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Approval voting and Shapley ranking

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  • DEHEZ Pierre,

    () (Université catholique de Louvain, CORE, Belgium)

  • GINSBURGH Victor,

    () (Université libre de Bruxelles and CORE)

Abstract

Approval voting allows voters to list any number of candidates. Their scores are obtained by summing the votes cast in their favor. Fractional voting instead follows the One-person-one-vote principle by endowing voters with a single vote that they may freely distribute among candidates. In this paper, we show that fairness requires the distribution of votes to be uniform. Uniform fractional voting corresponds to Shapley ranking that was introduced to rank wines as the Shapley value of a cooperative game with transferable utility. Here we analyze the properties of these "ranking games" and provide an axiomatic foundation to Shapley ranking. We also analyze Shapley ranking as a social welfare function and compare it to approval ranking.

Suggested Citation

  • DEHEZ Pierre, & GINSBURGH Victor,, 2018. "Approval voting and Shapley ranking," CORE Discussion Papers 2018012, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:2018012
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    References listed on IDEAS

    as
    1. Ginsburgh, Victor & Zang, Israël, 2012. "Shapley Ranking of Wines," Journal of Wine Economics, Cambridge University Press, vol. 7(02), pages 169-180, November.
    2. José Alcantud & Annick Laruelle, 2014. "Dis&approval voting: a characterization," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(1), pages 1-10, June.
    3. Antoinette Baujard & Herrade Igersheim, 2010. "Framed-field experiments on approval voting in political contexts. Some teachings," Post-Print halshs-00512525, HAL.
    4. François Maniquet & Philippe Mongin, 2015. "Approval voting and Arrow’s impossibility theorem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(3), pages 519-532, March.
    5. Steven Brams & Peter Fishburn, 2005. "Going from theory to practice: the mixed success of approval voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 25(2), pages 457-474, December.
    6. Saari,Donald G., 2008. "Disposing Dictators, Demystifying Voting Paradoxes," Cambridge Books, Cambridge University Press, number 9780521516051, July - De.
    7. Steven Brams & Richard Potthoff, 2015. "The paradox of grading systems," Public Choice, Springer, vol. 165(3), pages 193-210, December.
    8. Donald Saari & Jill Newenhizen, 1988. "The problem of indeterminacy in approval, multiple, and truncated voting systems," Public Choice, Springer, vol. 59(2), pages 101-120, November.
    9. Saari,Donald G., 2008. "Disposing Dictators, Demystifying Voting Paradoxes," Cambridge Books, Cambridge University Press, number 9780521731607, July - De.
    10. repec:wsi:igtrxx:v:19:y:2017:i:03:n:s0219198917500128 is not listed on IDEAS
    11. Bogomolnaia, Anna & Moulin, Herve & Stong, Richard, 2005. "Collective choice under dichotomous preferences," Journal of Economic Theory, Elsevier, vol. 122(2), pages 165-184, June.
    12. Pierre Dehez, 2017. "On Harsanyi Dividends and Asymmetric Values," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-36, September.
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    More about this item

    Keywords

    approval voting; Shapley value;

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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