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The Probability of Being Decisive

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  • Fischer, A J

Abstract

The probability of a voter being decisive (P[subscript D]), that is, of one vote affecting the outcome of an election, has generally been incorrectly calculated for the last twenty or more years. The method normally used is due to Banzhaf (1968) and generalised by Beck (1974). It assumes that voters know in advance how many people will vote for each candidate, which is clearly not the case. The correct formulation was given by Good and Mayer in 1975, but was ignored and has subsequently been all but forgotten since then. A simple explanation of these methods is given. Using the incorrect method, errors of magnitude of more than 10[superscript 100] in calculating P[subscript D] correctly can be made. The appropriateness of using a decision-theoretic formulation instead of a game-theoretic one is also discussed. Copyright 1999 by Kluwer Academic Publishers

Suggested Citation

  • Fischer, A J, 1999. "The Probability of Being Decisive," Public Choice, Springer, vol. 101(3-4), pages 267-283, December.
    • Handle: RePEc:kap:pubcho:v:101:y:1999:i:3-4:p:267-83
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    Cited by:

    1. 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.
    2. Ozgur Evren, 2009. "Altruism, Turnout and Strategic Voting Behavior," Levine's Working Paper Archive 814577000000000309, David K. Levine.
    3. Evren, Özgür, 2012. "Altruism and voting: A large-turnout result that does not rely on civic duty or cooperative behavior," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2124-2157.
    4. Dan Usher, 2014. "An alternative explanation of the chance of casting a pivotal vote," Rationality and Society, , vol. 26(1), pages 105-138, February.
    5. René Brink & Frank Steffen, 2012. "Axiomatizations of a positional power score and measure for hierarchies," Public Choice, Springer, vol. 151(3), pages 757-787, June.
    6. Mulligan, Casey B & Hunter, Charles G, 2003. "The Empirical Frequency of a Pivotal Vote," Public Choice, Springer, vol. 116(1-2), pages 31-54, July.
    7. Robert Grafstein, 2002. "What Rational Political Actors Can Expect," Journal of Theoretical Politics, , vol. 14(2), pages 139-165, April.
    8. Frank Daumann & Alfred Wassermann, 2009. "Does trading votes in national elections change election outcomes?," Public Choice, Springer, vol. 139(3), pages 429-441, June.
    9. Krishnakumar, Jaya & Müller, Tobias, 2012. "The political economy of immigration in a direct democracy: The case of Switzerland," European Economic Review, Elsevier, vol. 56(2), pages 174-189.
    10. Serge Blondel & Louis Lévy-garboua, 2011. "Can non-expected utility theories explain the paradox of not voting?," Economics Bulletin, AccessEcon, vol. 31(4), pages 3158-3168.
    11. Timo Goeschl, 2005. "Non-binding linked-issues referenda: Analysis and an application," Public Choice, Springer, vol. 124(3), pages 249-266, September.

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