Simpson points in planar problems with locational constraints. The round-norm case

The Simpson set is one of the most popular solution concepts in location models with voting. In this paper we address the problem of finding such a set for planar models with locational constraints when the metric in use is induced by a round norm. After formulating the problem as a mathematical program, we first propose a general algorithm that enables the evaluation of the corresponding objective function. Then, we show how to solve the problem by proving the existence of a finite dominating set of locations, the best of which can be found by inspection (using the evaluation algorithm proposed).