IDEAS home Printed from https://ideas.repec.org/p/ulp/sbbeta/2019-17.html
   My bibliography  Save this paper

Approval voting and Shapley ranking

Author

Listed:
  • Pierre Dehez
  • Victor Ginsburgh

Abstract

Approval voting allows electors to list any number of candidates and their 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 electors with a single vote that they may evenly distribute among several candidates. It corresponds to satisfaction approval voting introduced by Brams and Kilgour (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 (2012) as the Shapley value of a cooperative game with transferable utility. In the present paper, we provide an axiomatic foundation of Shapley ranking and analyze the properties of the resulting social welfare function.

Suggested Citation

  • Pierre Dehez & Victor Ginsburgh, 2019. "Approval voting and Shapley ranking," Working Papers of BETA 2019-17, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    • Handle: RePEc:ulp:sbbeta:2019-17
    as

    Download full text from publisher

    File URL: http://beta.u-strasbg.fr/WP/2019/2019-17.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. Saari,Donald G., 2008. "Disposing Dictators, Demystifying Voting Paradoxes," Cambridge Books, Cambridge University Press, number 9780521731607, October.
    5. 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.
    6. Bogomolnaia, Anna & Moulin, Herve & Stong, Richard, 2005. "Collective choice under dichotomous preferences," Journal of Economic Theory, Elsevier, vol. 122(2), pages 165-184, June.
    7. Ginsburgh, Victor & Zang, Israël, 2012. "Shapley Ranking of Wines," Journal of Wine Economics, Cambridge University Press, vol. 7(2), pages 169-180, November.
    8. Antoinette Baujard & Herrade Igersheim, 2010. "Framed-field experiments on approval voting in political contexts. Some teachings," Post-Print halshs-00512525, HAL.
    9. 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.
    10. 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.
    11. Steven Brams & Richard Potthoff, 2015. "The paradox of grading systems," Public Choice, Springer, vol. 165(3), pages 193-210, December.
    12. Robert J. Weber, 1995. "Approval Voting," Journal of Economic Perspectives, American Economic Association, vol. 9(1), pages 39-49, Winter.
    13. 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.
    14. Saari,Donald G., 2008. "Disposing Dictators, Demystifying Voting Paradoxes," Cambridge Books, Cambridge University Press, number 9780521516051, October.
    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, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ritu Dutta & Rajnish Kumnar & Surajit Borkotokey, 2023. "How to choose a Compatible Committee?," Papers 2308.03507, arXiv.org.
    2. 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.
    3. Ricardo Mart'inez & Joaqu'in S'anchez-Soriano, 2023. "Order preservation with dummies in the musseum pass problem," Papers 2307.00622, arXiv.org.
    4. 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..
    5. Gustavo Bergantiños & Juan D. Moreno-Ternero, 2023. "Decentralized revenue sharing from broadcasting sports," Public Choice, Springer, vol. 194(1), pages 27-44, January.
    6. 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.
    7. 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.
    8. 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..

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Erdamar, Bora & Sanver, M. Remzi & Sato, Shin, 2017. "Evaluationwise strategy-proofness," Games and Economic Behavior, Elsevier, vol. 106(C), pages 227-238.
    2. Conal Duddy & Ashley Piggins & William Zwicker, 2016. "Aggregation of binary evaluations: a Borda-like approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(2), pages 301-333, February.
    3. Carlos Alós-Ferrer & Ðura-Georg Granić, 2012. "Two field experiments on Approval Voting in Germany," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(1), pages 171-205, June.
    4. Markus Brill & Paul Gölz & Dominik Peters & Ulrike Schmidt-Kraepelin & Kai Wilker, 2022. "Approval-based apportionment," Post-Print hal-03816043, HAL.
    5. Justin Kruger & M. Remzi Sanver, 2021. "An Arrovian impossibility in combining ranking and evaluation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(3), pages 535-555, October.
    6. Markus Brill & Jean-François Laslier & Piotr Skowron, 2018. "Multiwinner approval rules as apportionment methods," Journal of Theoretical Politics, , vol. 30(3), pages 358-382, July.
    7. Antoinette Baujard & Frédéric Gavrel & Herrade Igersheim & Jean-François Laslier & Isabelle Lebon, 2014. "Who's favored by evaluative voting? An experiment conducted during the 2012 French presidential election," Working Papers halshs-01090234, HAL.
    8. Antoinette Baujard & Frédéric Gavrel & Herrade Igersheim & Jean-François Laslier & Isabelle Lebon, 2013. "Who’s Favored by Evaluative Voting ? An Experiment Conducted During the 2012 French Presidential Election," Working Papers of BETA 2013-08, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    9. Arnaud Dellis & Mandar Oak, 2016. "Multiple votes, multiple candidacies and polarization," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 1-38, January.
    10. Maurice Salles, 2014. "‘Social choice and welfare’ at 30: its role in the development of social choice theory and welfare economics," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(1), pages 1-16, January.
    11. Bouton, Laurent & Castanheira, Micael & Llorente-Saguer, Aniol, 2016. "Divided majority and information aggregation: Theory and experiment," Journal of Public Economics, Elsevier, vol. 134(C), pages 114-128.
    12. Neal D. Hulkower & John Neatrour, 2019. "The Power of None," SAGE Open, , vol. 9(1), pages 21582440198, March.
    13. Carlos Alós-Ferrer & Johannes Buckenmaier, 2018. "Strictly sincere best responses under approval voting and arbitrary preferences," ECON - Working Papers 302, Department of Economics - University of Zurich.
    14. Alós-Ferrer, Carlos & Buckenmaier, Johannes, 2019. "Strongly sincere best responses under approval voting and arbitrary preferences," Games and Economic Behavior, Elsevier, vol. 117(C), pages 388-401.
    15. Aki Lehtinen, 2011. "A welfarist critique of social choice theory," Journal of Theoretical Politics, , vol. 23(3), pages 359-381, July.
    16. Matías Núñez, 2014. "The strategic sincerity of Approval voting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(1), pages 157-189, May.
    17. Haradhan Kumar Mohajan, 2011. "Approval Voting: A Multi-outcome Election," KASBIT Business Journals (KBJ), Khadim Ali Shah Bukhari Institute of Technology (KASBIT), vol. 4, pages 77-88, December.
    18. Tanya Gibbs & Henry W. Chappell, Jr., 2021. "Elections with Multiple Positive and Negative Votes," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 38(1), pages 37-47, December.
    19. repec:ksb:journl:v:4:y:2011:i:1:p:77-88 is not listed on IDEAS
    20. Wu-Hsiung Huang, 2014. "Singularity and Arrow’s paradox," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(3), pages 671-706, March.
    21. Wesley H. Holliday & Eric Pacuit, 2020. "Arrow’s decisive coalitions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(2), pages 463-505, March.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ulp:sbbeta:2019-17. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/bestrfr.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.