juslin ( 1993 ).”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites Hoffrage, 1994

      Not checked in the free run.

    • cites Juslin, 1993

      Not checked in the free run.

  • May combine two claims.

    Interpretationown data

    The satisficing algorithms proposed perform inference from memory, use limited knowledge as input, and can profit from a lack of knowledge.

    “In contrast, the satisflcing algorithms proposed in this article perform inference from memory, they use limited knowledge as input, and as we will show, they can actually profit from a lack of knowledge.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: People rarely know all information on which an inference could be based; knowledge is limited.

  • May combine two claims.

    Interpretationreasoning

    The family of algorithms in PMM theory does not implement the classical ideal; search in memory is reduced to a minimum and there is no integration but rather substitution of pieces of information.

    “The family of algorithms in PMM theory does not implement this classical ideal.Search in memory for relevant information is reduced to a minimum, and there is no integration (but rather a substitution) of pieces of information.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning

    The Take The Best algorithm differs from standard linear tools for inference such as multiple regression, as well as from nonlinear neural networks that are compensatory in nature.

    “Thus, it differs from standard linear tools for inference such as multiple regression, as well as from nonlinear neural networks that are compensatory in nature.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation

    U.S. students make slightly more correct inferences about German city populations than about U.S. cities, and vice versa for German students.

    “For instance, U.S. students make slightly more correct inferences about German city populations ( about which they know little) than about U.S. cities, and vice versa for German students (Gigerenzer, 1993;Goldstein 1994;Goldstein & Gigerenzer, 1995;Hoffrage, 1994).”
    Quote in the paperSubstantial claim0 of 3 sources checked
    • cites Gigerenzer, 1993

      Not checked in the free run.

    • cites Goldstein 1994

      Not checked in the free run.

    • cites Goldstein & Gigerenzer, 1995

      Not checked in the free run.

  • May combine two claims.

    Interpretationreasoning

    The Take The Best algorithm stops search after the first discriminating cue is found, just as Simon's satisficing algorithm stops search after the first option that meets an aspiration level.

    “There is a close parallel with Simon's concept of”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation

    The less-is-more effect postulates conditions under which people with little knowledge make better inferences than those who know more, and this prediction has been experimentally confirmed.

    “Among the evidence for the empirical validity of the Take-The-Best algorithm are the tests of a bold prediction, the less-is-more effect, which postulates conditions under which people with little knowledge make better inferences than those who know more.This surprising prediction has been experimentally confirmed.”
    Quote in the paperSubstantial claim0 of 3 sources checked
    • cites Gigerenzer, 1993

      Not checked in the free run.

    • cites Goldstein 1994

      Not checked in the free run.

    • cites Hoffrage, 1994

      Not checked in the free run.

  • May combine two claims.

    Premisecitation

    The unit-weight linear model is a special case of the equal-weight linear model and has been advocated as a good approximation of weighted linear models.

    “The unit-weight linear model is a special case of the equalweight linear model (Huber, 1989) and has been advocated as a good approximation of weighted linear models (Dawes, 1979;Einhorn & Hogarth, 1975).”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites Huber, 1989

      Not checked in the free run.

    • cites Dawes, 1979

      Not checked in the free run.

    • cites Einhorn & Hogarth, 1975

      Not checked in the free run.

  • May combine two claims. The quote only partly states this claim.

    Interpretationreasoning

    Because Take The Best was fastest and made as many correct inferences as weighted tallying and more than others, the authors judged it the highest performing overall.

    “Because it was also the fastest, we judged the competition goes to the Take The Best algorithm as the highest performing, overall.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation

    Multiple regression creates weights that reflect covariances between predictors or cues and is commonly seen as an optimal way to integrate information into an estimate.

    “Multiple regression creates weights that reflect the covariances between predictors or cues and is commonly seen as an “optimal” way to integrate various pieces of information into an estimate (e.g., Brunswik, 1955;Hammond, 1966).”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites Brunswik, 1955

      Not checked in the free run.

    • cites Hammond, 1966

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    The weighted linear model is often viewed as an optimal rule for preferential choice under the idealization of independent dimensions or cues.

    “The weighted linear model (or some variant of it) is often viewed as an optimal rule for preferential choice, under the idealization of independent dimensions or cues (e.g., Keeney & Raiffa, 1993;Payne et al., 1993).”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites Keeney & Raiffa, 1993

      Not checked in the free run.

    • cites Payne et al., 1993

      Not checked in the free run.

  • May combine two claims.

    Interpretationreasoning

    Take The Best is already faster than any integration algorithm because it performs only a limited search and does not need to compute weighted sums of cue values.

    “The Take The Best algorithm is already faster than any of the integration algorithms, because it performs only a limited search and does not need to compute weighted sums of cue values.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationnone given

    The Minimalist algorithm needs neither information about the rank ordering of cue validities nor the discrimination history of the cues.

    “What we call the Minimalist algorithm needs neither information about the rank ordering of cue validities nor the discrimination history of the cues.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationown data

    The reason the Minimalist algorithm looks up fewer cue values than Take The Best is that cue validities and cue discrimination rates are negatively correlated, so randomly chosen cues tend to have larger discrimination rates.

    “The reason why the Minimalist algorithm looks up fewer cue values than the Take The Best algorithm is that cue validities and cue discrimination rates are negatively correlated (Table 1 ); therefore, randomly chosen cues tend to have larger discrimination rates than cues chosen by cue validity.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Interpretationnone given

    The Minimalist algorithm picks cues in a random order.

    “In its ignorance, the algorithm picks cues in a random order.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationnone given

    The Take The Last algorithm does not need a rank order of cues according to their validities; it only needs to know the direction in which a cue points.

    “This algorithm does not need a rank order of cues according to their validities; all that needs to be known is the direction in which a cue points.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning

    The classical norms may be sufficient but are not necessary for good inference in real environments.

    “The classical norms may be sufficient but are not necessary for good inference in real environments.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationnone given

    The record of last-used cues can be built independently of any knowledge about the structure of an environment and neither needs nor uses feedback about whether inferences are right or wrong.

    “Note that such a record can be built up independently of any knowledge about the structure of an environment and neither needs, nor uses, any feedback about whether inferences are right or wrong.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning

    Because tallying algorithms ignore negative information, the tally for an unrecognized object is always 0 and is always smaller than the tally for a recognized object, which is at least 1.

    “Because tallying algorithms ignore negative information, the tally for an unrecognized object is always 0 and, thus, is always smaller than the tally for a recognized object, which is at least 1 (for tallying, or .8 for weighted tallying, due to the positive value on the recognition cue).”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisenone given

    In the environment, there are more negative cue values than positive ones, and most cities have more negative cue values than positive ones.

    “In the environment, there are more negative cue values than positive ones (see the Appendix), and most cities have more negative cue values than positive ones.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Study design and conductnone given

    The authors reran the whole competition with randomly ordered pairs of cities.

    “We learned our lesson and reran the whole competition with randomly ordered of pairs of cities.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

    Interpretationnone given

    The Minimalist algorithm does not necessarily speed up search, but it tries to get by with even less knowledge than any other algorithm.

    “The Minimalist algorithm does not necessarily speed up search, but it tries to get by with even less knowledge than any other algorithm.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S4 (based).

    Premisenone given

    This division of labor is the basis on which much of the current research on judgment under uncertainty is built.

    “This division of labor is, in a nutshell, the basis on which much of the current research on judgment under uncertainty is built.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning

    If experts' vicarious functioning works according to the PMM algorithms, then they are correct in saying they use many predictors, but the decision is made by only one at any time.

    “If experts' vicarious functioning works according to the PMM algorithms, then they are correct in saying that they use many predictors, but the decision is made by only one at any time.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationown data

    High cue redundancy seems sufficient but is not necessary for the successful performance of the satisficing algorithms.

    “High cue redundancy, thus, does seem sufficient but is not neccomparing objects a, b, and c.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S2 (checkable).

    Premisecitation

    Some choices, such as who to treat first in an emergency room, need to be justified.

    “For instance, some choices (e.g., who to treat first in an emergency room) need to be justified (Tetlock, 1992 ).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Tetlock, 1992

      Not checked in the free run.

  • May combine two claims.

    Interpretationnone given

    Missing knowledge is necessary for intransitivities to occur; if all cue values are known, no intransitive inferences can possibly result.

    “Note that missing knowledge is necessary for intransitivities to occur.If all cue values are known, no intransitive inferences can possibly result.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationreasoning

    The traditional proposal for understanding the structure of environments in terms of ecological validities defined as linear correlations may not be adequate, as the power of nonlinear satisficing algorithms suggests.

    “The traditional proposal for understanding the structure of environments in terms of ecological validities defined as linear correlations (Brunswik, 1955 ) may not be adequate, as the power of the nonlinear satisficing algorithms suggests.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Brunswik, 1955

      Not checked in the free run.

  • Classified as probably not a substantial claim. May combine two claims.

    Premisenone given

    Since the nineteenth century, rational inference is commonly reduced to logic and probability theory, and psychological explanations are called on when things go wrong.

    “Since then, rational inference is commonly reduced to logic and probability theory, and psychological explanations are called on when things go wrong.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation

    Brunswik's proposal to model adaptive process by linear multiple regression has inspired a long tradition of neo-Brunswikian research, although empirical evidence for mental multiple regression is still controversial.

    “His proposal to model this adaptive process by linear multiple regression has inspired a long tradition of neo-Brunswikian research (B.Brehmer, 1994;Hammond, 1990), although the empirical evidence for mental multiple regression is still controversial (e.g., A. Brehmer & B. Brehmer, 1988).”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites B. Brehmer, 1994

      Not checked in the free run.

    • cites Hammond, 1990

      Not checked in the free run.

    • cites A. Brehmer & B. Brehmer, 1988

      Not checked in the free run.

  • Classified as probably not a substantial claim. May combine two claims.

    Premisecitation

    It has been reported that teachers, physicians, and other professionals claim to use seven or so criteria to make judgments, but experimental tests showed they often used only one criterion.

    “It has been reported sometimes that teachers, physicians, and other professionals claim that they use seven or so criteria to make judgments (e.g., when grading papers or making a differential diagnosis) but that experimental tests showed that they in fact often used only one criterion (Shepard, 1967).”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Shepard, 1967

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    Brunswik labeled this ability vicarious functioning and saw it as the most fundamental principle of a science of perception and cognition.

    “Brunswik labeled this ability vicarious functioning, in which he saw the most fundamental principle of a science of perception and cognition.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Brunswik (1955)

      Not checked in the free run.

  • May combine two claims.

    Interpretationnone given

    In real time and real environments, the possibility that an algorithm can make intransitive inferences does not mean it will make them all the time or that this feature will significantly hurt its accuracy.

    “In real time and real environments, the possibility that an algorithm (e.g., the Minimalist algorithm) can make intransitive inferences does not mean that it will make them all the time or that this feature of the algorithm will significantly hurt its accuracy.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationnone given

    Cognitive algorithms need to meet more important constraints than internal consistency: they need to be psychologically plausible, fast, and make accurate inferences in real-world environments.

    “Cognitive algorithms, however, need to meet more important constraints than internal consistency: (a) They need to be psychologically plausible, (b) they need to be fast, and (c) they need to make accurate inferences in real-world environments.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Einhorn and Hogarth suggested that unit-weight models can be expected to perform approximately as well as proper linear models when R^2 is moderate or low (around .5 or smaller) and predictors are correlated.

    “Einhorn and Hogarth (1975) suggested that unit-weight models can be expected to perform approximately as well as proper linear models when (a) R 2 from the regression model is in the moderate or low range (around .5 or smaller) and (b) predictors (cues) are correlated.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Einhorn and Hogarth (1975)

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

    Study design and conductnone given

    The transcription errors in two cue values do not affect the rank order of cue validities, should not have any noticeable effect on the results, and are irrelevant for the theoretical argument.

    “The two starred minus values are, in reality, plus values.Because of transcription errors, we ran all simulations with these two minus values.These do not affect the rank order of cue validities, should not have any noticeable effect on the results, and are irrelevant for our theoretical argument.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Study design and conductnone given

    The integration algorithms cannot be claimed to be the best ones, and it cannot be known a priori which small variations will succeed in the real-world environment.

    “We cannot claim that these integration algorithms are the best ones, nor can we know a priori which small variations will succeed in our bumpy real-world environment.”
    Quote in the paperSubstantial claim
53 of 53

  • The paper relies on this without support.

    People rarely know all information on which an inference could be based; knowledge is limited.

    “People rarely know all information on which an inference could be based, that is, knowledge is limited.”

  • The authors state this as an assumption.

    The Take The Best model is descriptively valid.

    “For the moment, we assume that the model is descriptively valid and investigate how accurate this satisficing algorithm is in drawing inferences about unknown aspects of a real-world environment.”

  • The paper relies on this without support.

    In many real-world situations, there are multiple pieces of information that are not independent but redundant.

    “In many real-world situations, however, there are multiple pieces of information, which are not independent, but redundant.”

  • The authors state this as an assumption.

    The Take The Best algorithm assumes a subjective rank order of cues according to their validities.

    “The Take The Best algorithm assumes a subjective rank order of cues according to their validities (as in Figure 1 ).”

  • The paper relies on this without support.

    The city population environment used in the simulations is representative of real-world environments for evaluating inference algorithms.

    “The competition showed a surprising result: The Take The Best algorithm drew as many correct inferences about unknown features of a real-world environment as any of the integration algorithms, and more than some of them.”

  • The paper relies on this without support.

    The simulated individuals' recognition and cue knowledge states are representative of human limited knowledge.

    “We ran the competition for all states of limited knowledge shown in Figure 4.”

  • The authors state this as an assumption.

    The various components of an alternative add up independently to its overall estimate or utility.

    “The assumption is that the various components of an alternative add up independently to its overall estimate or utility.”

  • The paper relies on this without support.

    The German city population environment and the nine cues are representative of real-world inference environments.

    “in the present environment”

  • The paper relies on this without support.

    The PMM family of cognitive algorithms captures how humans make inferences.

    “The PMM family of cognitive algorithms provides precise models that attempt to do so.”
9 of 9

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • Heuristics shaped by evolutionary pressures often perform remarkably well in natural settings despite their departure from statistical optimality.

    “These heuristics, shaped by evolutionary pressures, often perform remarkably well in natural settings despite their departure from statistical optimality (Cosmides and Tooby 1996; Gigerenzer and Goldstein 1996; Gigerenzer and Brighton 2009; Gigerenzer 2020; Marewski and Schooler 2011).”

    From The myth of the Bayesian brain (2025) · cites this paper as Gigerenzer and Goldstein 1996

    The Discussion reports that Take The Best performed as accurately as competing algorithms in a real-world environment despite violating classical norms of rational inference. The paper also says minds should be understood relative to the environments in which they evolved, but it does not establish that evolutionary pressures shaped the particular heuristics tested. The indexed passages provide section labels but no page numbers. (LLM, conf=0.84)

    Experimental — accuracy not yet measured

  • Natural selection tends to favor strategies that work well enough under real-world constraints, including limited time, energy, and computational capacity.

    “Natural selection tends to favor strategies that work well enough under real-world constraints, including limited time, energy, and computational capacity.”

    From The myth of the Bayesian brain (2025) · cites this paper as Gigerenzer and Goldstein 1996

    The Abstract and Discussion (page numbers unavailable) report that fast, simple strategies can perform well in real-world inference despite limits on time, knowledge, and computational power. The section “Can Satisficing Algorithms Get by With Even Less” also calls accuracy under limited knowledge adaptive. These passages do not establish the claim that natural selection favors such strategies or address limited energy. (LLM, conf=0.84)

    Experimental — accuracy not yet measured

  • This rational-optimal tradition aligns with longstanding philosophical and scientific aspirations to discover underlying rationality in human thought, extending back to the Enlightenment ideal.

    “This aligns with longstanding philosophical and scientific aspirations to discover underlying rationality in human thought, a project that extends back through the history of cognitive science to the Enlightenment ideal of human rationality (Gigerenzer and Goldstein 1996).”

    From The myth of the Bayesian brain (2025) · cites this paper as Gigerenzer and Goldstein 1996

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • Not every algorithm performed best with 100% of cue values known

    Minor

    The weighted linear model scored .627 with 20% of cue values known, but only .625 with 100% known. Thus, the 100% condition was not the best-performing condition for every algorithm.

1 of 1

Cites

Flagged first, then by citations

Research works printed but not linked: 12

  1. Darwin, C. ( 1965 ). The expressions of the emotions in man and animal. Chicago: University of Chicago Press. (Original work published 1872)
  2. DiFonzo, N. (1994). Piggybacked syllogisms for investor behavior. Probabilistic mental modeling in rumor-based stock market trading. Unpublished doctoral dissertation, Temple University, Philadelphia.
  3. In G. Wright & P. Ayton (Eds.), Subjective probability (pp. 129- 161 ). New York: Wiley.
  4. Goldstein, D. G. (1994). The less-is-more effect in inference. Unpub- lished master's thesis, University of Chicago.
  5. Hammond, K. R., & Wascoe, N. E. (Eds.). (1980). Realizations of Brunswik's representative design: New directions for methodology of social and behavioral science. San Francisco: Jossey-Bass.
  6. Keeney, R. L., & Raiffa, H. (1993). Decisions with multiple objectives. Cambridge, England: Cambridge University Press.
  7. Klayman, J., & Ha, Y. (1987). Confrmation, disconfirmation, and in- formation in hypothesis testing. Psychological Review, 94. 211-228.
  8. Krebs, J. R., & Davies, N. B. (1987). An introduction to behavioral ecology (2nd ed.). Oxford: Blackwell.
  9. Legendre, G., Raymond, W., & Smolensky, P. (1993). Analytic typol- ogy of case marking and grammatical voice. Proceedings of the Berke- ley Linguistics Society, 19, 464-478.
  10. Shepard, R. N. (1967). On subjectively optimum selections among multi-attribute alternatives. In W. Edwards & A. Tversky (Eds.), De- cision making (pp. 257-283 ). Baltimore: Penguin Books.
  11. In N. J. Castellan (Ed.), Individual and group decision making (pp. 87-108).
  12. Stephens, D. W., & Krebs, J. R. (1986). Foraging theory Princeton, N J: Princeton University Press.

Cited by

Sorted by citations

Related

Authors
Gigerenzer, G., & Goldstein, D. G.
Affiliations
Max Planck Society (DE)
ORCID
Venue
Psychological Review
Publisher
American Psychological Association (APA)
Published
1996-10
Volume
103
Issue
4
Pages
650-669
ISSN
  • 0033-295X (ISSN-L)
  • 1939-1471
DOI
10.1037/0033-295x.103.4.650
OpenAlex
W2159071801
Semantic Scholar
fe6796eb3da1d31a2463e7fb9202879f7a9d0c6b
Cited by
3,504
References
83
Citations by year
2026: 112 · 2025: 151 · 2024: 137 · 2023: 112 · 2022: 123 · 2021: 159 · 2020: 152 · 2019: 255 · 2018: 151 · 2017: 153 · 2016: 184 · 2015: 165 · 2014: 152 · 2013: 149 · 2012: 168
FWCI
21.30
Type
journal article
Language
en
Open access
Licence
other-oa
Locations
  • Psychological Review (publishedVersion)
  • PubMed (publishedVersion)
  • Max Planck Digital Library (submittedVersion, other-oa)
  • Max Planck Institute for Plasma Physics (submittedVersion)
  • Max Planck Digital Library (submittedVersion)
  • MPG.PuRe (Max Planck Society) (submittedVersion)
  • MPG.PuRe (Max Planck Society) (submittedVersion, other-oa)
Topics
  • Social Sciences › Decision Sciences › General Decision Sciences › Decision-Making and Behavioral Economics
  • Health Sciences › Medicine › Family Practice › Clinical Reasoning and Diagnostic Skills
  • Life Sciences › Neuroscience › Cognitive Neuroscience › Cognitive Science and Education Research
Keywords
bounded rationality, fast and frugal heuristics, satisficing, rational inference, inference speed, decision-making, multiple regression comparison
MeSH terms
Algorithms, Animals, Computer Simulation, Cues, Decision Making, Humans, Problem Solving, Reaction Time, Social Environment

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-09.

Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-09.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

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