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Twofold Optimality of the Relative Utilitarian Bargaining Solution

  • Pivato, Marcus

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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File URL: http://mpra.ub.uni-muenchen.de/2637/1/MPRA_paper_2637.pdf
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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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  1. Amrita Dhillon, 1998. "Extended Pareto rules and relative utilitarianism," Social Choice and Welfare, Springer, vol. 15(4), pages 521-542.
  2. Maskin, Eric, 1978. "A Theorem on Utilitarianism," Review of Economic Studies, Wiley Blackwell, vol. 45(1), pages 93-96, February.
  3. 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.
  4. 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.
  5. repec:cup:cbooks:9780521576475 is not listed on IDEAS
  6. Edi Karni, 2003. "Impartiality and interpersonal comparisons of variations in well-being," Social Choice and Welfare, Springer, vol. 21(1), pages 95-111, 08.
  7. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  8. Edi Karni, 1998. "Impartiality: Definition and Representation," Econometrica, Econometric Society, vol. 66(6), pages 1405-1416, November.
  9. Edi Karni & John A. Weymark, 1998. "An informationally parsimonious impartial observer theorem," Social Choice and Welfare, Springer, vol. 15(3), pages 321-332.
  10. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-30, October.
  11. DHILLON, Amrita & MERTENS, Jean-François, 1993. "Relative Utilitarianism," CORE Discussion Papers 1993048, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  12. Sobel, Joel, 2001. "Manipulation of Preferences and Relative Utilitarianism," Games and Economic Behavior, Elsevier, vol. 37(1), pages 196-215, October.
  13. 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.
  14. 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.
  15. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-18, May.
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