A Decomposition of Forecast Error in Prediction Markets.

We analyze sources of error in prediction market forecasts in order to boundthe difference between a security's price and the ground truth it estimates. Weconsider cost-function-based prediction markets in which an automated marketmaker adjusts security prices according to the history of trade. We decomposethe forecasting error into three components: sampling error, arising becausetraders only possess noisy estimates of ground truth; market-maker bias,resulting from the use of a particular market maker (i.e., cost function) tofacilitate trade; and convergence error, arising because, at any point in time,market prices may still be in flux. Our goal is to make explicit the tradeoffsbetween these error components, influenced by design decisions such as thefunctional form of the cost function and the amount of liquidity in the market.We consider a specific model in which traders have exponential utility andexponential-family beliefs representing noisy estimates of ground truth. Inthis setting, sampling error vanishes as the number of traders grows, but thereis a tradeoff between the other two components. We provide both upper and lowerbounds on market-maker bias and convergence error, and demonstrate vianumerical simulations that these bounds are tight. Our results yield newinsights into the question of how to set the market's liquidity parameter andinto the forecasting benefits of enforcing coherent prices across securities.