Single-dipped preferences with satiation: strong group strategy-proofness and unanimity

We study the problem of the location of a public facility that generates negative externalities. We consider that agents have single-dipped preferences with satiation: each agent considers a location as the worst, the "dip", and the farther the location is from the dip, the better for the agent. In addition, an agent might be indifferent between all the locations sufficiently far from his dip, reaching his highest level of satisfaction. We characterize the family of strongly group strategy-proof and unanimous rules. Opposite to previous results without satiation, the locations selected are not necessarily at the extremes of the alternatives' space.