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Fairness in group identification

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  • Cho, Wonki Jo

Abstract

We study the problem of classifying individuals into groups, using agents’ opinions on who belong to which group as input. Our focus is on the rules that satisfy equal treatment of equals, a minimal fairness property, in addition to independence of irrelevant opinions and non-degeneracy. We show that a rule satisfies the three axioms if and only if it is the liberal rule, a strong one-vote rule, a one-row rule, or a one-column rule. The last three families of rules can be ruled out by simple, intuitive properties. Thus, invoking equal treatment of equals, which is substantially weaker than symmetry, we obtain a characterization of the liberal rule.

Suggested Citation

  • Cho, Wonki Jo, 2018. "Fairness in group identification," Mathematical Social Sciences, Elsevier, vol. 94(C), pages 35-40.
    • Handle: RePEc:eee:matsoc:v:94:y:2018:i:c:p:35-40
    DOI: 10.1016/j.mathsocsci.2018.04.002
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    References listed on IDEAS

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    1. 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.
    2. Cho, Wonki Jo & Ju, Biung-Ghi, 2017. "Multinary group identification," Theoretical Economics, Econometric Society, vol. 12(2), May.
    3. Dimitrov, Dinko & Sung, Shao Chin & Xu, Yongsheng, 2007. "Procedural group identification," Mathematical Social Sciences, Elsevier, vol. 54(2), pages 137-146, September.
    4. 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.
    5. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-519, March.
    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.
    9. Cho, Wonki Jo & Park, Chang Woo, 2018. "Fractional group identification," Journal of Mathematical Economics, Elsevier, vol. 77(C), pages 66-75.
    10. Chun, Youngsub & Mitra, Manipushpak & Mutuswami, Suresh, 2014. "Characterizations of pivotal mechanisms in the queueing problem," Mathematical Social Sciences, Elsevier, vol. 72(C), pages 62-66.
    11. Murat Çengelci & M. Sanver, 2010. "Simple Collective Identity Functions," Theory and Decision, Springer, vol. 68(4), pages 417-443, April.
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