Reasoning with alternatives as Bayesian confirmation: revisiting the lawyers and engineers problem

Mathias Sablé-Meyer, Janek Guerrini, and Salvador Mascarenhas

Abstract

Irrationality observed in tasks such as the lawyers-engineers problem (Kahneman and Tversky 1973) has been interpreted in terms of representativeness, a heuristic argued to substitute actual reasoning about probabilities. We provide evidence that confirmation-theoretic reasoning, which yields insightful accounts of the conjunction fallacy (Tentori, Crupi, Russo, 2013, On the determinants of the conjunction fallacy. JEP.), extends to the lawyers-engineers problem and related fallacies.

We argue that, when faced with multiple options (hypotheses), reasoners often pick the one that best explains available information (evidence), and not simply the one with the highest posterior. We show that confirmation measures involving likelihoods (P(e|h)) together with posteriors (P(h|e)) provide a better model than posteriors alone in lawyers-engineers-like problems.

K&T’s original design could not distinguish non-probabilistic similarity judgments (representativeness) from sophisticated (probabilistic) confirmation. In a norming study, we collected priors (hypotheses and evidence), posteriors and likelihoods. We used pairs of real-world professions (hypotheses) and related one-sentence descriptions (evidence), asking participants for frequency judgments. An independent group then answered lawyers-engineers problems with the normed materials. We found more rational behavior than previous studies. Models leveraging likelihoods in addition to posteriors outperformed posteriors-alone models.

In another study we assessed whether familiar stereotypes and complex descriptions are essential features as originally argued. We distilled the task to its essence, conveying probabilistic distributions visually by displaying objects of two shapes (hypotheses) in one of two colors (evidence). In each trial, participants were told that an element had been picked randomly and were given its color, then had to guess its shape. We found results similar to the first experiment, showing that this reasoning process is independent of familiarity and does not require rich linguistic descriptions or individuating information.

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