Probability Distributions of Common Repeated Events Are Misestimated.

Abstract

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

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