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.
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