The two-agent claims-truncated proportional rule has no consistent extension: A constructive proof
We consider the problem of adjudicating conflicting claims. A rule to solve such problems 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 a that point. It says that each remaining claimant should receive what he received initially. We consider the version of the proportional rule that selects for each problem, the awards vector that is proportional to the vector of claims truncated at the amount to divide. We illustrate a geometric technique developed by Thomson (2001) by showing that the two-claimant truncated proportional rule has no consistent extension to general populations (Dagan and Volij, 1997).
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