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Twofold Optimality of the Relative Utilitarian Bargaining Solution

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  • Pivato, Marcus

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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Keywords: relative utilitarian; bargaining solution; impartial observer;

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  1. Maskin, Eric, 1978. "A Theorem on Utilitarianism," Review of Economic Studies, Wiley Blackwell, vol. 45(1), pages 93-96, February.
  2. Sobel, Joel, 2001. "Manipulation of Preferences and Relative Utilitarianism," Games and Economic Behavior, Elsevier, vol. 37(1), pages 196-215, October.
  3. Amrita Dhillon, 1998. "Extended Pareto rules and relative utilitarianism," Social Choice and Welfare, Springer, vol. 15(4), pages 521-542.
  4. Ehud Kalai, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Discussion Papers 179, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. 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.
  6. Edi Karni, 1998. "Impartiality: Definition and Representation," Econometrica, Econometric Society, vol. 66(6), pages 1405-1416, November.
  7. DHILLON, Amrita & MERTENS, Jean-François, . "Relative utilitarianism," CORE Discussion Papers RP -1398, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  8. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  9. Edi Karni, 2003. "Impartiality and interpersonal comparisons of variations in well-being," Social Choice and Welfare, Springer, vol. 21(1), pages 95-111, 08.
  10. 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.
  11. Ng, Yew-Kwang, 1975. "Bentham or Bergson? Finite Sensibility, Utility Functions and Social Welfare Functions," Review of Economic Studies, Wiley Blackwell, vol. 42(4), pages 545-69, October.
  12. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-18, May.
  13. 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.
  14. Edi Karni & John A. Weymark, 1998. "An informationally parsimonious impartial observer theorem," Social Choice and Welfare, Springer, vol. 15(3), pages 321-332.
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