Three public goods and lexicographic preferences : replacement principle

Abstract

We study the problem of locating multiple public goods for a group of agents with single-peaked preferences over an interval. An alternative specifies for each public good a location. In Miyagawa (1998) each agent consumes only his most preferred public good without rivalry. We extend preferences lexicographically and characterize the class of rules satisfying Pareto-optimality and replacementdomination. We show that for three public goods, this results in a very similar characterization to Miyagawa (2001a): only the two rules which either always chooses the left-most Pareto-optimal alternative or always chooses the rightmost Pareto-optimal alternative satisfy these properties. This is in contrast to Ehlers (2002) who showed that for two goods the corresponding characterization is substantially different to Miyagawa (2001a).