A limit theorem on the dual core of a distributive social system

I consider abstract social systems where the distribution of wealth is an object of common concern. I study, in particular, the systems where liberal distributive social contracts consist of the Pareto-efficient distributions that are unanimously preferred to the initial distribution. I define a Dual Distributive Core from a process of decentralized auction on the budget shares of Lindahl associated with net transfers, operated by coalitions aiming at increasing the value of the public good for their members while maintaining their utility levels. I establish that the dual distributive core converges, as the number of distributive agents becomes large relative to the number of agent types, to a typically finite number of distributive liberal social contracts, which correspond to the Lindahl equilibria that are unanimously preferred to the initial distribution. This process of decentralized auction provides a theoretical foundation for contractual policies of redistribution. The comparison with the usual notion of core with public goods (Foley 1970) yields the following results in this context: the Foley-core is a subset, generally proper, of the set of liberal distributive social contracts; it does not contain, in general, distributive Lindahl equilibria.