NOTIONS OF EQUAL, OR EQUIVALENT, OPPORTUNITIES

We formulate and study three concepts of equity designed to capture ce rtain notions of ''equal'', or 'equivalent'', opportunities. The centr al concept is that of a family of choice sets. Given such a family B, a feasible allocation z is alternatively required to be such that (i) there is B is-an-element-of B such that each agent i maximizes his sat isfaction in B at z(i), (ii) there is B is-an-element-of B such that e ach agent i is indifferent between z(i) and the maximizer of his satis faction in B, (iii) for each agent i there is B(i) is-an-element-of B 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 appropri ately choosing B. We identify conditions on B guaranteeing that the re sulting allocations be efficient. We apply the definitions to economie s with only private goods, and to economies with public goods.