Necessary and Sufficient Conditions for Prediction Market Accuracy

Résumé

We consider a binary-event prediction market in which traders have heterogeneous prior beliefs. We derive conditions so that the prediction market is accurate in the sense that the equilibrium price equals the mean of traders’ beliefs. We show that the prediction market is accurate i) for all distributions of beliefs if and only if the utility function is logarithmic, and ii) for all strictly concave utility functions if and only if the distribution of beliefs is symmetric about one half. We also exhibit a necessary and sufficient condition for the equilibrium price to be always above or below the mean beliefs for all symmetric beliefs distributions.