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...

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 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>