Xue-Zhong He, and Nicolas Treich, “Heterogeneous Beliefs and Prediction Market Accuracy”, TSE Working Paper, n. 13-394, August 20, 2012.
We consider a prediction market in which traders have heterogeneous prior beliefs in probabilities. In the two-state case, we derive necessary and sufficient conditions so that the prediction market is accurate in the sense that the equilibrium state price equals the mean probabilities of traders' beliefs. We also provide a necessary and sufficient condition for the well documented favorite-longshot bias. In an extension to many states, we revisit the results of Varian (1985) on the relationship between equilibrium state price and belief heterogeneity.
Xue-Zhong He, and Nicolas Treich, “Prediction market prices under risk aversion and heterogeneous beliefs”, Journal of Mathematical Economics, vol. 70, May 2017, pp. 105–114.