The Nakamura number is an appropriate invariant of a simple game to study the existence of social equilibria and the possibility of cycles. For symmetric (quota) games its number can be obtained by an easy formula. For ...

Many real-world voting systems consist of voters that occur in just two different types. Indeed, each voting system with a “House” and a “Senate” is of that type. Here we present structural characterizations and an explicit ...

Gvozdeva, Hemaspaandra, and Slinko (2011) 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 C-alpha ...

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 ...

Voting is a commonly applied method for the aggregation of the preferences of multiple agents into a joint decision. If preferences are binary, i.e., “yes” and “no”, every voting system can be described by a (monotone) ...

Some distinguished types of voters, as vetoes, passers or nulls, as well as some others, play a significant role in voting systems because they are either the most powerful or the least powerful voters in the game independently ...