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Polarization and the US Electoral College

In light of the 2000 and 2016 presidential elections, there has been doubt about whether the electoral college is a "fair'' way of selecting a presidential candidate. Rather than taking a position on the issue, this paper attempts to quantify the importance of such a discussion. Toward this end, we consider a voting model based on regional and personal biases, which provides a unifying framework for other probabilistic models in the literature along with offering new ones. Our main contribution is the derivation of simple expressions for the asymptotic likelihood of a "referendum paradox,'' whereby one candidate wins the election according to the electoral college, but loses the popular vote. We then consider how this likelihood varies depending on the heterogeneity of opinions within and across regions of a country, which may also differ in population. We conclude that rising polarization of political beliefs leading up to the 2020 election has made these two election formats increasingly more incompatible.