Hierarchy of players in swap robust votinggames and minimal winning coalitions

Ordinarily, the process of decision making by a committee through voting is mod-elled by a monotonic game the range of whose characteristic function is restricted tof0; 1g: The decision rule that governs the collective action of a voting body induces ahierarchy in the set of players in terms of the a-priori influence that the players haveover the decision making process. In order to determine this hierarchy in a swap robustgame, one has to either evaluate a number-based power index (e.g., the Shapley-Shubikindex, the Banzhaf-Coleman index) for each player or conduct a pairwise comparisonbetween players in order to …nd out whether there exists a coalition in which player i isdesirable over another player j as a coalition partner. In this paper we outline a muchsimpler and more elegant mechanism to determine the ranking of players in terms oftheir a-priori power using only minimal winning coalitions, rather than the entire setof winning coalitions.[...]