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The Empirical Frequency of a Pivotal Vote

  • Casey B. Mulligan
  • Charles G. Hunter

Empirical distributions of election margins are computing using data on 16,577 U.S. Congressional and 40,036 state legislator election returns. 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 a 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. In contrast, the distribution of state legislature election margins is clearly monotonic, with closer margins more likely, except for very close and very lopsided elections. The frequency of one vote elections is compared with total votes, and with the frequencies suggested by some theoretical models of voting. Roughly one of every 30,000 elections with 100,000 votes are decided by one vote. For elections with 5,000 or 20,000 votes, the frequencies are 1/1500 or 1/6000, respectively. This inverse relationship between election size and the frequency of one vote margins is found in two 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.

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Paper provided by Harris School of Public Policy Studies, University of Chicago in its series Working Papers with number 0025.

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Date of creation: Oct 2000
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Handle: RePEc:har:wpaper:0025
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  1. Chamberlain, Gary & Rothschild, Michael, 1981. "A note on the probability of casting a decisive vote," Journal of Economic Theory, Elsevier, vol. 25(1), pages 152-162, August.
  2. Fischer, A J, 1999. " The Probability of Being Decisive," Public Choice, Springer, vol. 101(3-4), pages 267-83, December.
  3. Howard Margolis, 1977. "Probability of a tie election," Public Choice, Springer, vol. 31(1), pages 135-138, September.
  4. Glaeser, Edward L & Sacerdote, Bruce & Scheinkman, Jose A, 1996. "Crime and Social Interactions," The Quarterly Journal of Economics, MIT Press, vol. 111(2), pages 507-48, May.
  5. Timothy J. Feddersen & Wolfgang Pesendorfer, 1995. "The Swing Voter's Curse," Discussion Papers 1064, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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