Interpreting Prediction Market Prices as Probabilities
While most empirical analysis of prediction markets treats prices of binary options as predictions of the probability of future events, Manski (2004) has recently argued that there is little existing theory supporting this practice. We provide relevant analytic foundations, describing sufficient conditions under which prediction markets prices correspond with mean beliefs. Beyond these specific sufficient conditions, we show that for a broad class of models prediction market prices are usually close to the mean beliefs of traders. The key parameters driving trading behavior in prediction markets are the degree of risk aversion and the distribution of beliefs, and we provide some novel data on the distribution of beliefs in a couple of interesting contexts. We find that prediction markets prices typically provide useful (albeit sometimes biased) estimates of average beliefs about the probability an event occurs.
We would like to thank Ray Fair, Brian Galebach, Robin Hanson, Robert Hahn, Ed Kaplan, Brian Knight, Charles Manski, Marco Ottaviani, David Pennock, Erik Snowberg, Peter Norman Sørensen, Betsey Stevenson, Rob Stevenson and Abe Wickelgren for useful conversations and insights. Wolfers gratefully acknowledges the support of a Hirtle, Callaghan & Co. -- Geewax, Terker and Co. Research Fellowship, Microsoft Research, the Mack Center for Technological Innovation, and the support of the Zull/Lurie Real Estate Center.