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Multinary group identification

Author

Listed:
  • Cho, Wonki Jo

    (School of Economics, Sogang University)

  • Ju, Biung-Ghi

    (Department of Economics, Seoul National University)

Abstract

Group identification refers to the problem of classifying individuals into groups (e.g., racial or ethnic classification). We consider a multinary group identification model where memberships to three or more groups are simultaneously determined based on individual opinions on who belong to what groups. Our main axiom requires that membership to each group, say the group of J's, should depend only on the opinions on who is a J and who is not (that is, independently of the opinions on who is a K or an L). This shares the spirit of Arrow's independence of irrelevant alternatives and therefore is termed independence of irrelevant opinions. Our investigation of multinary group identification and the independence axiom reports a somewhat different message from the celebrated impossibility result by Arrow (1951). We show that the independence axiom, together with symmetry and non-degeneracy, implies the liberal rule (each person self-determines her own membership). This characterization provides a theoretical foundation for the self-identification method commonly used for racial or ethnic classifications.

Suggested Citation

  • Cho, Wonki Jo & Ju, Biung-Ghi, 2017. "Multinary group identification," Theoretical Economics, Econometric Society, vol. 12(2), May.
    • Handle: RePEc:the:publsh:2156
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    References listed on IDEAS

    as
    1. Dinko Dimitrov & Thierry Marchant & Debasis Mishra, 2012. "Separability and aggregation of equivalence relations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(1), pages 191-212, September.
    2. 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.
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    4. Dimitrov, Dinko & Sung, Shao Chin & Xu, Yongsheng, 2007. "Procedural group identification," Mathematical Social Sciences, Elsevier, vol. 54(2), pages 137-146, September.
    5. Dimitrov, D.A. & Sung, S.C., 2003. "On the Axiomatic Characterization of "Who is a J?"," Discussion Paper 2003-89, Tilburg University, Center for Economic Research.
    6. 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.
    7. Samet, Dov & Schmeidler, David, 2003. "Between liberalism and democracy," Journal of Economic Theory, Elsevier, vol. 110(2), pages 213-233, June.
    8. Miller, Alan D., 2008. "Group identification," Games and Economic Behavior, Elsevier, vol. 63(1), pages 188-202, May.
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    10. Blau, Julian H, 1972. "A Direct Proof of Arrow's Theorem," Econometrica, Econometric Society, vol. 40(1), pages 61-67, January.
    11. 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.
    12. Guha, Ashok, 1972. "Neutrality, Monotonicity, and the Right of Veto," Econometrica, Econometric Society, vol. 40(5), pages 821-826, September.
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    Citations

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    Cited by:

    1. Alcantud, José Carlos R. & Laruelle, Annick, 2018. "Collective identity functions with status quo," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 159-166.
    2. Federico Fioravanti & Fernando Tohmé, 2021. "Alternative Axioms in Group Identification Problems," Journal of Classification, Springer;The Classification Society, vol. 38(2), pages 353-362, July.
    3. John Craven, 2023. "Self-designation and group allocation," Theory and Decision, Springer, vol. 94(1), pages 121-133, January.
    4. Cho, Wonki Jo & Park, Chang Woo, 2018. "Fractional group identification," Journal of Mathematical Economics, Elsevier, vol. 77(C), pages 66-75.
    5. Cho, Wonki Jo & Ju, Biung-Ghi, 2020. "Group identification: An integrated approach," Games and Economic Behavior, Elsevier, vol. 123(C), pages 171-181.
    6. Cho, Wonki Jo, 2018. "Fairness in group identification," Mathematical Social Sciences, Elsevier, vol. 94(C), pages 35-40.
    7. 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.
    8. Federico Fioravanti & Fernando Tohmé, 2020. "Asking Infinite Voters ‘Who is a J?’: Group Identification Problems in ℕ$\mathbb {N}$," Journal of Classification, Springer;The Classification Society, vol. 37(1), pages 58-65, April.
    9. Craven, John, 2024. "Aggregation of ranked categories," Mathematical Social Sciences, Elsevier, vol. 129(C), pages 27-33.
    10. Cho, Wonki Jo & Moreno-Ternero, Juan D., 2024. "On reaching social consent," Journal of Mathematical Economics, Elsevier, vol. 110(C).

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    More about this item

    Keywords

    Group identification; independence of irrelevant opinions; symmetry; liberalism; one-vote rules;
    All these keywords.

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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