Overconfidence by bayesian rational agents

This paper derives two mechanisms through which Bayesian-rational individuals with differing priors will tend to be relatively overconfident about their estimates and predictions, in the sense of overestimating the precision of these estimates. The intuition behind one mechanism is slightly ironic: in trying to update optimally, Bayesian agents overweight information of which they over-estimate the precision and underweight in the opposite case. This causes overall an over-estimation of the precision of the final estimate, which tends to increase as agents get more data.