Prediction markets are emerging as a powerful and accurate method of aggregating information from populations of experts (and non-experts). Traders in prediction markets are incentivized to reveal their information through buying and selling "securities" for events such as "Romney to win the primary in Illinois". The prices of securities reflect the aggregate belief about the events and the key challenge is to correctly price the securities.

We present a new automated market maker for providing liquidity across multiple logically interrelated securities. Our approach lies somewhere between the industry standard---treating related securities as independent and thus not transmitting any information from one security to another---and a full combinatorial market maker for which pricing is computationally intractable. Our market maker, based on convex optimization and constraint generation, is tractable like independent securities yet propagates some information among related securities like a combinatorial market maker, resulting in more complete information aggregation. Our techniques borrow heavily from variational inference in exponential families. We prove several favorable properties of our scheme and evaluate its information aggregation performance on survey data involving hundreds of thousands of complex predictions about the 2008 U.S. presidential election.

Joint work with Sebastien Lahaie and David Pennock.