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Approval voting and Shapley ranking

Author

Listed:
  • Pierre Dehez

    (University of Louvain)

  • Victor Ginsburgh

    (University of Brussels)

Abstract

Approval voting allows electors to list any number of candidates and their final scores are obtained by summing the votes cast in their favor. Equal-and-even cumulative voting instead follows the One-person-one-vote principle by endowing each elector with a single vote that may be distributed evenly among several candidates. It corresponds to satisfaction approval voting, introduced by Brams and Kilgour (in: Fara et al (eds) Voting power and procedures. Essays in honor of Dan Fesenthal and Moshé Machover, Springer, Heidelberg, 2014) as an extension of approval voting to a multiwinner election. It also corresponds to the concept of Shapley ranking, introduced by Ginsburgh and Zang (J Wine Econ 7:169–180, 2012) as the Shapley value of a cooperative game with transferable utility. In the present paper, we provide an axiomatic foundation for Shapley ranking and analyze the properties of the resulting social welfare function.

Suggested Citation

  • Pierre Dehez & Victor Ginsburgh, 2020. "Approval voting and Shapley ranking," Public Choice, Springer, vol. 184(3), pages 415-428, September.
    • Handle: RePEc:kap:pubcho:v:184:y:2020:i:3:d:10.1007_s11127-019-00729-w
    DOI: 10.1007/s11127-019-00729-w
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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 & D. Marc Kilgour & Richard F. Potthoff, 2019. "Multiwinner approval voting: an apportionment approach," Public Choice, Springer, vol. 178(1), pages 67-93, January.
    3. 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.
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    7. 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.
    8. Saari,Donald G., 2008. "Disposing Dictators, Demystifying Voting Paradoxes," Cambridge Books, Cambridge University Press, number 9780521516051, September.
    9. Steven J. Brams & D. Marc Kilgour, 2014. "Satisfaction Approval Voting," Studies in Choice and Welfare, in: Rudolf Fara & Dennis Leech & Maurice Salles (ed.), Voting Power and Procedures, edition 127, pages 323-346, Springer.
    10. Steven Brams & Richard Potthoff, 2015. "The paradox of grading systems," Public Choice, Springer, vol. 165(3), pages 193-210, December.
    11. 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.
    12. Saari,Donald G., 2008. "Disposing Dictators, Demystifying Voting Paradoxes," Cambridge Books, Cambridge University Press, number 9780521731607, September.
    13. 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.
    14. Bogomolnaia, Anna & Moulin, Herve & Stong, Richard, 2005. "Collective choice under dichotomous preferences," Journal of Economic Theory, Elsevier, vol. 122(2), pages 165-184, June.
    15. Antoinette Baujard & Herrade Igersheim, 2010. "Framed Field Experiments on Approval Voting: Lessons from the 2002 and 2007 French Presidential Elections," Studies in Choice and Welfare, in: Jean-François Laslier & M. Remzi Sanver (ed.), Handbook on Approval Voting, chapter 0, pages 357-395, Springer.
    16. Jean-François Laslier & M. Remzi Sanver (ed.), 2010. "Handbook on Approval Voting," Studies in Choice and Welfare, Springer, number 978-3-642-02839-7, December.
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    Cited by:

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    2. Yakov Ben-Haim, 2021. "Approval and plurality voting with uncertainty: Info-gap analysis of robustness," Public Choice, Springer, vol. 189(1), pages 239-256, October.
    3. Ritu Dutta & Rajnish Kumnar & Surajit Borkotokey, 2023. "How to choose a Compatible Committee?," Papers 2308.03507, arXiv.org.
    4. Victor Ginsburgh & Juan D. Moreno-Ternero, 2023. "The Eurovision Song Contest: voting rules, biases and rationality," Journal of Cultural Economics, Springer;The Association for Cultural Economics International, vol. 47(2), pages 247-277, June.
    5. Ricardo Martínez & Joaquín Sánchez-Soriano, 2021. "Mathematical indices for the influence of risk factors on the lethality of a disease," ThE Papers 21/02, Department of Economic Theory and Economic History of the University of Granada..
    6. Ritu Dutta & Souvik Roy & Surajit Borkotokey, 2023. "The Generalized Shapley Value of Cooperative Games as a Social Preference Function," Group Decision and Negotiation, Springer, vol. 32(2), pages 277-300, April.
    7. Ricardo Mart'inez & Joaqu'in S'anchez-Soriano, 2023. "Order preservation with dummies in the musseum pass problem," Papers 2307.00622, arXiv.org.
    8. Ricardo Martínez & Joaquín Sánchez-Soriano, 2021. "Social solidarity with dummies in the museum pass problem," ThE Papers 21/11, Department of Economic Theory and Economic History of the University of Granada..

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    More about this item

    Keywords

    Approval voting; Equal-and-even cumulative voting; Ranking game; Shapley value;
    All these keywords.

    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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