We study competition between political parties in repeated elections with probabilistic voting. This model entails multiple equilibria, and we focus on cases where political collusion occurs. When parties hold different opinions on some policy, they may take different policy positions that do not coincide with the median voter's preferred policy platform. In contrast, when parties have a mutual understanding on a particular policy, their policy positions may converge (on some dimension) but not to the median voter's preferred policy. That is to say, parties can tacitly collude with one another, despite political competition. Collusion may collapse, for instance, after the entry of a new political party. This model rationalizes patterns in survey data from Sweden, where politicians on different sides of the political spectrum take different positions on economic policy but similar positions on refugee intake-diverging from the average voter's position, but only until the entry of a populist party.