Abstract
Bayesian approaches presuppose that following the coherence conditions of probability theory makes probabilistic judgments more accurate. But other influential theories claim accurate judgments (with high “ecological rationality”) do not need to be coherent. Empirical results support these latter theories, threatening Bayesian models of intelligence; and suggesting, moreover, that “heuristics and biases” research, which focuses on violations of coherence, is largely irrelevant. We carry out a higher-power experiment involving poker probability judgments (and a formally analogous urn task), with groups of poker novices, occasional poker players, and poker experts, finding a positive relationship between coherence and accuracy both between groups and across individuals. Both the positive relationship in our data, and past null results, are captured by a sample-based Bayesian approximation model, where a person's accuracy and coherence both increase with the number of samples drawn. Thus, we reconcile the theoretical link between accuracy and coherence with apparently negative empirical results.
Highlights
Bayesians, whether in cognitive and brain sciences, artificial intel ligence, or statistics, assume that achieving accurate probabilistic beliefs and judgments is assisted by following the coherence constraints of probability theory, as embodied, for example, in graphical probabilistic models
We modelled the experiment of Berg et al (2016) using the same Bayesian sampling model and parameters used for the poker experts
We found these results with coherence and accuracy assessed on different sets of judg ments, ensuring that these results were not confounded by the formal link between coherence and accuracy
Summary
Whether in cognitive and brain sciences, artificial intel ligence, or statistics, assume that achieving accurate probabilistic beliefs and judgments is assisted by following the coherence constraints of probability theory, as embodied, for example, in graphical probabilistic models. Influential lines of theoretical and empirical research have proposed that, in many real-world situations, coherence is of little value, both in terms of accuracy (Berg, Biele, & Gigerenzer, 2016) and in terms of more general ecological and functional norms (e.g., Gigerenzer, 2019; Hammond, 2000), threatening the foundations of the Bayesian approach.. There are strong theoretical reasons for linking coherence and ac curacy. Under reasonable assump tions of accuracy measures, it has been proved that for any incoherent set of estimates there exists at least one coherent set of estimates that is more accurate with respect to all possible outcomes
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
