Continuous Location Theory Under Majority Rule

This paper studies, from a theoretical point of view, a single-facility location problem in a normed space. It is assumed that the facility has a finite or an infinite number of users and the location is selected under majority rule where, between two feasible locations, each user prefers the closer one. In general normed space three concepts of solutions—Condorcet points, Simpson points and plurality points—are geometrically described. In a two-dimensional space, practical methods of construction are given as well as the relationships between Condorcet points, plurality points, and medians; in the same framework, when the norm is polyhedral or the number of users is finite, it is proved that each Condorcet point is a solution to the associated Fermat-Weber problem.