<p>We discuss the strategic situation in the Barcelona Town Council after the elections held on May 28, 2023. This institution is described as a simple game, and the Shapley–Shubik index is applied to measure the initial power distribution among the parties. We introduce some ideological incompatibilities in the game and, finally, we discuss the existence of stable coalition structures in the different stated scenarios when the power payoffs to the players are computed using the proportional partitional Shapley value. The key point is the formation of a stable coalition structure. Broadly speaking, a coalition structure is stable if the payoff obtained by each player cannot be increased by a unilateral change in their choice of coalition. In a previous paper, we showed that any simple game admits stable coalition structures when the payoffs are computed using the proportional partitional Shapley value. We find the stable coalition structures for each of the situations analyzed. The results show a fairly complicated problem that the involved politicians and parties should try to solve for the benefit of Barcelona citizens.</p>