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Multiperson Utility

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  • Lloyd S. Shapley

    (UCLA)

  • Manel Baucells

    (UCLA)

Abstract

We approach the problem of preference aggregation by endowing both individuals and coalitions with partially-ordered or incomplete cardinal preferences. Consistency across preferences for coalitions comes in the form of the Extended Pareto Rule: if two disjoint coalitions A and B prefer x to y, then so does the coalition A*B. The Extended Pareto Rule has important consequences for the social aggregation of individual preferences. Restricting attention to the case of complete individual preferences, and assuming complete preferences for some pairs of agents (interpersonal comparisons of utility units), we discover that the Extended Pareto Rule imposes a "no arbitrage" condition in the terms of utility comparison between agents. Furthermore, if all the individuals and pairs have complete preferences and certain non-degeneracy conditions are met, then we witness the emergence of a complete preference ordering for coalitions of all sizes. The corresponding utilities are a weighted sum of individual utilities, with the n-1 independent weights obtained from the preferences of n-1 pairs forming a spanning tree in the group. Keywords: Preference aggregation, Incomplete preferences, Extended Pareto Rule.

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Bibliographic Info

Paper provided by UCLA Department of Economics in its series UCLA Economics Working Papers with number 779.

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Date of creation: 01 Jul 1998
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Handle: RePEc:cla:uclawp:779

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Web page: http://www.econ.ucla.edu/

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  1. Manel Baucells & Lloyd S. Shapley, 2000. "Multiperson Utility," Econometric Society World Congress 2000 Contributed Papers 0078, Econometric Society.
  2. Juan Dubra & Fabio Maccheroni & Efe Oki, 2001. "Expected utility theory without the completeness axiom," ICER Working Papers - Applied Mathematics Series 11-2001, ICER - International Centre for Economic Research.
  3. Kalai, Ehud & Schmeidler, David, 1977. "Aggregation Procedure for Cardinal Preferences: A Formulation and Proof of Samuelson's Impossibility Conjecture," Econometrica, Econometric Society, vol. 45(6), pages 1431-38, September.
  4. Sen, Amartya, 1970. "Interpersonal Aggregation and Partial Comparability," Econometrica, Econometric Society, vol. 38(3), pages 393-409, May.
  5. Amrita Dhillon & Jean-Francois Mertens, 1999. "Relative Utilitarianism," Econometrica, Econometric Society, vol. 67(3), pages 471-498, May.
  6. Costis Skiadas, 1997. "Conditioning and Aggregation of Preferences," Econometrica, Econometric Society, vol. 65(2), pages 347-368, March.
  7. Edi Karni, 2003. "Impartiality and interpersonal comparisons of variations in well-being," Social Choice and Welfare, Springer, vol. 21(1), pages 95-111, 08.
  8. Amrita Dhillon, 1998. "Extended Pareto rules and relative utilitarianism," Social Choice and Welfare, Springer, vol. 15(4), pages 521-542.
  9. Schmeidler, David, 1969. "Competitive Equilibria in Markets with a Continuum of Traders and Incomplete Preferences," Econometrica, Econometric Society, vol. 37(4), pages 578-85, October.
  10. Saposnik, Rubin, 1975. "Social Choice with Continuous Expression of Individual Preferences," Econometrica, Econometric Society, vol. 43(4), pages 683-90, July.
  11. Truman F. Bewley, 1986. "Knightian Decision Theory: Part 1," Cowles Foundation Discussion Papers 807, Cowles Foundation for Research in Economics, Yale University.
  12. Sen, Amartya K, 1977. "On Weights and Measures: Informational Constraints in Social Welfare Analysis," Econometrica, Econometric Society, vol. 45(7), pages 1539-72, October.
  13. Peter A. Diamond, 1967. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparison of Utility: Comment," Journal of Political Economy, University of Chicago Press, vol. 75, pages 765.
  14. DeMeyer, Frank & Plott, Charles R, 1971. "A Welfare Function Using 'Relative Intensity' of Preference," The Quarterly Journal of Economics, MIT Press, vol. 85(1), pages 179-86, February.
  15. Rigotti, Luca & Shannon, Chris, 2001. "Uncertainty and Risk in Financial Markets," Department of Economics, Working Paper Series qt7pp7113z, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  16. Manel Baucells & Rakesh K. Sarin, 2003. "Group Decisions with Multiple Criteria," Management Science, INFORMS, vol. 49(8), pages 1105-1118, August.
  17. Luce, R Duncan & Krantz, David H, 1971. "Conditional Expected Utility," Econometrica, Econometric Society, vol. 39(2), pages 253-71, March.
  18. James S. Dyer & Rakesh K. Sarin, 1979. "Group Preference Aggregation Rules Based on Strength of Preference," Management Science, INFORMS, vol. 25(9), pages 822-832, September.
  19. 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.
  20. Fishburn, Peter C, 1973. "A Mixture-Set Axiomatization of Conditional Subjective Expected Utility," Econometrica, Econometric Society, vol. 41(1), pages 1-25, January.
  21. Sobel, Joel, 2001. "Manipulation of Preferences and Relative Utilitarianism," Games and Economic Behavior, Elsevier, vol. 37(1), pages 196-215, October.
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