This paper offers graphic illustration of so-called “valence” models of candidates responding to their perceptions of voter location in a two-party system. Models by Groseclose and others show how the combination of candidate uncertainty about the median voter location, nonzero candidate valence, and policy motivated candidates leads to departures from the median voter prediction. With one policy dimension, either there exists an equilibrium where the candidates do not converge to the median (or any other common position) or there exists no equilibrium. We offer illustrations based on plausible conditions. Under some conditions we show an equilibrium where candidates locate at separate policy positions. Under others, we illustrate the absence of equilibrium.