Approximately Strategy-proof Mechanisms for (Constrained) Facility Location

Mechanism design for facility location (or selection of alternatives in a metric space) has been studied for decades. While strategy-proof, efficient mechanisms exist for unconstrained, one-dimensional, single-facility problems, guarantees of strategy-proofness and efficiency often break when allowing: (a) multiple dimensions; (b) multiple facilities; or (c) constraints on the feasible placement of facilities. We address these more general problems, providing several possibility/impossibility results with respect to individual and group strategy-proofness in both constrained and unconstrained problems. We also bound the incentive for manipulation in median-like mechanisms in settings where strategyproofness is not possible. We complement our results with empirical analysis of both electoral and geographic facility data, showing that the odds of successful manipulation, and more importantly, the gains and impact on social welfare, are small in practice (much less than worst-case theoretical bounds).