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

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

Abstract

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
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Handle: RePEc:tse:wpaper:25866

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  1. Roger B. Myerson, 1994. "Population Uncertainty and Poisson Games," Discussion Papers 1102R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  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. 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.
  4. Robert J. Weber, 1995. "Approval Voting," Journal of Economic Perspectives, American Economic Association, vol. 9(1), pages 39-49, Winter.
  5. 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.
  6. Kuga, Kiyoshi & Nagatani, Hiroaki, 1974. "Voter Antagonism and the Paradox of Voting," Econometrica, Econometric Society, vol. 42(6), pages 1045-67, November.
  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. Dominique Lepelley & Ahmed Louichi & Hatem Smaoui, 2006. "On Ehrhart Polynomials and Probability Calculations in Voting Theory," Economics Working Paper Archive (University of Rennes 1 & University of Caen) 200610, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS.
  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.
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Cited by:
  1. Le Breton, Michel & Lepelley, Dominique, 2012. "Une Analyse de la Loi Electorale du 29 Juin 1820," TSE Working Papers 12-312, Toulouse School of Economics (TSE).

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