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Classification aggregation without unanimity

Author

Listed:
  • Cailloux, Olivier
  • Hervouin, Matthieu
  • Ozkes, Ali I.
  • Sanver, M. Remzi

Abstract

A classification is a surjective mapping from a set of objects to a set of categories. A classification aggregation function aggregates every vector of classifications into a single one. We show that every citizen sovereign and independent classification aggregation function is essentially a dictatorship. This impossibility implies an earlier result of Maniquet and Mongin (2016), who show that every unanimous and independent classification aggregation function is a dictatorship. The relationship between the two impossibilities is reminiscent to the relationship between Wilson’s (1972) and Arrow’s (1951) impossibilities in preference aggregation. Moreover, while the Maniquet-Mongin impossibility rests on the existence of at least three categories, we propose an alternative proof technique that covers the case of two categories, except when the number of objects is also two. We also identify all independent and unanimous classification aggregation functions for the case of two categories and two objects.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matsoc:v:128:y:2024:i:c:p:6-9
    DOI: 10.1016/j.mathsocsci.2024.01.002
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    References listed on IDEAS

    as
    1. Ozkes, Ali Ihsan & Sanver, M. Remzi, 2017. "Absolute qualified majoritarianism: How does the threshold matter?," Economics Letters, Elsevier, vol. 153(C), pages 20-22.
    2. Dietrich, Franz, 2015. "Aggregation theory and the relevance of some issues to others," Journal of Economic Theory, Elsevier, vol. 160(C), pages 463-493.
    3. Maniquet, François & Mongin, Philippe, 2016. "A theorem on aggregating classifications," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 6-10.
    4. MANIQUET, François & MONGIN, Philippe, 2014. "Judgment aggregation theory can entail new social choice results," LIDAM Discussion Papers CORE 2014054, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Rubinstein, Ariel & Fishburn, Peter C., 1986. "Algebraic aggregation theory," Journal of Economic Theory, Elsevier, vol. 38(1), pages 63-77, February.
    6. Bonifacio Llamazares, 2013. "On the structure of voting systems between two alternatives," Review of Economic Design, Springer;Society for Economic Design, vol. 17(3), pages 239-248, September.
    7. Wilson, Robert, 1972. "Social choice theory without the Pareto Principle," Journal of Economic Theory, Elsevier, vol. 5(3), pages 478-486, December.
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