Notions of equal,or equivalent,opportunities

We formulate and study three concepts of equity designed to capture certain notions of equal, or equivalent, opportunities. The central concept is that of a family of choice sets. Given such a family , a feasible allocation z is alternatively required to be such that (i) there is B such that each agent i maximizes his satisfaction in B at z _i , (ii) there is B such that each agent i is indifferent between z _i and the maximizer of his satisfaction in B, (iii) for each agent i there is B _i such that z _i maximizes agent i's satisfaction in the union of the B _j and z _i is in B _i . Most of the standard concepts of equity can be obtained as particular cases of these general definitions by appropriately choosing . We identify conditions on guaranteeing that the resulting allocations be efficient. We apply the definitions to economies with only private goods, and to economies with public goods.This is a revised version of an earlier paper circulated under the title of Notions of equal opportunities. Early drafts were presented at the Conference on Economic Models and Distributive Justice, held in Bruxelles and Namur, January 1987, and at the Public Choice Society meeting in Tucson, Arizona, March 1987. The author thanks the participants, in particular T. Schwartz, for their comments, and NSF for its support, under grant No. 85 11136 and 88 09822. The suggestions of two anonymous referees, D. Diamantaras, L. Gevers, and H. Konishi are also gratefully acknowledged.