Probability Distributions of Common Repeated Events are Misestimated

Abstract

Accurately estimating the prospective probability distribution arising from repeated events with known probabilities, such as the number of heads in ten coin flips, represents a simple aptitude necessary for explicit Bayesian updating and useful in optimal decisions in the face of future uncertainty. Across elicitation methods and decision scenarios, people express beliefs that are systematically biased relative to the actual distribution. Participant beliefs reflect a “wizard-hat” shaped distribution, over-estimating the tails and under-estimating the shoulders of the distribution, relative to the actual bell-curve shape. While experts are relatively more accurate than novices, both show significant bias. The bias is not explained by regression to the mean, random error or participant heterogeneity, and is exacerbated by increasing the number of repeated events. The findings caution against assuming Bayesian belief formation in models of statistical reasoning about explicit prospective beliefs based on repeated events with known probabilities.

Keywords: Bayesian models, heuristics, inference, judgment, risk and uncertainty, statistical reasoning