A New Axiomatization of the Banzhaf Index for Games with Abstention

(3, 2)-Simple games are a model for voting situation in which players can vote not only in favour or against a proposal but they can also abstain. Also in this model, power indices are used to evaluate the power of players. In particular, the Banzhaf index and the Shapley–Shubik index have been generalized to define analogous power indices in the context of games with abstention. In this work we provide a new axiomatization of the Banzhaf index for games with abstention, to underline its properties and increase the justification of the use of this index as a solution concept also in the family of games with abstention