Priorities in the location of multiple public facilities

A collective decision problem is described by a set of agents, a pro…le of single-peaked preferences over the real line and a number k of public facilities to be located. We consider public facilities that do not su¤er from congestion and are non-excludable. We provide a characterization of the class of rules satisfying Pareto-e¢ ciency, object-population monotonicity and sovereignty. Each rule in the class is a priority rule that selects locations according to a predetermined priority ordering among “interest groups”. We characterize each of the subclasses of priority rules that respectively satisfy anonymity, hiding-proofness and strategy-proofness. In particular, we prove that a priority rule is strategy-proof if and only if it partitions the set of agents into a …xed hierarchy. Alternatively, any such rule can be viewed as a collection of …xed-populations generalized peakselection median rules (Moulin, 1980), that are linked across populations, in a way that we describe. Keywords: Multiple public facilities, Priority rules, Hierarchical rules, Object-population-monotonicity, Sovereignty, Anonymity, Strategy-proofness, Generalized median rules, Hiding-proofness. JEL classi…cation codes: D60; D63; D70; D71; H41. We thank Anna Bogomolnaia, Haluk Ergin, Lars Ehlers, Bettina Klaus, François Maniquet, Hervé Moulin, Jorge L. Garcia Ramirez, Yves Sprumont and William Thomson for helpful conversations or comments. Part of this paper was written when the …rst author visited the Université de Montréal, and when the second author visited Maastricht University. Financial support from CIREQ and METEOR is gratefully acknowledged. yMaastricht University and CORE. zUniversité de Montréal and CIREQ.