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

Takahiro Suzuki and Masahide Horita

Mathematical Social Sciences, 2024, vol. 129, issue C, 12-19

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.

Keywords: Social ranking problem; Preference extension; Ceteris paribus comparison; Self-reflection (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matsoc:v:129:y:2024:i:c:p:12-19

DOI: 10.1016/j.mathsocsci.2024.02.003

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