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The Empirical Frequency of a Pivotal Vote

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  • Casey B. Mulligan
  • Charles G. Hunter

Abstract

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.

Suggested Citation

  • Casey B. Mulligan & Charles G. Hunter, 2000. "The Empirical Frequency of a Pivotal Vote," Working Papers 0025, Harris School of Public Policy Studies, University of Chicago.
  • Handle: RePEc:har:wpaper:0025
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    Cited by:

    1. Lirong Xia, 2020. "How Likely Are Large Elections Tied?," Papers 2011.03791, arXiv.org, revised Jul 2021.
    2. Tyran, Jean-Robert & Sausgruber, Rupert, 2006. "A little fairness may induce a lot of redistribution in democracy," European Economic Review, Elsevier, vol. 50(2), pages 469-485, February.
    3. Louis Kaplow & Scott Duke Kominers, 2020. "On the Representativeness of Voter Turnout," NBER Working Papers 26913, National Bureau of Economic Research, Inc.
    4. Andrew Leigh, 2009. "Does the World Economy Swing National Elections?," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(2), pages 163-181, April.
    5. Alan Gerber & Mitchell Hoffman & John Morgan & Collin Raymond, 2020. "One in a Million: Field Experiments on Perceived Closeness of the Election and Voter Turnout," American Economic Journal: Applied Economics, American Economic Association, vol. 12(3), pages 287-325, July.
    6. David K. Levine & Andrea Mattozzi, 2020. "Voter Turnout with Peer Punishment," American Economic Review, American Economic Association, vol. 110(10), pages 3298-3314, October.
    7. Amrita Dillon & GANI ALDASHEV, 2015. "Voter Turnout and Political Rents," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 17(4), pages 528-552, August.
    8. Darren Grant & Michael Toma, 2008. "Elemental tests of the traditional rational voting model," Public Choice, Springer, vol. 137(1), pages 173-195, October.
    9. Brad R. Taylor, 2016. "Exit and the Epistemic Quality of Voice," Economic Affairs, Wiley Blackwell, vol. 36(2), pages 133-144, June.
    10. John Maloney & Andrew Pickering, 2008. "Ideology, Competence and Luck: What determines general election results?," Bristol Economics Discussion Papers 08/607, School of Economics, University of Bristol, UK.
    11. Andrew Gelman & Nate Silver & Aaron Edlin, 2012. "What Is The Probability Your Vote Will Make A Difference?," Economic Inquiry, Western Economic Association International, vol. 50(2), pages 321-326, April.
    12. Louis Kaplow & Scott Duke Kominers, 2017. "Who will vote quadratically? Voter turnout and votes cast under quadratic voting," Public Choice, Springer, vol. 172(1), pages 125-149, July.
    13. David K Levine & Andrea Mattozzi, 2016. "Voter Participation with Collusive Parties," Levine's Working Paper Archive 786969000000001234, David K. Levine.
    14. Lyytikäinen, Teemu & Tukiainen, Janne, 2019. "Are voters rational?," European Journal of Political Economy, Elsevier, vol. 59(C), pages 230-242.
    15. de Mouzon, Olivier & Laurent, Thibault & Le Breton, Michel & Moyouwou, Issofa, 2020. "“One Man, One Vote” Part 1: Electoral Justice in the U.S. Electoral College: Banzhaf and Shapley/Shubik versus May," TSE Working Papers 20-1074, Toulouse School of Economics (TSE).
    16. Aaron Edlin & Andrew Gelman & Noah Kaplan, 2007. "Voting as a Rational Choice: Why and How People Vote to Improve the Well-Being of Others," NBER Working Papers 13562, National Bureau of Economic Research, Inc.
    17. Ozgur Evren, 2009. "Altruism, Turnout and Strategic Voting Behavior," Levine's Working Paper Archive 814577000000000309, David K. Levine.
    18. Sandra Breux & Jérôme Couture & Nicole Goodman, 2017. "Fewer voters, higher stakes? The applicability of rational choice for voter turnout in Quebec municipalities," Environment and Planning C, , vol. 35(6), pages 990-1009, September.
    19. Federico Revelli & Tsung-Sheng Tsai, 2019. "Ties," CESifo Working Paper Series 7786, CESifo.
    20. Bhatt, Rachana & Dechter, Evgenia & Holden, Richard, 2020. "Registration costs and voter turnout," Journal of Economic Behavior & Organization, Elsevier, vol. 176(C), pages 91-104.
    21. Deniz Guvercin, 2019. "Going to the Polls or Feeding Children? An Empirical Investigation of Voter Turnout among Turkish Women with Children at Home," Bogazici Journal, Review of Social, Economic and Administrative Studies, Bogazici University, Department of Economics, vol. 33(1), pages 1-16.
    22. Andrew Gelman & Nate Silver & Aaron Edlin, 2009. "What is the probability your vote will make a difference?," NBER Working Papers 15220, National Bureau of Economic Research, Inc.
    23. Eric Crampton & Andrew Farrant, 2004. "Expressive and Instrumental Voting: The Scylla and Charybdis of Constitutional Political Economy," Constitutional Political Economy, Springer, vol. 15(1), pages 77-88, March.
    24. Stefano Demichelis & Amrita Dhillon, 2010. "Learning in Elections and Voter Turnout," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 12(5), pages 871-896, October.
    25. François Facchini & Louis Jaeck, 2021. "Populism and the rational choice model: The case of the French National Front," Rationality and Society, , vol. 33(2), pages 196-228, May.

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    More about this item

    Keywords

    election; voting; frequency; pivotal vote;
    All these keywords.

    JEL classification:

    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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