It is well known that he influence relation orders the voters the same way as the classical Banzhaf and Shapley–Shubik indices do when they are extended to the voting games with abstention (VGA) in the class of complete games. Moreover, all hierarchies for the influence relation are achievable...

The desirability relation was introduced by Isbell (1958) to qualitatively compare the a priori influence of voters in a simple game. In this paper, we extend this desirability relation to simple games with coalition structure. In these games, players organize themselves into a priori disjoint...

A well-known result in Social Choice theory is the following: every scoring rule (positional rules) violates Condorcet consistency. A rule is Condorcet consistent when it selects the alternative that is preferred to every other alternative by a majority of individuals. In this paper, we...

The purpose of this paper is to present a structural specification of the Shapley- Shubik and Banzhaf power indices in a weighted voting rule. We compare them in term of the cardinality of the sets of power vectors (PV). This is done in different situations where the quota or the number of seats...

The desirability relation was introduced by Isbell (A class of simple games 25: 423–439, <CitationRef CitationID="CR8">1958</CitationRef>) to qualitatively compare the a priori influence of voters in a simple game. In this paper, we extend this desirability relation to simple games with coalition structure. In these games, players...</citationref>