The Power of Omaha and Florida in the 2008 U.S. Presidential Election

The United States, uniquely among all countries, elects its head of state using a two-tiered system called the Electoral College. If we view the states that make up the Electoral College as voters and make some simplifying assumptions, it is possible to use the theory of voting and voting power to measure the power of the individual states in a presidential election. Modeling the Electoral College in this way and measuring the power of the states has been done by several authors, including J. Banzhaf [2] and I. Mann and L. Shapley [7]. However, this type of model uses only the formal rules of an election and does not take into account the particulars of a given election, for example, how likely a given state is to vote for a particular candidate. One of the simplifying assumptions that is made in this type of modeling is that every state uses a winner-take-all system to award its electoral votes. In theory, two states—Maine and Nebraska—do not use a winner-take-all system, although until recently their votes had never been split. However, in the 2008 presidential election, Nebraska split its electoral votes: Barack Obama received one electoral vote from the second congressional district (the district containing Omaha), while John McCain received the remaining electoral votes from Nebraska. One implication of this is that models of voting power in the Electoral College up to this point do not accurately apply to the 2008 election, since they assume no splitting of electoral votes. In this paper we discuss yes-no voting systems and the Banzhaf power index, and look at how these have been applied to the Electoral College. Then we look at a way to use these ideas to model power in the 2008 U.S. presidential election, by taking into account the probability that a given voter—in this case a state or congressional district—votes for one of the two major candidates. Because of the