Bayesian probability estimates are not necessary to make choices satisfying Bayes' rule in elementary situations.
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Probabilistic relations were inferred from a set of pictures, followed by a choice which was made to maximize the chance of a preferred outcome.Computer-simulated scenarios revealed that the heuristics produced correct choices reasonably often under specific base rates and likelihood ratios.Summing up we conclude that natural sampling results in most choices conforming to Bayes' rule.
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Affiliation: Department of Cognitive Psychology, Faculty of Psychology, University of Warsaw Warsaw, Poland.
ABSTRACT
This paper has two aims. First, we investigate how often people make choices conforming to Bayes' rule when natural sampling is applied. Second, we show that using Bayes' rule is not necessary to make choices satisfying Bayes' rule. Simpler methods, even fallacious heuristics, might prescribe correct choices reasonably often under specific circumstances. We considered elementary situations with binary sets of hypotheses and data. We adopted an ecological approach and prepared two-stage computer tasks resembling natural sampling. Probabilistic relations were inferred from a set of pictures, followed by a choice which was made to maximize the chance of a preferred outcome. Use of Bayes' rule was deduced indirectly from choices. Study 1 used a stratified sample of N = 60 participants equally distributed with regard to gender and type of education (humanities vs. pure sciences). Choices satisfying Bayes' rule were dominant. To investigate ways of making choices more directly, we replicated Study 1, adding a task with a verbal report. In Study 2 (N = 76) choices conforming to Bayes' rule dominated again. However, the verbal reports revealed use of a new, non-inverse rule, which always renders correct choices, but is easier than Bayes' rule to apply. It does not require inversion of conditions [transforming P(H) and P(D/H) into P(H/D)] when computing chances. Study 3 examined the efficiency of three fallacious heuristics (pre-Bayesian, representativeness, and evidence-only) in producing choices concordant with Bayes' rule. Computer-simulated scenarios revealed that the heuristics produced correct choices reasonably often under specific base rates and likelihood ratios. Summing up we conclude that natural sampling results in most choices conforming to Bayes' rule. However, people tend to replace Bayes' rule with simpler methods, and even use of fallacious heuristics may be satisfactorily efficient. No MeSH data available. Related in: MedlinePlus |
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Mentions: By definition, the pre-Bayesian strategy always gives opposite answers to the evidence-only strategy (Figure 6) and, indeed, we observed its diametrically opposite behavior for all size – base rate combinations. A decision maker should understand that probabilities do not exceed one, i.e., (d + e)/(d + f) ≤ 1 and (d + e)/(e + g) ≤ 1. This implies 2(d + e) ≤ (d + f + e + g), 2b ≤a and b/a ≤ 0.5, and means that the strategy is not applicable for base rates exceeding 1/2. With these assumptions, the strategy renders choices conforming to Bayes’ rule with a probability of 56.0% for medium base rates, and 72.6% for low base rates. |
View Article: PubMed Central - PubMed
Affiliation: Department of Cognitive Psychology, Faculty of Psychology, University of Warsaw Warsaw, Poland.
No MeSH data available.