Forecasting the vote: A theoretical comparison of election markets and public opinion polls

The dominant methodology for short-term forecasting of electoral outcomes uses trial-heat polls, where respondents report their current electoral preferences (not their election-day predictions). Election markets, where self-selected participants trade shares of candidates at prices predictive of election-day results, provide an alternative method that often produces more accurate forecasts. Consequently, increasing attention is being paid to this methodology. However, it is poorly understood and lacks theoretical justification. Surprisingly, the rationale for forecasting using trial-heat polls has not been completely developed either. We develop the justification for using both election markets and public opinion polls to forecast electoral outcomes, giving conditions under which each method performs ideally. For the ideal case, we prove (under the reasonable assumption that market participants are aware of the poll results) that the mean square prediction error for the market forecast is smaller than that of any forecast based on one or more polls. The case in which the assumptions supporting each method fail is also considered. It is often reasonable to expect that the best case results hold approximately, in which case the market forecast should also beat any poll-based forecast. We also compare the bias and variance of market and poll-based forecasts; our results suggest the utility of using the series of market prices to study the course of campaigns.