Partial-implementation invariance and claims problems

Bas Dietzenbacher (), Yuki Tamura and William Thomson ()
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Bas Dietzenbacher: Maastricht University
William Thomson: University of Rochester

Social Choice and Welfare, 2024, vol. 63, issue 1, No 9, 203-229

Abstract: Abstract In the context of claims problems, we formulate an axiom of invariance of a rule with respect to its “partial implementation”: having applied the rule to a problem in its domain of definition, we imagine some claimants picking up their awards and we consider the problem of distributing what remains of the endowment among the other claimants: in this problem, the claims of the first group of claimants are set equal to zero and the endowment is adjusted down by the sum of their awards; we require of a rule that it assign 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 the two requirements relate to known axioms and ask whether they are preserved by certain operators that have been defined on the space of rules. Our main result is a characterization in our fixed-population framework of a family of rules introduced and characterized by Young (Math Oper Res 12(3):398–414, 1987) in a variable-population framework. These rules are known under the name of “parametric rules”.

Date: 2024
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DOI: 10.1007/s00355-024-01528-z

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