# American Institute of Mathematical Sciences

March & April  2015, 2(3&4): 363-382. doi: 10.3934/jdg.2015011

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

 1 Department of Economics, University of Rochester, Rochester, NY 14627, United States

Received  July 2015 Revised  October 2015 Published  November 2015

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.
Citation: William Thomson. For claims problems, another compromise between the proportional and constrained equal awards rules. Journal of Dynamics & Games, 2015, 2 (3&4) : 363-382. doi: 10.3934/jdg.2015011
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