This paper analyzes a non-smooth model of probabilistic voting with two parties and a broad family of other-regarding behavior, including fairness and quasi-maximin preferences, income-dependent altruism, and inequity aversion. The paper provides conditions for equilibrium existence and uniqueness. It also characterizes the Nash equilibrium in pure strategies when parties hold either symmetric payoffs, or minor forms of asymmetries. The characterization shows that the two parties converge to an equilibrium policy that maximizes a mixture of a ``self-regarding utilitarian'' social welfare function and an aggregate of society's other-regarding preferences. These results are shown to be applicable to other non-smooth frameworks, such as probabilistic voting with loss averse voters. The characterization also shows that the direction and the size of the inefficiencies emerging from electoral competition depend in a subtle way on the nature of the other-regarding preferences (and resp., loss aversion).