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Twofold Optimality of the Relative Utilitarian Bargaining Solution

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Author Info
Pivato, Marcus

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Abstract

Given a bargaining problem, the `relative utilitarian' (RU) solution maximizes the sum total of the bargainer's utilities, after having first renormalized each utility function to range from zero to one. We show that RU is `optimal' in two very different senses. First, RU is the maximal element (over the set of all bargaining solutions) under any partial ordering which satisfies certain axioms of fairness and consistency; this result is closely analogous to the result of Segal (2000). Second, RU offers each person the maximum expected utility amongst all rescaling-invariant solutions, when it is applied to a random sequence of future bargaining problems which are generated using a certain class of distributions; this is somewhat reminiscent of the results of Harsanyi (1953) and Karni (1998).

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 2637.

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Date of creation: 09 Apr 2007
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Handle: RePEc:pra:mprapa:2637

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Related research
Keywords: relative utilitarian; bargaining solution; impartial observer;

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Find related papers by JEL classification:
D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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  1. John C. Harsanyi, 1953. "Cardinal Utility in Welfare Economics and in the Theory of Risk-taking," Journal of Political Economy, University of Chicago Press, vol. 61, pages 434. [Downloadable!] (restricted)
  2. Weymark, J.A., 1990. "A Reconsideration Of The Harsanyi-Sen Debate On Utilitarianism," UBC Departmental Archives 90-03, UBC Department of Economics.
  3. Amrita Dhillon & Jean-Francois Mertens, 1999. "Relative Utilitarianism," Econometrica, Econometric Society, vol. 67(3), pages 471-498, May.
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  4. Edi Karni, 2003. "Impartiality and interpersonal comparisons of variations in well-being," Social Choice and Welfare, Springer, vol. 21(1), pages 95-111, 08. [Downloadable!] (restricted)
  5. Maskin, Eric, 1978. "A Theorem on Utilitarianism," Review of Economic Studies, Blackwell Publishing, vol. 45(1), pages 93-96, February. [Downloadable!] (restricted)
  6. Sobel, Joel, 2001. "Manipulation of Preferences and Relative Utilitarianism," Games and Economic Behavior, Elsevier, vol. 37(1), pages 196-215, October. [Downloadable!] (restricted)
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  7. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-18, May. [Downloadable!] (restricted)
  8. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-30, October. [Downloadable!] (restricted)
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  9. Edi Karni, 1998. "Impartiality: Definition and Representation," Econometrica, Econometric Society, vol. 66(6), pages 1405-1416, November.
  10. Amrita Dhillon, 1998. "Extended Pareto rules and relative utilitarianism," Social Choice and Welfare, Springer, vol. 15(4), pages 521-542. [Downloadable!] (restricted)
  11. Edi Karni & John A. Weymark, 1998. "An informationally parsimonious impartial observer theorem," Social Choice and Welfare, Springer, vol. 15(3), pages 321-332. [Downloadable!] (restricted)
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  12. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April. [Downloadable!] (restricted)
  13. John C. Harsanyi, 1955. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility," Journal of Political Economy, University of Chicago Press, vol. 63, pages 309. [Downloadable!] (restricted)
  14. Uzi Segal, 2000. "Let's Agree That All Dictatorships Are Equally Bad," Journal of Political Economy, University of Chicago Press, vol. 108(3), pages 569-589, June. [Downloadable!] (restricted)
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