The Empirical Frequency of a Pivotal Vote

Empirical distributions of election margins are computing using data on U.S. Congressional and state legislator election returns. We present some of the first empirical calculations of the frequency of close elections, showing that one of every 100,000 votes cast in U.S. elections, and one of every 15,000 votes cast in state elections, 'mattered' in the sense that they were cast for a candidate that officially tied or won by one vote. Very close elections are more rare than the independent binomial model predicts. The evidence also suggests that recounts, and other margin-specific election procedures, are quite relevant determinants of the frequency of a pivotal vote. Although moderately close elections (winning margin of less than ten percentage points) are more common than landslides, the distribution of moderately close U.S. election margins is approximately uniform. The distribution of state legislature election margins is clearly monotonic, with closer margins more likely, except for very close and very lopsided elections. We find an inverse relationship between election size and the frequency of one vote margins in both data sets over a wide range of election sizes, with the exception of the smallest U.S. elections for which the frequency increases with election size.