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Rationality and Society
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Efficient Fair Division

Help the Worst off or Avoid Envy?

Steven J. Brams

New York University, steven.brams{at}nyu.edu

Daniel L. King

Sarah Lawrence College, dking{at}mail.slc.edu

Two or more players rank a set of indivisible items from best to worst. An efficient allocation of items is characterized, which may satisfy such properties as maximin, Borda maximin, and envy-avoidance. Whereas the two maximin properties are in conflict with envy-avoidance, there is always an efficient allocation that does not ensure envy, but it may not be maximin or Borda maximin. Computer calculations show that maximin allocations lead to envy quite often, but Borda maximin allocations do so only rarely. Implications of the theoretical findings for real-world fair-division problems are discussed.

Key Words: Borda count • envy-freeness • fair division • maximin • Pareto-optimality

Rationality and Society, Vol. 17, No. 4, 387-421 (2005)
DOI: 10.1177/1043463105058317
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