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This paper is a twofold contribution. First, it contributes to the problem of enumerating some classes of simple games and in particular provides the number of weighted games with minimum and the number of weighted games for the dual class as well. Second, we focus on the special case of bipartite complete games with minimum, and we compare and rank these games according to the behavior of some efficient power indices of players of type 1 (or of type 2). The main result of this second part establishes all allowable rankings of these games when the Shapley-Shubik power index is used on players of type 1. [ABSTRACT FROM AUTHOR]

When analyzing mathematically decision mechanisms ruled by voting it is sometimes convenient to include abstention as a possible alternative for the voters. In classical simple games, abstention, if considered, is formally equivalent to voting against the proposal. Simple games with alternatives are useful to study voting systems where abstention does not favour any of the options. In this work, we axiomatically characterize the Shapley–Shubik index for simple games with alternatives and apply it to an example taken from real life. [ABSTRACT FROM AUTHOR]

This paper provides “ready-to-apply” procedures, based on generating functions, which allow to compute power indices in weighted majority games restricted by an a priori system of unions. We illustrate these methods by an application to the International Monetary Fund. We compare the empirical properties of the coalitional and traditional power indices keeping the game fixed or allowing for variations in its set of parameters. [ABSTRACT FROM AUTHOR]