# On the location of public bads: strategy-proofness under two-dimensional single-dipped preferences

Working paper

Issue number:

RM/12/040

Publisher:

Maastricht University

Year:

2012

In a model with ﬁnitely many agents who have single-dipped Euclidean preferences on a polytope in the Euclidean plane, a rule assigns to each proﬁle of reported dips a point of the polytope. A single-best point is a point which is the unique point at maximal distance from some other point of the polytope. It is proved that any strategy-proof and Pareto optimal rule is a dictatorship unless the polytope has exactly two single- best points or it has exactly four single-best points which form the vertices of a rectangle. In the latter cases strategy-proof and Pareto optimal rules can be obtained by committee voting (simple games) between the single- best alternatives. This framework models situations where public bads such as garbage dumping grounds or nuclear plants have to be located within a conﬁned region.