"Sampling Plus Correction Explains Biases in Probability Estimates"

People’s probability estimates have been used to argue that people are irrational: effects such as conservatism and the conjunction fallacy show that these estimates are inconsistent with one another. However, recent work has shown that probability estimates are surprisingly consistent with the laws of probability theory, assuming the estimates are corrupted by noise: the probability theory plus noise model (Costello & Watts, 2014; 2016; 2017; Costello, Watts, & Fisher, 2018). Here we introduce a new computational framework that assumes estimation is a two-stage process: 1) samples are drawn from a complex posterior probability distribution, and 2) a deterministic correction is applied to produce better, yet biased estimates. Our correction is the result of exact Bayesian inference with a generic prior distribution describing how likely each of the true probabilities are, and can be implemented as a simple linear transformation of the sample counts. This correction step is necessary because sampling is approximate inference and retains uncertainty as to the true probabilities being sampled. While more rational than probability theory plus noise, our account predicts exactly the same average probability estimates. Additionally, it outperforms the probability theory plus noise model by better matching the variability of people’s probability estimates.

Contact: Jesse Preston