Weighted Majoritarian Rules for the Location of Multiple Public Facilities

We consider collective decision problems given by a profile of single-peaked preferences defined over
the real line and a set of pure public facilities to be located on the line. In this context, Bochet and Gordon
(2012) provide a large class of priority rules based on efficiency, object-population monotonicity and
sovereignty. Each such rule is described by a fixed priority ordering among interest groups. We show that
any priority rule which treats agents symmetrically — anonymity — respects some form of coherence
across collective decision problems — reinforcement — and only depends on peak information — peakonly
— is a weighted majoritarian rule. Each such rule defines priorities based on the relative size of the
interest groups and specific weights attached to locations. We give an explicit account of the richness of
this class of rules.