Many real systems are made of strongly interacting networks, with profound consequences on their dynamics. Here, we consider the case of two interacting social networks and, in the context of a simple model, we address the case of political elections. Each network represents a competing party and every agent, on the election day, can choose to be either active in one of the two networks (vote for the corresponding party) or to be inactive in both (not vote). The opinion dynamics during the election campaign is described through a simulated annealing algorithm. We find that for a large region of the parameter space the result of the competition between the two parties allows for the existence of pluralism in the society, where both parties have a finite share of the votes. The central result is that a densely connected social network is key for the final victory of a party. However, small committed minorities can play a crucial role, and even reverse the election outcome.