Natural Sampling: Rationality without Base Rates

Kleiter, Gernot D.

doi:10.1007/978-1-4612-4308-3_27

Cited by 104 publications

(83 citation statements)

References 16 publications

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“…As a result, these algorithms work well when the data take the form of event frequencies and work less well when the data take other forms (i.e., proportions or single-event probabilities). In addition, when the relevant data take the form of event frequencies, normative algorithms are often much simpler than they would be otherwise (Gigerenzer & Hoffrage, 1995;Kleiter, 1994).…”

Section: Discussionmentioning

confidence: 99%

Effects of a Relative-Frequency Elicitation Question on Likelihood Judgment Accuracy: The Case of External Correspondence

Price

1998

Organizational Behavior and Human Decision Processes

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In three experiments, college students judged the likelihood that they chose the correct alternative for each of 40 two-alterna-tive, generalknowledge items. They responded either to a rela-tive-frequency elicitation question ("Out of 100 questions for which you felt this certain of the answer, how many would you answer correctly?") or to a probability elicitation question ("What is the probability that you chose the correct answer?"). Judg-ments in response to the relative-frequency elicitation question tended to be lower, exhibit less scatter, and express complete certainty less often than judgments in response to the probability elicitation question. Two types of explanation for these effects are considered. First, the effect of the relative-frequency elicitation question may be to reduce random response error in participants' likelihood judgments. Second, the relativefrequency elicitation question may encourage the use of frequency information and simpler algorithms for making likelihood judgments.Behavioral decision researchers have shown repeatedly that the way one person asks another for a judgment can have important effects on the judgment itself. These effects are typically referred to as framing effects (Yates, 1990). The present research concerns one such framing effect in the domain of likelihood judgment. Specifically, it concerns the effects of a relative-frequency elicitation question (e.g., "In 100 cases like this one, how many times would target event

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Section: Discussionmentioning

confidence: 99%

Effects of a Relative-Frequency Elicitation Question on Likelihood Judgment Accuracy: The Case of External Correspondence

Price

1998

Organizational Behavior and Human Decision Processes

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“…The physician does not need to keep track of the base rate of the disease. Her modern counterpart, the medical student who struggles with singleevent probabilities presented in medical textbooks, may on the other hand have to rely on a calculator and end up with little understanding of the result (see Figure 1, right side (Kleiter, 1994).…”

Section: P(h)mentioning

confidence: 99%

“…Her modern counterpart, the medical student who struggles with singleevent probabilities presented in medical textbooks, may on the other hand have to rely on a calculator and end up with little understanding of the result (see Figure 1, right side). 1 Henceforth, when we use the term frequency format, we always refer to frequencies as denned by the natural sampling tree in Figure (Kleiter, 1994).…”

Section: P(h)mentioning

confidence: 99%

How to improve Bayesian reasoning without instruction: Frequency formats.

Gigerenzer¹,

Hoffrage²

1995

Psychological Review

1,758

1,789

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Is the mind, by design, predisposed against performing Bayesian inference? Previous research on base rate neglect suggests that the mind lacks the appropriate cognitive algorithms. However, any claim against the existence of an algorithm, Bayesian or otherwise, is impossible to evaluate unless one specifies the information format in which it is designed to operate. The authors show that Bayesian algorithms are computationally simpler in frequency formats than in the probability formats used in previous research. Frequency formats correspond to the sequential way information is acquired in natural sampling, from animal foraging to neural networks. By analyzing several thousand solutions to Bayesian problems, the authors found that when information was presented in frequency formats, statistically naive participants derived up to 50% of all inferences by Bayesian algorithms. Non-Bayesian algorithms included simple versions of Fisherian and Neyman-Pearsonian inference.

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“…Th e result is a probability of 47% that the person will lie. With natural frequencies, Bayesian computations become simpler (Gigerenzer & Hoff rage, 1995;Kleiter, 1994): Natural frequencies are illustrated by the tree in Figure 1. Th ere are a cases (e.g., people), of which b cases show H (e.g., they are liars) and c cases do not.…”

Section: Red Nose Problem: Natural Frequenciesmentioning

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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Natural Sampling: Rationality without Base Rates

Cited by 104 publications

References 16 publications

Effects of a Relative-Frequency Elicitation Question on Likelihood Judgment Accuracy: The Case of External Correspondence

Effects of a Relative-Frequency Elicitation Question on Likelihood Judgment Accuracy: The Case of External Correspondence

How to improve Bayesian reasoning without instruction: Frequency formats.

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

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