Outcomes of voting and planning in single facility location problems

Abstract

For a given set of users located at the vertices of a network N, we consider the location of a single facility. Two different decision making procedures, voting among the users and minimizing total distance travelled by the users, are compared. Provided that a voting solution exists, it is shown that the two solutions sets coincide if N is a so-called cactus. For general networks, the outcomes of the two procedures are compared in terms of the cyclic structure of N and the number of users.