Interpreting the Predictive Uncertainty of
Elections, *Journal of Politics*, 2009,

provides an interpretation of the uncertainty that exists on election morning as to who will win. The interpretation is based on the theory that there are a number of possible conditions of nature than can exist on election day, of which one is drawn. Political betting markets provide a way of trying to estimate this uncertainty. (Polling standard errors do not provide estimates of this type of uncertainty. They estimate sample-size uncertainty, which can be driven close to zero with a large enough sample.)

This paper also introduces a "ranking assumption," which puts restrictions
on the possible conditions of nature that can exist on election day.
Take as an example the vote in each state for the Democratic candidate for
president. Rank the states by the probability on the day of the election
that the candidate wins the
state. The ranking assumption says that if the candidate wins state *i*,
he or she wins every state ranked above state *i*.

Given some ranking, the ranking assumption can be tested by simply looking to see after the fact if the candidate won a state ranked lower than one he or she lost. In the paper the assumption was tested for the 2004 and 2008 presidential elections using Intrade probabilities at 6am Eastern standard time on the day of the election. The test is thus a test of the joint hypothesis that the Intrade probabilities are right and the ranking assumption is right. Using the Intrade probabilities, the ranking assumption was perfect in 2004 and off by one in 2008. In 2008 Missouri was ranked above Indiana, and Obama won Indiana and lost Missouri. Both of these elections were very close. Obama won Indiana with 50.477 percent of the two-party vote and lost Missouri with 49.937 percent of the two-party vote. Otherwise, 2008 was perfect.

Evidence is also presented in the paper, although this is not a test of the ranking assumption, that Intrade traders used the ranking assumption to price various contracts.

Since this paper was written, the ranking assumption has been tested using more recent elections. These tests are documented on this site. Return to the main page for the listing.