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Fair sharing under dichotomous preferences

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  • Duddy, Conal

Abstract

In an important article on collective choice with dichotomous preferences, Bogomolnaia et al. (2005) propose a fairness criterion called fair welfare share. We argue that this criterion permits mechanisms that are not fair and we propose an alternative fairness concept called proportional sharing. It guarantees to each subgroup, such as a social class, gender or ethnic group, a fair probability that at least one of its members will like the final outcome. It is compatible with anonymity, neutrality, ex ante efficiency and strategy-proofness if and only if there are at most four agents or at most three possible outcomes.

Suggested Citation

  • Duddy, Conal, 2015. "Fair sharing under dichotomous preferences," Mathematical Social Sciences, Elsevier, vol. 73(C), pages 1-5.
    • Handle: RePEc:eee:matsoc:v:73:y:2015:i:c:p:1-5
    DOI: 10.1016/j.mathsocsci.2014.10.005
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    References listed on IDEAS

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    1. Bhaskar Dutta & Hans Peters & Arunava Sen, 2008. "Strategy-proof cardinal decision schemes," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(4), pages 701-702, May.
    2. Bogomolnaia, Anna & Moulin, Herve & Stong, Richard, 2005. "Collective choice under dichotomous preferences," Journal of Economic Theory, Elsevier, vol. 122(2), pages 165-184, June.
    3. Gibbard, Allan, 1977. "Manipulation of Schemes That Mix Voting with Chance," Econometrica, Econometric Society, vol. 45(3), pages 665-681, April.
    4. 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:

    1. Tom Demeulemeester & Dries Goossens & Ben Hermans & Roel Leus, 2023. "Fair integer programming under dichotomous and cardinal preferences," Papers 2306.13383, arXiv.org, revised Apr 2024.
    2. Brandl, Florian & Brandt, Felix & Greger, Matthias & Peters, Dominik & Stricker, Christian & Suksompong, Warut, 2022. "Funding public projects: A case for the Nash product rule," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    3. Mashbat Suzuki & Jeremy Vollen, 2024. "Maximum Flow is Fair: A Network Flow Approach to Committee Voting," Papers 2406.14907, arXiv.org.
    4. Markus Brill & Paul Gölz & Dominik Peters & Ulrike Schmidt-Kraepelin & Kai Wilker, 2022. "Approval-based apportionment," Post-Print hal-03816043, HAL.
    5. Gogulapati Sreedurga & Soumyarup Sadhukhan & Souvik Roy & Yadati Narahari, 2022. "Characterization of Group-Fair Social Choice Rules under Single-Peaked Preferences," Papers 2207.07984, arXiv.org.
    6. Felix Brandt & Matthias Greger & Erel Segal-Halevi & Warut Suksompong, 2023. "Coordinating Charitable Donations," Papers 2305.10286, arXiv.org, revised Sep 2024.
    7. Freeman, Rupert & Pennock, David M. & Peters, Dominik & Wortman Vaughan, Jennifer, 2021. "Truthful aggregation of budget proposals," Journal of Economic Theory, Elsevier, vol. 193(C).
    8. Xiaohui Bei & Guangda Huzhang & Warut Suksompong, 2020. "Truthful fair division without free disposal," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(3), pages 523-545, October.
    9. Florian Brandl & Felix Brandt & Matthias Greger & Dominik Peters & Christian Stricker & Warut Suksompong, 2022. "Funding public projects: A case for the Nash product rule," Post-Print hal-03818329, HAL.
    10. Soroush Ebadian & Anson Kahng & Dominik Peters & Nisarg Shah, 2022. "Optimized Distortion and Proportional Fairness in Voting," Post-Print hal-03834512, HAL.
    11. Haris Aziz & Xinhang Lu & Mashbat Suzuki & Jeremy Vollen & Toby Walsh, 2023. "Best-of-Both-Worlds Fairness in Committee Voting," Papers 2303.03642, arXiv.org, revised Dec 2023.
    12. Florian Brandl & Felix Brandt & Matthias Greger & Dominik Peters & Christian Stricker & Warut Suksompong, 2020. "Funding Public Projects: A Case for the Nash Product Rule," Papers 2005.07997, arXiv.org, revised Oct 2021.
    13. Xiaohui Bei & Guangda Huzhang & Warut Suksompong, 2018. "Truthful Fair Division without Free Disposal," Papers 1804.06923, arXiv.org, revised Apr 2020.

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