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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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  1. Wilson, Mark C. & Pritchard, Geoffrey, 2007. "Probability calculations under the IAC hypothesis," Mathematical Social Sciences, Elsevier, vol. 54(3), pages 244-256, December.
  2. Robert J. Weber, 1995. "Approval Voting," Journal of Economic Perspectives, American Economic Association, vol. 9(1), pages 39-49, Winter.
  3. 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.
  4. 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.
  5. Roger B. Myerson, 1994. "Population Uncertainty and Poisson Games," Discussion Papers 1102, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Nathaniel Beck, 1975. "A note on the probability of a tied election," Public Choice, Springer, vol. 23(1), pages 75-79, September.
  7. 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.
  8. Özgür Evren, 2012. "Altruism and Voting: A Large-Turnout Result That Does not Rely on Civic Duty or Cooperative Behavior," Working Papers w0173, Center for Economic and Financial Research (CEFIR).
  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. Kuga, Kiyoshi & Nagatani, Hiroaki, 1974. "Voter Antagonism and the Paradox of Voting," Econometrica, Econometric Society, vol. 42(6), pages 1045-67, November.
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