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Size approval voting

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  • Alcalde-Unzu, J.
  • Vorsatz, M.

    (Microeconomics & Public Economics)

Abstract

We propose a new class of voting rules, called Size Approval Voting. According to this rule, the efective weight of a vote from a given individual depends on how many other alternatives the very same individual votes for. In particular, weights are assumed to be non-negative and weakly decreasing in the number of approved alternatives. Then, for a given pro¯le of individual votes, all those alternatives with the maximal sum of weighted votes are elected. We show in our axiomatic analysis that the family of all Size Approval Voting is characterized by a set of natural properties.
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Suggested Citation

  • Alcalde-Unzu, J. & Vorsatz, M., 2007. "Size approval voting," Research Memorandum 008, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    • Handle: RePEc:unm:umamet:2007008
    DOI: 10.26481/umamet.2007008
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    References listed on IDEAS

    as
    1. Jordi Massó & Marc Vorsatz, 2008. "Weighted approval voting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(1), pages 129-146, July.
    2. Sertel, Murat R., 1988. "Characterizing approval voting," Journal of Economic Theory, Elsevier, vol. 45(1), pages 207-211, June.
    3. Carlos Alós-Ferrer, 2006. "A Simple Characterization of Approval Voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(3), pages 621-625, December.
    4. Bernardo Moreno & M. Socorro Puy, 2005. "The scoring rules in an endogenous election," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 25(1), pages 115-125, October.
    5. Jean-François Laslier & Karine Straeten, 2008. "A live experiment on approval voting," Experimental Economics, Springer;Economic Science Association, vol. 11(1), pages 97-105, March.
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    7. 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.
    8. Ching, Stephen, 1996. "A Simple Characterization of Plurality Rule," Journal of Economic Theory, Elsevier, vol. 71(1), pages 298-302, October.
    9. Baigent, Nick & Xu, Yongsheng, 1991. "Independent necessary and sufficient conditions for approval voting," Mathematical Social Sciences, Elsevier, vol. 21(1), pages 21-29, February.
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    12. Sawyer, Jack & MacRae, Duncan, 1962. "Game Theory and Cumulative Voting in Illinois: 1902–1954," American Political Science Review, Cambridge University Press, vol. 56(4), pages 936-946, December.
    13. Steven Brams & Peter Fishburn & Samuel Merrill, 1988. "The responsiveness of approval voting: Comments on Saari and Van Newenhizen," Public Choice, Springer, vol. 59(2), pages 121-131, November.
    14. Miguel Angel Ballester & Pedro Rey-Biel, 2007. "Sincere Voting with Cardinal Preferences: Approval Voting," UFAE and IAE Working Papers 675.07, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    15. Gerald J. Glasser, 1959. "Game Theory and Cumulative Voting for Corporate Directors," Management Science, INFORMS, vol. 5(2), pages 151-156, January.
    16. Dellis, Arnaud & Oak, Mandar P., 2006. "Approval voting with endogenous candidates," Games and Economic Behavior, Elsevier, vol. 54(1), pages 47-76, January.
    17. Merrill, Samuel & Nagel, Jack, 1987. "The Effect of Approval Balloting on Strategic Voting under Alternative Decision Rules," American Political Science Review, Cambridge University Press, vol. 81(2), pages 509-524, June.
    18. Marc Vorsatz, 2007. "Approval Voting on Dichotomous Preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(1), pages 127-141, January.
    19. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-1041, November.
    20. Roberts, Fred S., 1991. "Characterizations of the plurality function," Mathematical Social Sciences, Elsevier, vol. 21(2), pages 101-127, April.
    21. Francesco Sinopoli & Bhaskar Dutta & Jean-François Laslier, 2006. "Approval voting: three examples," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(1), pages 27-38, December.
    22. Chun-Hsien Yeh, 2008. "An efficiency characterization of plurality rule in collective choice problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 34(3), pages 575-583, March.
    23. Fishburn, Peter C., 1978. "Axioms for approval voting: Direct proof," Journal of Economic Theory, Elsevier, vol. 19(1), pages 180-185, October.
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    Cited by:

    1. Olivier Gergaud & Victor Ginsburgh & Juan D. Moreno-Ternero, 2020. "Wine Ratings," Working Papers ECARES 2020-38, ULB -- Universite Libre de Bruxelles.
    2. Gustavo Bergantiños & Juan D. Moreno-Ternero, 2023. "Decentralized revenue sharing from broadcasting sports," Public Choice, Springer, vol. 194(1), pages 27-44, January.
    3. Alcalde-Unzu, Jorge & Moreno-Ternero, Juan D. & Weber, Shlomo, 2022. "The measurement of the value of a language," Journal of Economic Theory, Elsevier, vol. 203(C).
    4. Chris Dong & Patrick Lederer, 2023. "Refined Characterizations of Approval-based Committee Scoring Rules," Papers 2312.08799, arXiv.org, revised Mar 2024.
    5. Martínez, Ricardo & Moreno, Bernardo, 2017. "Qualified voting systems," Mathematical Social Sciences, Elsevier, vol. 88(C), pages 49-54.
    6. Brandl, Florian & Peters, Dominik, 2022. "Approval voting under dichotomous preferences: A catalogue of characterizations," Journal of Economic Theory, Elsevier, vol. 205(C).
    7. Ginsburgh, Victor & Moreno-Ternero, Juan D. & Weber, Shlomo, 2017. "Ranking languages in the European Union: Before and after Brexit," European Economic Review, Elsevier, vol. 93(C), pages 139-151.
    8. 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.
    9. Susumu Cato & Stéphane Gonzalez & Eric Rémila & Philippe Solal, 2022. "Approval voting versus proportional threshold methods: so far and yet so near," Working Papers halshs-03858356, HAL.
    10. Alcalde-Unzu, Jorge & Vorsatz, Marc, 2014. "Non-anonymous ballot aggregation: An axiomatic generalization of Approval Voting," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 69-78.
    11. Efthymios Athanasiou & Juan D. Moreno-Ternero & Shlomo Weber, 2015. "Language learning and communicative benefits," Working Papers 15.09, Universidad Pablo de Olavide, Department of Economics.
    12. Gergaud, Olivier & Ginsburgh, Victor & Moreno-Ternero, Juan D., 2021. "Wine Ratings: Seeking a Consensus among Tasters via Normalization, Approval, and Aggregation," Journal of Wine Economics, Cambridge University Press, vol. 16(3), pages 321-342, August.
    13. 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.
    14. Haris Aziz & Markus Brill & Vincent Conitzer & Edith Elkind & Rupert Freeman & Toby Walsh, 2017. "Justified representation in approval-based committee voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(2), pages 461-485, February.
    15. Alcalde-Unzu, Jorge & Vorsatz, Marc, 2014. "Non-anonymous ballot aggregation: An axiomatic generalization of Approval Voting," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 69-78.
    16. Trevor Leach & Robert C. Powers, 2020. "Majority rule on j-rich ballot spaces," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(4), pages 639-655, April.
    17. 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.
    18. Clinton Gubong Gassi, 2024. "Weighted scoring rules for selecting a compatible committee," Working Papers 2024-04, CRESE.

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    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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