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The Probability of Casting a Decisive Vote: From IC to IAC trhough Ehrhart's Polynomials and Strong Mixing


  • Le Breton, Michel
  • Lepelley, Dominique
  • Smaoui, Hatem


The main purpose of this paper is to estimate the probability of casting a decisive vote for a class or random electorate models encompassing the celebrated IC and IAC models. The emphasis is on the impact of correlation across votes on the order of magnitude of this event. Our proof techniques use arguments from probability theory on one hand and the geometry of convex polytopes on the other hand.

Suggested Citation

  • Le Breton, Michel & Lepelley, Dominique & Smaoui, Hatem, 2012. "The Probability of Casting a Decisive Vote: From IC to IAC trhough Ehrhart's Polynomials and Strong Mixing," IDEI Working Papers 722, Institut d'Économie Industrielle (IDEI), Toulouse.
  • Handle: RePEc:ide:wpaper:25852

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    References listed on IDEAS

    1. 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.
    2. Dominique Lepelley & Ahmed Louichi & Hatem Smaoui, 2008. "On Ehrhart polynomials and probability calculations in voting theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(3), pages 363-383, April.
    3. Berg, Sven, 1990. "The Probability of Casting a Decisive Vote: The Effects of a Caucus," Public Choice, Springer, vol. 64(1), pages 73-92, January.
    4. Roger B. Myerson, 1998. "Population uncertainty and Poisson games," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(3), pages 375-392.
    5. Wilson, Mark C. & Pritchard, Geoffrey, 2007. "Probability calculations under the IAC hypothesis," Mathematical Social Sciences, Elsevier, vol. 54(3), pages 244-256, December.
    6. repec:cup:apsrev:v:87:y:1993:i:01:p:102-114_09 is not listed on IDEAS
    7. 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.
    8. repec:cup:apsrev:v:48:y:1954:i:03:p:787-792_00 is not listed on IDEAS
    9. Romano, Joseph P. & Wolf, Michael, 2000. "A more general central limit theorem for m-dependent random variables with unbounded m," Statistics & Probability Letters, Elsevier, vol. 47(2), pages 115-124, April.
    10. Kuga, Kiyoshi & Nagatani, Hiroaki, 1974. "Voter Antagonism and the Paradox of Voting," Econometrica, Econometric Society, vol. 42(6), pages 1045-1067, November.
    11. Robert J. Weber, 1995. "Approval Voting," Journal of Economic Perspectives, American Economic Association, vol. 9(1), pages 39-49, Winter.
    12. Michel Le Breton & Dominique Lepelley, 2014. "Une analyse de la loi électorale du 29 juin 1820," Revue économique, Presses de Sciences-Po, vol. 65(3), pages 469-518.
    13. Nathaniel Beck, 1975. "A note on the probability of a tied election," Public Choice, Springer, vol. 23(1), pages 75-79, September.
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    More about this item

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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