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Which set of agents plays a key role? An impossibility in transforming binary relations

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  • Suzuki, Takahiro
  • Horita, Masahide

Abstract

When provided with the performance ranking of multiple sets of agents as input, which set of agents is expected to play the key role? To address this question, we introduce a new rule (transformation rule) that maps a performance ranking over sets of agents into a contributing ranking over sets of agents. Preference extension (PE) and social ranking problem (SRP) represent two special cases. We prove an impossibility theorem: in a sufficiently rich environment, there is no transformation rule that satisfies ceteris paribus weak dominance, self-reflection, and triple-acyclicity. The impossibility is novel in that it is degenerated in PE/SRP models.

Suggested Citation

  • Suzuki, Takahiro & Horita, Masahide, 2024. "Which set of agents plays a key role? An impossibility in transforming binary relations," Mathematical Social Sciences, Elsevier, vol. 129(C), pages 12-19.
    • Handle: RePEc:eee:matsoc:v:129:y:2024:i:c:p:12-19
    DOI: 10.1016/j.mathsocsci.2024.02.003
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    References listed on IDEAS

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    1. Gehrlein, William V., 1985. "The Condorcet criterion and committee selection," Mathematical Social Sciences, Elsevier, vol. 10(3), pages 199-209, December.
    2. Fishburn, Peter C., 1992. "Signed orders and power set extensions," Journal of Economic Theory, Elsevier, vol. 56(1), pages 1-19, February.
    3. Thomas C. Ratliff, 2003. "Some startling inconsistencies when electing committees," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(3), pages 433-454, December.
    4. Timothy C. Y. Chan & Justin A. Cho & David C. Novati, 2012. "Quantifying the Contribution of NHL Player Types to Team Performance," Interfaces, INFORMS, vol. 42(2), pages 131-145, April.
    5. Kamwa, Eric, 2017. "On stable rules for selecting committees," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 36-44.
    6. Giulia Bernardi & Roberto Lucchetti & Stefano Moretti, 2019. "Ranking objects from a preference relation over their subsets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(4), pages 589-606, April.
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