The wisdom of the crowd and prediction markets

Thanks to digital innovation, the wisdom of the crowd, which aims at gathering information (e.g. Wikipedia) and making a prediction (e.g. using prediction markets) from a group’s aggregated inputs, has been widely appreciated. An innovative survey design, based on a Bayesian learning framework, called the Bayesian truth serum (BTS), was proposed previously to reduce the bias in the simple majority rule by asking additional survey questions. A natural question is whether we can extend the BTS framework to prediction markets (not just polls). To do so, this paper proposes two estimators, one based on a prediction market alone and the other based on both the market and a poll question. We show that both estimators are consistent within the BTS framework, under different sets of regularity conditions. Simulations are conducted to examine the convergence of different estimators. A real data set of sports betting is used to demonstrate the effectiveness of one estimator.