The purpose of this article is to define and to prove formally the existence of an equilibrium under proportional representation, as well as partially to characterize it. Specifically, let m be the quota that represents the minimal number of voters necessary for a candidate to be elected. We show that there is a set of elected candidates, each choosing an alternative and each receiving at least m votes, such that no other potential candidate, by offering an additional alternative, can secure at least m votes for himself. We then investigate the structure, at equilibrium, of the set of individuals who support a given candidate, as well as study stability properties of the equilibrium. We also provide necessary and sufficient conditions for the equilibrium to consist of a single candidate, thus generalizing Black's median-voter result.