Abstract.
Suppose that a certain quantity M of money and a finite number of indivisible items are to be distributed among n people, all of whom have equal claims on the whole. Different allocations are presented using various criteria of fairness in the special case where each player's utility function is additively separable. An allocation is “money-egalitarian-equivalent” (MEE) if each player's monetary valuation of his or her bundle is a fixed constant. We show that there is an essentially unique allocation that is MEE and Pareto-optimal; it is also envy-free. Alternatively, the “gain” of a player may be defined as the difference between how the player evaluates his bundle and an exact nth part of the whole according to his numerical evaluation of the whole. A “gain-maximin” criterion would maximize the minimum gain obtained by any player. We show that Knaster's procedure finds an allocation which is optimal under the gain-maximin criterion. That allocation is not necessarily envy-free, so we also find the envy-free allocation that is optimal under the gain-maximin criterion among all envy-free allocations. It turns out that, even though there exist allocations that are simultaneously envy-free and Pareto-optimal, this optimal allocation may fail to be Pareto-optimal, and it may also violate monotonicity criteria.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 30 September 1996/Accepted: 6 March 2002
The author would like to thank Professor William Thomson for a discussion on this subject; and he would like to thank the anonymous referees, who made many substantive suggestions for improving this paper – shortening it, streamlining the arguments, improving the terminology, making further ties with the literature, and improving the exposition.
Rights and permissions
About this article
Cite this article
Willson, S. Money-egalitarian-equivalent and gain-maximin allocations of indivisible items with monetary compensation. Soc Choice Welfare 20, 247–259 (2003). https://doi.org/10.1007/s003550200178
Issue Date:
DOI: https://doi.org/10.1007/s003550200178