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Obtaining representations for probabilities of voting outcomes with effectively unlimited precision integer arithmetic

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  • William V. Gehrlein

    ()
    (University of Delaware, Department of Business Administration, Newark, DE 19716, USA)

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    Abstract

    A procedure is developed to obtain representations for the probability of election outcomes with the Impartial Anonymous Culture Condition and the Maximal Culture Condition. The procedure is based upon a process of performing arithmetic with integers, while maintaining absolute precision with very large integer numbers. The procedure is then used to develop probability representations for a number of different voting outcomes, which have to date been considered to be intractable to obtain with the use of standard algebraic techniques.

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    Bibliographic Info

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

    Volume (Year): 19 (2002)
    Issue (Month): 3 ()
    Pages: 503-512

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    Handle: RePEc:spr:sochwe:v:19:y:2002:i:3:p:503-512

    Note: Received: 13 June 2000/Accepted: 22 January 2001
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    Cited by:
    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. Sascha Kurz & Nikolas Tautenhahn, 2013. "On Dedekind’s problem for complete simple games," International Journal of Game Theory, Springer, vol. 42(2), pages 411-437, May.
    3. Gehrlein, William V. & Moyouwou, Issofa & Lepelley, Dominique, 2013. "The impact of voters’ preference diversity on the probability of some electoral outcomes," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 352-365.
    4. Wilson, Mark C. & Pritchard, Geoffrey, 2007. "Probability calculations under the IAC hypothesis," Mathematical Social Sciences, Elsevier, vol. 54(3), pages 244-256, December.
    5. Cervone, Davide P. & Dai, Ronghua & Gnoutcheff, Daniel & Lanterman, Grant & Mackenzie, Andrew & Morse, Ari & Srivastava, Nikhil & Zwicker, William S., 2012. "Voting with rubber bands, weights, and strings," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 11-27.
    6. Achill Schürmann, 2013. "Exploiting polyhedral symmetries in social choice," Social Choice and Welfare, Springer, vol. 40(4), pages 1097-1110, April.
    7. Fabrice Barthélémy & Dominique Lepelley & Mathieu Martin, 2013. "On the likelihood of dummy players in weighted majority games," Social Choice and Welfare, Springer, vol. 41(2), pages 263-279, July.
    8. Gehrlein, William V., 2004. "The effectiveness of weighted scoring rules when pairwise majority rule cycles exist," Mathematical Social Sciences, Elsevier, vol. 47(1), pages 69-85, January.

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