Partial-implementation invariance and claims problems

Bas Dietzenbacher, Yuki Tamura, William Thomson

Research output: Working paper / PreprintWorking paper

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In the context of claims problems, we formulate an invariance axiom of a rule with respect to its “partial implementation”: having applied the rule to a problem and distributed their awards to some of the claimants, we consider the problem obtained by setting the claims of these claimants equal to zero and decreasing the endowment by the sum of their awards; we require that in this problem the rule assigns to each remaining claimant the same amount as it did initially. We formulate several variants of this requirement of “partial-implementation invariance” and a “converse” of it. We investigate how it relates to known axioms and ask whether it is preserved under certain “operators” that have been defined on the space of rules. Our main result is a fixed-population characterization of a family of rules introduced and characterized by Young (1987) in a variable-population framework, known as the “parametric rules”.
Original languageEnglish
PublisherMaastricht University, Graduate School of Business and Economics
Number of pages33
Publication statusPublished - 30 Mar 2023

Publication series

SeriesGSBE Research Memoranda

JEL classifications

  • d63 - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
  • d71 - "Social Choice; Clubs; Committees; Associations"
  • d74 - "Conflict; Conflict Resolution; Alliances"


  • claims problems
  • partial-implementation invariance
  • consistency
  • Young's rules


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