Far from the madding crowd: collective wisdom in prediction markets

We investigate market selection and bet pricing in a repeated prediction market model. We derive the conditions for long-run survival of more than one agent (the crowd) and quantify the information content of prevailing prices in the case of fractional Kelly traders with heterogeneous beliefs. It turns out that, apart some non-generic situations, prices do not converge, neither almost surely nor on average, to true probabilities, nor are they always nearer to the truth than the beliefs of all surviving agents. This implies that, in general, prediction market prices are not maximum likelihood estimators of the true probabilities. However, when more than one agent survives, the average price emerging from a prediction market approximates the true probability with lower information loss than any individual belief.