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On Ehrhart polynomials and probability calculations in voting theory

  • Dominique Lepelley


  • Ahmed Louichi


  • Hatem Smaoui


In voting theory, analyzing how frequent is an event (e.g. a voting paradox) is, under some specific but widely used assumptions, equivalent to computing the exact number of integer solutions in a system of linear constraints. Recently, some algorithms for computing this number have been proposed in social choice literature by Huang and Chua [17] and by Gehrlein ([12, 14]). The purpose of this paper is threefold. Firstly, we want to do justice to Eug`ene Ehrhart, who, more than forty years ago, discovered the theoretical foundations of the above mentioned algorithms. Secondly, we present some efficient algorithms that have been recently developed by computer scientists, independently from voting theorists. Thirdly, we illustrate the use of these algorithms by providing some original results in voting theory.

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Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 30 (2008)
Issue (Month): 3 (April)
Pages: 363-383

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Handle: RePEc:spr:sochwe:v:30:y:2008:i:3:p:363-383
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  1. Pierre Favardin & Dominique Lepelley & Jérôme Serais, 2002. "original papers : Borda rule, Copeland method and strategic manipulation," Review of Economic Design, Springer, vol. 7(2), pages 213-228.
  2. William V. Gehrlein, 2002. "Obtaining representations for probabilities of voting outcomes with effectively unlimited precision integer arithmetic," Social Choice and Welfare, Springer, vol. 19(3), pages 503-512.
  3. William Gehrlein, 2004. "Consistency in Measures of Social Homogeneity: A Connection with Proximity to Single Peaked Preferences," Quality & Quantity: International Journal of Methodology, Springer, vol. 38(2), pages 147-171, April.
  4. Pierre Favardin & Dominique Lepelley, 2006. "Some Further Results on the Manipulability of Social Choice Rules," Post-Print halshs-00068839, HAL.
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