Naive and Yet Enlightened: From Natural Frequencies to Fast and Frugal Decision Trees

Martignon, Laura; Vitouch, Oliver; Takezawa, Masanori; Forster, Malcolm R.

doi:10.1002/047001332x.ch10

Cited by 80 publications

(44 citation statements)

References 7 publications

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“…Th is does not exclude the possibility that other representations also foster insight, specifi cally if they mimic the structure of natural frequencies and lead to the same computational facilitation (e.g., Gigerenzer, 2002). More generally, any numerical information can be represented in various forms, as Roman and Arabic numbers illustrate, but these are not neutral forms for the same content, because they actually facilitate certain computations and insights, and hinder others (Martignon, Vitouch, Takezawa, & Forster, 2003). As the physicist Richard Feynman remarked, diff erent representations of the same mathematical formula can evoke varied mental pictures and lead to new solutions (Feynman, 1967, p. 53).…”

Section: Resultsmentioning

confidence: 99%

Children can solve Bayesian problems: the role of representation in mental computation

2006

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Abstract. Can children reason the Bayesian way? We argue that the answer to this question depends on how numbers are represented, because a representation can do part of the computation. We test, for the fi rst time, whether Bayesian reasoning can be elicited in children by means of natural frequencies. We show that when information was presented to fourth, fi fth, and sixth graders in terms of probabilities, their ability to estimate the Bayesian posterior probability was zero. Yet when the same information was presented in natural frequencies, Bayesian reasoning showed a steady increase from fourth to sixth grade, reaching an average level of 19%, 39%, and 53%, respectively, in two studies. Sixth graders' performance with natural frequencies matched the performance of adults with probabilities. But this general increase was accompanied by striking individual diff erences. More than half of the sixth graders solved most or all problems, whereas one third could not solve a single one. An analysis of the children's responses provides evidence for the use of three non-Bayesian strategies. Th ese follow an overlapping wave model of development and continue to be observed in the minds of adults. More so than adults' probabilistic reasoning, children's reasoning depends on a proper representation of information.

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Section: Resultsmentioning

confidence: 99%

Children can solve Bayesian problems: the role of representation in mental computation

2006

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“…Focusing on mini-ultimatum games, in which the proposer chooses between two fixed income distributions for both players-for example, 3:5 versus 2:8-and the responder gets to accept or reject it, Fischbacher et al modeled people's choice in terms of fast and frugal decision trees. A fast and frugal tree is defined as a classification tree that allows for a classification at each level of the tree (Martignon, Vitouch, Takezawa, & Forster, 2003). A fast and frugal tree consists of the same building blocks as the take-thebest heuristic: ordered search, one-reason stopping rule, and decision making on the basis of one reason.…”

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confidence: 99%

Fast and Frugal Heuristics: Tools of Social Rationality

2009

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“…Additive prototype models compute a representative (average) member of each class and compare how far away each feature combination is from this prototype. Fast and Frugal trees reach between 39% and 61% classification accuracy if constructed by the max(val+,valÀ) and zigzag(val+,valÀ) tree construction methods (Martignon, Vitouch, Takezawa, & Forster, 2003), respectively, while in our task 100% accuracy is achievable.…”

Section: Environment 1: Deterministic Taskmentioning

confidence: 80%

Naïve and Robust: Class‐Conditional Independence in Human Classification Learning

2017

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Humans excel in categorization. Yet from a computational standpoint, learning a novel probabilistic classification task involves severe computational challenges. The present paper investigates one way to address these challenges: assuming class-conditional independence of features. This feature independence assumption simplifies the inference problem, allows for informed inferences about novel feature combinations, and performs robustly across different statistical environments. We designed a new Bayesian classification learning model (the dependence-independence structure and category learning model, DISC-LM) that incorporates varying degrees of prior belief in class-conditional independence, learns whether or not independence holds, and adapts its behavior accordingly. Theoretical results from two simulation studies demonstrate that classification behavior can appear to start simple, yet adapt effectively to unexpected task structures. Two experiments-designed using optimal experimental design principles-were conducted with human learners. Classification decisions of the majority of participants were best accounted for by a version of the model with very high initial prior belief in class-conditional independence, before adapting to the true environmental structure. Class-conditional independence may be a strong and useful default assumption in category learning tasks.

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Naive and Yet Enlightened: From Natural Frequencies to Fast and Frugal Decision Trees

Cited by 80 publications

References 7 publications

Children can solve Bayesian problems: the role of representation in mental computation

Children can solve Bayesian problems: the role of representation in mental computation

Fast and Frugal Heuristics: Tools of Social Rationality

Naïve and Robust: Class‐Conditional Independence in Human Classification Learning

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