On the Dimensionality of Voting Games

In a yes/no voting game, a set of voters must determine whether to accept or reject a given alternative. Weighted voting games are a well-studied subclass of yes/no voting games, in which each voter has a weight, and an alternative is accepted if the total weight of its supporters exceeds a certain threshold. Weighted voting games are naturally extended to k-vector weighted voting games, which are intersections of k different weighted voting games: a coalition wins if it wins in every component game. The dimensionality, k, of a kvector weighted voting game can be understood as a measure of the complexity of the game. In this paper, we analyse the dimensionality of such games from the point of view of complexity theory. We consider the problems of equivalence, (checking whether two given voting games have the same set of winning coalitions), and minimality, (checking whether a given k-vector voting game can be simplified by deleting one of the component games, or, more generally, is eq...

• Type: Conference
• Year: 2008
• Where: AAAI
• Authors: Edith Elkind, Leslie Ann Goldberg, Paul W. Goldberg, Michael Wooldridge
• Keywords: AAAI 2008, Intelligent Agents, Voting Game, Weighted Voting Game, Yes/no Voting Games