  We analyze sources of error in prediction market forecasts in order to bound
the difference between a security's price and the ground truth it estimates. We
consider cost-function-based prediction markets in which an automated market
maker adjusts security prices according to the history of trade. We decompose
the forecasting error into three components: sampling error, arising because
traders only possess noisy estimates of ground truth; market-maker bias,
resulting from the use of a particular market maker (i.e., cost function) to
facilitate 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 tradeoffs
between these error components, influenced by design decisions such as the
functional form of the cost function and the amount of liquidity in the market.
We consider a specific model in which traders have exponential utility and
exponential-family beliefs representing noisy estimates of ground truth. In
this setting, sampling error vanishes as the number of traders grows, but there
is a tradeoff between the other two components. We provide both upper and lower
bounds on market-maker bias and convergence error, and demonstrate via
numerical simulations that these bounds are tight. Our results yield new
insights into the question of how to set the market's liquidity parameter and
into the forecasting benefits of enforcing coherent prices across securities.
