Regular distributive social systems

We consider abstract social systems of private property, made of n individuals endowed with nonpaternalistic interdependent preferences, who interact through exchanges on competitive markets and Pareto-improving lump-sum transfers. The transfers follow from a distributive liberal social contract defined as a redistribution of initial endowments such that the resulting market equilibrium allocation is both: (i) a distributive optimum (i.e., is Pareto-efficient relative to individual interdependent preferences) and (ii) unanimously weakly preferred to the initial market equilibrium. We elicit minimal conditions for meaningful social contract redistribution in this setup, namely, the weighted sums of individual interdependent utility functions, built from arbitrary positive weights, have suitable properties of nonsatiation and inequality aversion; individuals have diverging views on redistribution, in some suitable sense, at (inclusive) distributive optima; and the initial market equilibrium is not a distributive optimum. We show that the relative interior of the set of social contract allocations is then a simply connected smooth manifold of dimension n − 1. We also show that the distributive liberal social contract rules out transfer paradoxes in Arrow–Debreu social systems. We show, finally, that the liberal social contract yields a norm of collective action for the optimal provision of any pure public good.