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Approval Voting and Shapley Ranking

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  • Pierre Dehez
  • Victor Ginsburgh

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-onevote principle by endowing voters with a single vote that they may freely distribute among candidates. In this paper, we show that to be fair, such a ranking requires a uniform distribution. It corresponds to Shapley ranking that was introduced to rank wines as the Shapley value of a cooperative game with transferable utility. 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

  • Pierre Dehez & Victor Ginsburgh, 2018. "Approval Voting and Shapley Ranking," Working Papers ECARES 2018-09, ULB -- Universite Libre de Bruxelles.
  • Handle: RePEc:eca:wpaper:2013/269405
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    References listed on IDEAS

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    1. Ginsburgh, Victor & Zang, Israël, 2012. "Shapley Ranking of Wines," Journal of Wine Economics, Cambridge University Press, vol. 7(2), pages 169-180, November.
    2. Steven J. Brams & Peter C. Fishburn, 2010. "Going from Theory to Practice: The Mixed Success of Approval Voting," Studies in Choice and Welfare, in: Jean-François Laslier & M. Remzi Sanver (ed.), Handbook on Approval Voting, chapter 0, pages 19-37, Springer.
    3. 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.
    4. Antoinette Baujard & Herrade Igersheim, 2010. "Framed-field experiments on approval voting in political contexts. Some teachings," Post-Print halshs-00512525, HAL.
    5. 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.
    6. Saari,Donald G., 2008. "Disposing Dictators, Demystifying Voting Paradoxes," Cambridge Books, Cambridge University Press, number 9780521516051, February.
    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, February.
    10. 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.
    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. Jean-François Laslier & M. Remzi Sanver (ed.), 2010. "Handbook on Approval Voting," Studies in Choice and Welfare, Springer, number 978-3-642-02839-7, August.
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    More about this item

    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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