Collective Choice with Linear Utilities

This note considers a property, called “limited shared weak preferences” (LSWP), in the context of a model with linear utility functions defined on a polyhedron of alternatives. As special cases, we capture the distributive politics model with externalities in consumption, and we capture collective choice of lotteries by expected utility-maximizing agents. We give a simple sufficient condition for LSWP, which plays an important role in the analysis of stationary equilibria in spatial bargaining games and in the analysis of covering and dominance in social choice theory.