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Copmment on Egalitarianism under Incomplete Information

The paper aims at extending the egalitarian principle to environments with incomplete information. The approach is primarily axiomatic, focusing on the characteristic property of monotonicity: no member of the society should be worse off when more collective decisions are available. I start by showing the incompat- ibility of this property with incentive efficiency, even in quasi-linear environments. This serious impossibility result does not follow from the mere presence of incentive constraints, but instead from the fact that information is incomplete (asymmetric information at the time of making a decision). I then weaken the monotonicity property so as to require it only when starting from incentive compatible mecha- nisms at which interim utilities are transferable (in a weak sense). Adding other axioms in the spirit of Kalai's (Econometrica, 1977, Theorem 1) classical character- ization of the egalitarian principle under complete information, I obtain a partial characterization of a natural extension of the lex-min solution to problems with incomplete information. Next, I prove that, in each social choice problem, there is a unique way of rescaling the participants' interim utilities so as to make this solu- tion compatible with the ex-ante utilitarian principle. These two criteria coincides in the rescaled utilities exactly at the incentive ecient mechanisms that maxi- mize Harsanyi and Selten's (Management Science, 1972) weighted Nash product. These concepts are illustrated on classical examples of profit-sharing, public good production and bilateral trade. The richness of the topic of social choice under in- complete information is illustrated by considering two alternative extensions of the egalitarian principle { one based on an idea of equity from the point of view of the individuals themselves (given their private information) instead of an uninformed third party (social planner or arbitrator), and another notion based on the idea of

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Paper provided by Brown University, Department of Economics in its series Working Papers with number 2010-4.

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Date of creation: 2010
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Handle: RePEc:bro:econwp:2010-4
Contact details of provider: Postal: Department of Economics, Brown University, Providence, RI 02912

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  18. de Clippel, Geoffroy & Minelli, Enrico, 2004. "Two-person bargaining with verifiable information," Journal of Mathematical Economics, Elsevier, vol. 40(7), pages 799-813, November.
  19. John C. Harsanyi & Reinhard Selten, 1972. "A Generalized Nash Solution for Two-Person Bargaining Games with Incomplete Information," Management Science, INFORMS, vol. 18(5-Part-2), pages 80-106, January.
  20. Moulin, Herve, 1985. "Egalitarianism and Utilitarianism in Quasi-linear Bargaining," Econometrica, Econometric Society, vol. 53(1), pages 49-67, January.
  21. Mirrlees, James A, 1971. "An Exploration in the Theory of Optimum Income Taxation," Review of Economic Studies, Wiley Blackwell, vol. 38(114), pages 175-208, April.
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  24. Pazner, Elisha A & Schmeidler, David, 1978. "Egalitarian Equivalent Allocations: A New Concept of Economic Equity," The Quarterly Journal of Economics, MIT Press, vol. 92(4), pages 671-87, November.
  25. Moulin, Hervé, 2009. "Almost budget-balanced VCG mechanisms to assign multiple objects," Journal of Economic Theory, Elsevier, vol. 144(1), pages 96-119, January.
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  28. Yves SPRUMONT, 2009. "Relative Egalitarianism and Related Criteria," Cahiers de recherche 02-2009, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  29. Moulin, Herve, 1994. "Serial Cost-Sharing of Excludable Public Goods," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 305-25, April.
  30. Geoffroy de Clippel, 2004. "The Type-Agent Core for Exchange Economies with Asymmetric Information," Working Papers 2004-18, Brown University, Department of Economics.
  31. Thomson, William, 1983. "Problems of fair division and the Egalitarian solution," Journal of Economic Theory, Elsevier, vol. 31(2), pages 211-226, December.
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