Interpreting the Predictive Uncertainty of Elections

This paper provides an interpretation of the uncertainty that exists at the beginning of the day of an election as to who will win. It is based on the theory that there are a number of possible conditions of nature that can exist on election day, of which one is drawn. Political betting markets like Intrade provide a way of trying to estimate this uncertainty. It is argued that polling standard errors do not provide estimates of this type of uncertainty. They instead estimate sample-size uncertainty, which can be driven close to zero with a large enough sample. This paper also introduces a ranking assumption concerning dependencies across U.S. states, which puts restrictions on the possible conditions of nature than can exist on election day. The joint hypothesis that the last-day Intrade ranking is correct and the ranking assumption is correct predicts the exact outcomes of the 2004 presidential election and the 2006 Senate election. Although not a test of the ranking assumption, there is evidence that the Intrade traders used the ranking assumption to price contracts in the 2004 presidential election. This was not the case, however, in the 2006 Senate election. Finally, it is shown if the ranking assumption is correct, the two political parties should spend all their money on a few states, which seems consistent with their actual behavior in 2004. ∗Cowles Foundation and International Center for Finance, Yale University, New Haven, CT 06520-8281. Voice: 203-432-3715; Fax: 203-432-6167; email: [email protected]; website: http://fairmodel.econ.yale.edu. I am indebted to Keith Chen, Don Green, Ed Kaplan, SteveMorris, Sharon Oster, JustinWolfers, and Eric Zitzewitz for helpful discussions and comments and toMike Knesevitch at Intrade for supplying me with some of the data. This paper is a substantially revised version of an earlier paper entitled “Predicting Electoral College Victory Probabilities from State Probability Data,” November 2004.