Symmetric (3,2) simple games serve as models for anonymous voting systems in which each voter may vote "yes," abstain, or vote "no," the outcome is "yes" or "no," and all voters play interchangeable roles. The extension to symmetric (j,2) simple games, in which each voter chooses from among j...

We propose a new power index based on the minimum sum representation (MSR) of a weighted voting game. The MSR offers a redesign of a voting game, such that voting power as measured by the MSR index becomes proportional to voting weight. The MSR index is a coherent measure of power that is...

Let us consider that somebody is extremely interested in increasing the probability of a proposal to be approved by a certain committee and that to achieve this goal he/she is prepared to pay off one member of the committee. In a situation like this one, and assuming that vote-buying is allowed...

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...