U.S. Presidential Elections and the referendum paradox

Abstract

In the United States, the president is elected by the Electoral College (EC) and not directly by individual voters. This can give rise to a so-called 'referendum paradox' in which one candidate receives more popular votes than any other, but this candidate is not elected. The 2000 election is an example of this phenomenon. Can the EC be reformed so that a referendum paradox never arises? We consider varying three natural parameters. First, we consider changing the method of apportioning seats in the House of Representatives to states. Second, we consider changing the total number of seats in the House. Intuition suggests that as the number of seats approaches the number of voters, the referendum paradox should disappear. Finally, we consider varying the fixed and proportional components of each state's EC vote. Using data from U.S. presidential elections we show that none of these reforms can prevent a referendum paradox from occurring. We conclude that susceptibility to a referendum paradox is an inescapable feature of the system for electing presidents. An interesting corollary of our analysis is that seemingly insignificant changes to the EC can cause different candidates to be elected president.