Índexs de poder. La importància de la CUP al Parlament de Catalunya l'any 2015

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2021, Director: Mikel Álvarez-Mozos[en] The main goal of this project is to study simple games and, more specifically, the subclass of weighted majority games, seeing how these games can be represented mathematically and are especially useful when we evaluate and represent voting processes where voters can form coalitions to get a desired result. To do so, it will be necessary to review the most important concepts and demostrations related to cooperative games. In addition, we will study the power of the players who form a certain simple game, which is based on the influence they have to make their will prevail in a voting and we will study the two most important power indices when evaluating this influence within a voting system, the Shapley-Shubik index and the Banzhaf index. Finally, we will analyze the results of the elections to the Parliament of Catalonia in 2015 and introduce the games with incompatibilities and a priori unions to calculate the real power of the parliamentary groups that participated and explain the why for the different circumstances that occurred until the investiture