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On Ehrhart Polynomials and Probability Calculations in Voting Theory

Author

Listed:
  • Dominique Lepelley

    (CERESUR – University of la Reunion)

  • Ahmed Louichi

    (CREM – CNRS)

  • Hatem Smaoui

    (CREM – CNRS)

Abstract

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 Eugène 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.

Suggested Citation

  • 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.
    • Handle: RePEc:tut:cremwp:200610
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    File URL: https://crem-doc.univ-rennes1.fr/wp/2006/ie-200610.pdf
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    References listed on IDEAS

    as
    1. William V. Gehrlein, 2002. "Obtaining representations for probabilities of voting outcomes with effectively unlimited precision integer arithmetic," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(3), pages 503-512.
    2. Pierre Favardin & Dominique Lepelley & Jérôme Serais, 2002. "original papers : Borda rule, Copeland method and strategic manipulation," Review of Economic Design, Springer;Society for Economic Design, vol. 7(2), pages 213-228.
    3. Pierre Favardin & Dominique Lepelley, 2006. "Some Further Results on the Manipulability of Social Choice Rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(3), pages 485-509, June.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    voting rules; manipulability; polytopes; lattice points; algorithms.;

    JEL classification:

    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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