Twofold Optimality of the Relative Utilitarian Bargaining Solution

Pivato, Marcus (2007): Twofold Optimality of the Relative Utilitarian Bargaining Solution. Forthcoming in:

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).

• Item Type: MPRA Paper
• Institution: Department of Mathematics, Trent University
• Language: English
• Keywords: relative utilitarian; bargaining solution; impartial observer
• Subjects: D - Microeconomics > D6 - Welfare Economics > D63 - Equity, Justice, Inequality, and Other Normative Criteria and Measurement; D - Microeconomics > D7 - Analysis of Collective Decision-Making > D71 - Social Choice; Clubs; Committees; Associations

References

Cao, X., 1982. Preference functions and bargaining solutions. In: Proceeedings of the 21st IEEE Conference on Decision and Control. Vol. 1. pp. 164-171.

d'Aspremont, C., Gevers, L., 1977. Equity and the informational basis of collective choice. Review of Economic Studies 44, 199-209.

Dhillon, A., 1998. Extended Pareto rules and relative utilitarianism. Soc. Choice Welf. 15 (4), 521-542.

Dhillon, A., Mertens, J.-F., 1999. Relative utilitarianism. Econometrica 67 (3), 471-498.

Harsanyi, J., 1953. Cardinal utility in welfare economics and in the theory of risk-taking. Journal of Political Economy 61 (434-435).

Harsanyi, J., 1955. Cardinal welfare, individualistic ethics and interpersonal comparisons of utility. Journal of Political Economy 63, 309-321.

Harsanyi, J., 1977. Rational behaviour and bargaining equilibrium in games and social situations. Cambridge UP, Cambridge, UK.

Kalai, E., 1977. Proportional solutions to bargaining situations: interpersonal utility comparisons. Econometrica 45 (7), 1623-1630.

Kalai, E., Smorodinsky, M., 1975. Other solutions to Nash's bargaining problem. Econometrica 43, 513-518.

Karni, E., 1998. Impartiality: definition and representation. Econometrica 66 (6), 1405-1415.

Karni, E., 2003. Impartiality and interpersonal comparisons of variations in well-being. Soc. Choice Welf. 21 (1), 95-111.

Karni, E., Weymark, J. A., 1998. An informationally parsimonious impartial observer theorem. Soc. Choice Welf. 15 (3), 321-332.

Maskin, E., 1978. A theorem on utilitarianism. Rev. Econom. Stud. 45 (1), 93-96. Muthoo, A., 1999. Bargaining theory with applications. Cambridge UP, Cambridge, UK.

Myerson, R. B., 1981. Utilitarianism, egalitarianism, and the timing effect in social choice problems. Econometrica 49 (4), 883-897.

Nash, J., 1950. The bargaining problem. Econometrica 18, 155-162.

Ng, Y.-K., October 1975. Bentham or Bergson? Finite sensibility, utility functions, and social welfare functions. Review of Economic Studies 42, 545-569.

Ng, Y.-K., 1985. The utilitarian criterion, finite sensibility, and the weak majority preference principle. A response. Soc. Choice Welf. 2 (1), 37-38.

Ng, Y.-K., 2000. From separability to unweighted sum: a case for utilitarianism. Theory and Decision 49 (4), 299-312.

Roemer, J. E., 1998. Theories of Distributive Justice. Harvard UP, Cambridge, MA.

Segal, U., 2000. Let's agree that all dictatorships are equally bad. Journal of Political Economy 108 (3), 569-589.

Sobel, J., 2001. Manipulation of preferences and relative utilitarianism. Games Econom. Behav. 37 (1), 196-215.

Weymark, J. A., 1991. A reconsideration of the Harsanyi-Sen debate on utilitarianism. In: Elster, J., Roemer, J. (Eds.), Interpersonal comparisons of well-being. Cambridge UP, Cambridge, UK, pp. 255-320.