Priorities in the location of multiple public facilities

Abstract

A collective decision problem is described by a set of agents, a profile of single-peaked preferences over the real line and a number of public facilities to be located. We consider public facilities that do not suffer from congestion and are non-excludable. We characterize the class of rules satisfying Pareto-efficiency, 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 the subclasses of priority rules that respectively satisfy anonymity, avoid the no-show paradox, strategy-proofness and population-monotonicity. In particular, we prove that a priority rule is strategy-proof if and only if it partitions the set of agents into a fixed hierarchy. Any such rule can also be viewed as a collection of generalized peak-selection median rules, that are linked across populations, in a way that we describe.

Weighted majoritarian rules for the location of multiple public facilities

“…The proof of this result can be found in Bochet and Gordon (2012). We now give examples of priorities attached to rules described in Theorem 1.…”

“…On the other hand, in the situation of a population increase, sovereignty protects the rights of the newcomers. Bochet and Gordon (2012) show that the combination of e¢ ciency, objectpopulation monotonicity and sovereignty characterizes a subclass of priority rules. To de…ne these rules, we need to introduce a class of binary relations called priorities over any nonempty subset S of T .…”

“…Since any two distinct maximal peak-unanimous subpro…les 5 In particular, an almost complete binary relation over T is never re ‡exive. 6 A priority is not a partial order, as it is not fully transitive.…”

“…A priority is anonymous if it satis…es the following condition. For all R M ; R N ; R 0 M 0 ; R 0 N 0 2 T ; such that (i) R M and R N are non-overlapping, (ii) R 0 M 0 and R 0 N 0 are non-overlapping, (iii) for all R 2 R; we have jfi 2 M : R i = Rgj = jfi 2 M 0 : R 0 i = Rgj ; (iv) for all R 2 R; we have jfi 2 N : Bochet and Gordon (2012) characterized the subclass of anonymous priority rules. We state it below and omit its straightforward proof.…”

“…Ehlers (2002Ehlers ( , 2003, Bochet and Gordon (2012), Heo (2012), Ehlers and Gordon (2011) provide axiomatic characterizations for this model. Umezawa (2012) considers the location of two facilities on a tree network.…”