# On the existence of consistent rules to adjudicate conflicting claims: a constructive geometric approach

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## Abstract

For the problem of adjudicating conflicting claims, a rule is consistent if the choice it makes for each problem is always in agreement with the choice it makes for each “reduced problem” obtained by imagining that some claimants leave with their awards and reassessing the situation from the viewpoint of the remaining claimants. We develop a general technique to determine whether a given two-claimant rule admits a consistent extension to general populations, and to identify this extension if it exists. We apply the technique to a succession of examples.

## Keywords

Claims problems Consistent extensions Proportional rule Constrained equal awards rule Constrained equal losses rule## JEL Classification

C79 D63 D74## Preview

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