Pseudo Lindahl Equilibrium as a Collective Choice Rule

A collective choice problem specifies a finite set of alternatives from which a group of expected utility maximizers must choose. We associate a collective pseudo market with every collective choice problem and establish the existence and efficiency of pseudo Lindahl equilibrium (PLE) allocations. We also associate a cooperative bargaining problem with every collective choice problem and define a set-valued solution concept, the ω-weighted Nash bargaining set where ω is a vector of welfare weights. We provide axioms that characterize the ω-weighted Nash bargaining set. Our main result shows that ω-weighted Nash bargaining set payoffs are also the PLE payoffs of the corresponding collective pseudo market with the same utility functions and incomes ω. We define a pseudo core for collective pseudo markets and show that pseudo Lindahl equilibria are in the pseudo core. We characterize the set of PLE outcomes of discrete allocation problems and show that they contain the set of pseudo Walrasian equilibrium outcomes.