We conduct an experiment in which subjects participate in a first-price auction against an automaton that bids randomly in a given range. The subjects first place a bid in the auction. They are then given an incentivized elicitation of their beliefs of the opponent's bid. Despite having been told that the bid of the opponent is drawn from a uniform distribution, we find that a majority of subjects report beliefs that have a peak in the interior of the range. This result is robust across seven different experimental treatments. While not expected at the outset, these single-peaked beliefs have precedence in the experimental psychology judgments literature. Our results suggest that an elicitation of probability beliefs can result in responses that are more concentrated than the objectively known or induced truth. We provide indicative evidence that such individual belief reports can be rationalized by well-defined subjective beliefs that differ from the objective truth. Our findings offer an explanation for the conservatism and overprecision biases in Bayesian updating. Finally, our findings suggest that probabilistic forecasts of uncertain events might have less variance than the actual events.
All Science Journal Classification (ASJC) codes
- Sociology and Political Science
- Applied Psychology
- Economics and Econometrics
- Belief elicitation
- Quadratic scoring rule