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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.

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Paper provided by Toulouse School of Economics (TSE) in its series TSE Working Papers with number 12-313.

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Date of creation: Jun 2012
Date of revision: Apr 2014
Handle: RePEc:tse:wpaper:25866
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Web page: http://www.tse-fr.eu/

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  1. Dominique Lepelley & Ahmed Louichi & Hatem Smaoui, 2008. "On Ehrhart polynomials and probability calculations in voting theory," Social Choice and Welfare, Springer, vol. 30(3), pages 363-383, April.
  2. 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.
  3. Kuga, Kiyoshi & Nagatani, Hiroaki, 1974. "Voter Antagonism and the Paradox of Voting," Econometrica, Econometric Society, vol. 42(6), pages 1045-67, November.
  4. Philip Straffin, 1977. "Homogeneity, independence, and power indices," Public Choice, Springer, vol. 30(1), pages 107-118, June.
  5. Roger B. Myerson, 1994. "Population Uncertainty and Poisson Games," Discussion Papers 1102R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Robert J. Weber, 1995. "Approval Voting," Journal of Economic Perspectives, American Economic Association, vol. 9(1), pages 39-49, Winter.
  7. Wilson, Mark C. & Pritchard, Geoffrey, 2007. "Probability calculations under the IAC hypothesis," Mathematical Social Sciences, Elsevier, vol. 54(3), pages 244-256, December.
  8. Le Breton, Michel & Lepelley, Dominique, 2012. "Une Analyse de la Loi Electorale du 29 Juin 1820," IDEI Working Papers 721, Institut d'Économie Industrielle (IDEI), Toulouse.
  9. 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.
  10. 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.
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