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...

Voting power theories measure the ability of voters to influence the outcome of an election under a given voting rule. In general, each theory gives a different evaluation of power, raising the question of their appropriateness, and calling for the need to identify classes of rules for which...

The influence relation was introduced by Isbell [Isbell, J.R., 1958. A class of simple games. Duke Math. J. 25, 423-439] to qualitatively compare the a priori influence of voters in a simple game, which by construction allows only "yes" and "no" votes. We extend this relation to voting games...

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>

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 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...

We study the stability of decision making in committees. A policy proposal introduced by a committee member is either adopted or abandoned in favor of a new proposal after deliberations. If a proposal is abandoned, it is in spite of the committee member who introduced it, who does not cooperate...

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...