In this paper, we characterize the games in which Johnston, Shapley–Shubik and Penrose–Banzhaf–Coleman indices are ordinally equivalent, meaning that they rank players in the same way. We prove that these three indices are ordinally equivalent in semicomplete simple games, which is a newly...

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...

Gvozdeva et al. (Int J Game Theory, doi:<ExternalRef> <RefSource>10.1007/s00182-011-0308-4</RefSource> <RefTarget Address="10.1007/s00182-011-0308-4" TargetType="DOI"/> </ExternalRef>, <CitationRef CitationID="CR17">2013</CitationRef>) have introduced three hierarchies for simple games in order to measure the distance of a given simple game to the class of (roughly) weighted voting games. Their third class <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$${\mathcal {C}}_\alpha $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi mathvariant="script">C</mi> <mi mathvariant="italic">α</mi> </msub> </math> </EquationSource> </InlineEquation>...</equationsource></equationsource></inlineequation></citationref></refsource></externalref>

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...

It is well known that he influence relation orders the voters the same way as the classical Banzhaf and Shapley–Shubik indices do when they are extended to the voting games with abstention (VGA) in the class of complete games. Moreover, all hierarchies for the influence relation are achievable...