This paper considers voting situations in which the vote takes place iteratively. If a coalition replaces the status quo a with a contestant b, then b becomes the new status quo, and the vote goes on until a candidate is reached that no winning coalition is willing to replace. It is well known...

We study minimum integer representations of weighted games, i.e. representations where the weights are integers and every other integer representation is at least as large in each component. Those minimum integer representations, if they exist at all, are linked with some solution concepts in...

In this paper, we introduce eight power indices that admit a probabilistic interpretation for voting rules with abstention or with three levels of approval in the input, briefly (3, 2) games. We analyze the analogies and discrepancies between standard known indices for simple games and the...

Tomiyama [Tomiyama, Y., 1987. Simple game, voting representation and ordinal power equivalence. International Journal on Policy and Information 11, 67-75] proved that, for every weighted majority game, the preorderings induced by the classical Shapley-Shubik and Penrose-Banzhaf-Coleman indices...