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Fractional group identification

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  • Cho, Wonki Jo
  • Park, Chang Woo
Abstract
We study group identification problems, the objective of which is to classify agents into groups based on individual opinions. Our point of departure from the literature is to allow membership to be fractional, to qualify the extent of belonging. Examining implications of independence of irrelevant opinions, we identify and characterize four nested families of rules. The four families include the weighted-average rules, which are obtained by taking a weighted average of all entries of a problem, and the fractional consent rules, which adapt the consent rules from the binary model to our multinary setup, balancing two principles in group identification, namely liberalism and social consent. Existing characterizations of the one-vote rules, the consent rules, and the liberal rule follow from ours.

Suggested Citation

  • Cho, Wonki Jo & Park, Chang Woo, 2018. "Fractional group identification," Journal of Mathematical Economics, Elsevier, vol. 77(C), pages 66-75.
    • Handle: RePEc:eee:mateco:v:77:y:2018:i:c:p:66-75
    DOI: 10.1016/j.jmateco.2018.06.004
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    References listed on IDEAS

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    1. Samet, Dov & Schmeidler, David, 2003. "Between liberalism and democracy," Journal of Economic Theory, Elsevier, vol. 110(2), pages 213-233, June.
    2. Miller, Alan D., 2008. "Group identification," Games and Economic Behavior, Elsevier, vol. 63(1), pages 188-202, May.
    3. Dimitrov, Dinko & Sung, Shao Chin & Xu, Yongsheng, 2007. "Procedural group identification," Mathematical Social Sciences, Elsevier, vol. 54(2), pages 137-146, September.
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    6. Biung-Ghi Ju, 2010. "Individual powers and social consent: an axiomatic approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(4), pages 571-596, April.
    7. Cho, Wonki Jo & Ju, Biung-Ghi, 2017. "Multinary group identification," Theoretical Economics, Econometric Society, vol. 12(2), May.
    8. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, vol. 100(2), pages 295-328, October.
    9. Biung-Ghi Ju, 2013. "On the characterization of liberalism by Samet and Schmeidler," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 359-366, February.
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    12. Nicolas, Houy, 2007. ""I want to be a J!": Liberalism in group identification problems," Mathematical Social Sciences, Elsevier, vol. 54(1), pages 59-70, July.
    13. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
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    Cited by:

    1. Federico Fioravanti & Fernando Tohm'e, 2019. "Fuzzy Group Identification Problems," Papers 1912.05540, arXiv.org, revised Jul 2021.
    2. Federico Fioravanti, 2024. "Fuzzy Classification Aggregation," Working Papers 312, Red Nacional de Investigadores en Economía (RedNIE).
    3. Cho, Wonki Jo, 2018. "Fairness in group identification," Mathematical Social Sciences, Elsevier, vol. 94(C), pages 35-40.
    4. 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.
    5. Cho, Wonki Jo & Moreno-Ternero, Juan D., 2024. "On reaching social consent," Journal of Mathematical Economics, Elsevier, vol. 110(C).
    6. Federico Fioravanti, 2024. "Fuzzy Classification Aggregation," Papers 2402.17620, arXiv.org, revised Aug 2024.

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