Let P be a simple rectilinear polygon with N vertices, endowed with a rectilinear metric, and let the location of n users in P be given. There are a number of procedures to locate a facility for a given family of users. If a voting procedure is used, the chosen point x should satisfy the following property: no other point y of the polygon P is closer to an absolute majority of users. Such a point is called a Condorcet point. If a planning procedure is used, such as minimization of the average distance to the users, the optimal solution is called a median point. The paper proves that Condorcet and median points of a simple rectilinear polygon coincide and presents an O(N+nlogN) algorithm for computing these sets. If all users are located on vertices of a polygon P, then the running time of the algorithm becomes O(N+n).
