Implementation via code of rights
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Implementation of a social choice rule can be thought of as a design of power (re)distribution in the society whose ”equilibrium outcomes” coincide with the alternatives chosen by the social choice rule at any preference profile of the society. In this paper, we introduce a new societal framework for implementation which takes the power distribution in the society, represented by a code of rights, as its point of departure. We examine and identify how implementation via code of rights (referred to as gamma implementation) is related to classical Nash implementation via mechanism. We characterize gamma implementability when the state space on which the rights structure is to be specified consists of the alternatives from which a social choice is to be made. We show that any social choice rule is gamma implementable if it satisfies pivotal oligarchic monotonicity condition that we introduce. Moreover, pivotal oligarchic monotonicity condition combined with Pareto optimality is sufficient for a non-empty valued social choice rule to be gamma implementable. Finally we revisit liberal’s paradox of A.K. Sen, which turns out to fit very well into the gamma implementation framework.