Three public goods and lexicographic preferences: replacement principle

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 (Mechanisms for providing a menu of public goods. University of Rochester., 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 replacement-domination. We show that for three public goods, this results in a very similar characterization to Miyagawa (Social Choice Welfare 18:527-541, 2001a): only the two rules which either always chooses the left-most Pareto-optimal alternative or always chooses the right-most Pareto-optimal alternative satisfy these properties. This is in contrast to Ehlers (J Math Econom 37:1-15, 2002) who showed that for two goods the corresponding characterization is substantially different to Miyagawa (Social Choice Welfare 18:527-541, 2001a).