On arbitration schemes for a wealth distribution problem

• Published in: Theory and decision 1978-07, Vol.9 (3), p.295-312
• Main Author: Neave, Edwin H
• Format: Article
• Language: English
• Subjects: Arbitration/Arbitrator; Distribution/Distributions; Wealth/Wealthy
• ISSN: 0040-5833; 1573-7187
• DOI: 10.1007/BF00133457

An arbitration scheme is developed for resolving a distribution of wealth problem by applying J. F. Nash's assumptions ('The Bargaining Problem,' Econometrica, 1950, 18, 155-162) to marginal rather than to total utilities. The problem considered is that of distributing a fixed amount of wealth between two claimants, & properties of this problem's Nash solution are compared with those of the marginal utility solution. The Nash solution is shown to emphasize application of symmetry considerations to the status quo ante, & the marginal utility solution emphasizes their application to the players' postarbitration positions (as measured by functions that fully describe the players' utilities but that are independent of positive linear transformations). While the Nash assumptions are appropriate for many arbitration problems in which a solution reflects the players' status quo ante positions, the marginal utility assumptions are useful when it is desired that a solution attempt to minimize postarbitration differences between the players' positions. The latter seem to be preferable in contexts where an arbitrator weights the solution's effects on outcomes more heavily than he weights considerations of the status quo ante. Examples are situations such as those involving income redistribution, where attempts to reduce inequality may guide the redistribution decisions. The effects on each type of solution of changes in the status quo ante are related to the risk preference properties of the players' utilities. 1 Figure. AA.