What do prediction markets predict?

We show that prediction markets cannot be relied on to always elicit any interesting statistic of aggregate beliefs. Formal derivations of the bets placed in prediction markets can be viewed as demands for state-contingent commodities. We provide derivations for two popular cases, log utility and Constant Relative Risk Aversion (CRRA) utility, connecting these derivations to familiar scoring rules. We then use these results to demonstrate how the properties of prediction markets depend critically on the assumed homogeneity of participants.