For claims problems, another compromise between the proportional and constrained equal awards rules

William  Thomson

doi:10.3934/jdg.2015011

Article Contents

2015, Volume 2, Issue 3&4: 363-382. Doi: 10.3934/jdg.2015011

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For claims problems, another compromise between the proportional and constrained equal awards rules

William Thomson^1,

1.
Department of Economics, University of Rochester, Rochester, NY 14627

Received: June 30, 2015

Revised: September 30, 2015

Published: June 2015

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Abstract

For the problem of adjudicating conflicting claims, we propose to compromise in the two-claimant case between the proportional and constrained equal awards rules by taking, for each problem, a weighted average of the awards vectors these two rules recommend. We allow the weights to depend on the claims vector, thereby generating a large family of rules. We identify the members of the family that satisfy particular properties.We then ask whether the rules can be extended topopulations of arbitrary sizes by imposing ``consistency": the recommendation made foreach problem should be ``in agreement" with the recommendation madefor each reduced problem that results when some claimants have received theirawards and left. We show that only the proportional and constrained equal awards rules qualify.We also study a dual compromise between the proportional and constrained equal losses rules.

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Mathematics Subject Classification: 62P20, 91B15, 97M40.

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