Games with multiple alternatives applied to voting systems

Abstract

We describe voting mechanisms to study voting systems as well as electoral systems and parliamentary organizations. These mechanisms are base on the so-called power indices of simple games with alternatives. The classical power indices applied to simple games just consider two options, yes/agree or not/reject. Here we also consider the abstention option, whose condition is allowed in most voting rules. In fact, we consider the extended Shapley–Shubik and Banzhaf indices to measure the power of the player/voter or the coalition in real voting systems.