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A Theorem on Aggregating Classifications

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  • Mongin, Philippe

  • Maniquet, Francois

Abstract

Suppose that a group of individuals must classify objects into three or more categories, and does so by aggregating the individual classifications. We show that if the classifications, both individual and collective, are required to put at least one object in each category, then no aggregation rule can satisfy a unanimity and an independence condition without being dictatorial. This impossibility theorem extends a result that Kasher and Rubinstein (1997) proved for two categories and complements another that Dokow and Holzman (2010) obtained for three or more categories under the condition that classifications put at most one object in each category. The paper discusses an interpretation of its result both in terms of Kasher and Rubinstein's group identification problem and in terms of Dokow and Holzman's task assignment problem.

Suggested Citation

  • Mongin, Philippe & Maniquet, Francois, 2015. "A Theorem on Aggregating Classifications," HEC Research Papers Series 1116, HEC Paris.
    • Handle: RePEc:ebg:heccah:1116
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    2. Justin Kruger & M. Remzi Sanver, 2021. "An Arrovian impossibility in combining ranking and evaluation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(3), pages 535-555, October.
    3. Jansen, C. & Schollmeyer, G. & Augustin, T., 2018. "A probabilistic evaluation framework for preference aggregation reflecting group homogeneity," Mathematical Social Sciences, Elsevier, vol. 96(C), pages 49-62.
    4. Ozkes, Ali I. & Sanver, M. Remzi, 2023. "Uniform random dictatorship: A characterization without strategy-proofness," Economics Letters, Elsevier, vol. 227(C).
    5. Cailloux, Olivier & Hervouin, Matthieu & Ozkes, Ali I. & Sanver, M. Remzi, 2024. "Classification aggregation without unanimity," Mathematical Social Sciences, Elsevier, vol. 128(C), pages 6-9.
    6. Marc Fleurbaey, 2020. "Philippe Mongin 1950–2020," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(3), pages 399-403, October.
    7. Craven, John, 2024. "Aggregation of ranked categories," Mathematical Social Sciences, Elsevier, vol. 129(C), pages 27-33.
    8. Fioravanti, Federico, 2025. "Fuzzy classification aggregation," Mathematical Social Sciences, Elsevier, vol. 135(C).
    9. Fioravanti, Federico, 2025. "Expert classification aggregation," Mathematical Social Sciences, Elsevier, vol. 137(C).
    10. Jean Baccelli & Marcus Pivato, 2021. "Philippe Mongin (1950–2020)," Theory and Decision, Springer, vol. 90(1), pages 1-9, February.

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    JEL classification:

    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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