Pre-print, Working paper: We analyze Approval Voting in Poisson games endowing voters with private values over three candidates. We firsts how that any stable equilibrium is discriminatory: one candidate is commonly regarded as out of contention. We fully characterize stable equilibria and divide them into two classes. In direct equilibria, best responses depend only on ordinal preferences. In indirect equilibria, preference intensities matter. Counter-intuitively, any stable equilibrium violates the ordering conditions, a set of belief restrictions used to derive early results in the literature. We finally use Monte-Carlo simulations to estimate the prevalence of the different sorts of equilibria and their likelihood to elect a Condorcet winner.