Automated analysis of weighted voting games

Abstract

Weighted voting games (WVGs) are an important mechanism for modeling scenarios where a group of agents must reach agreement on some issue over which they have different preferences. However, for such games to be effective, they must be well designed. Thus, a key concern for a mechanism designer is to structure games so that they have certain desirable properties. In this context, two such properties are PROPER and STRONG. A game is PROPER if for every coalition that is winning, its complement is not. A game is STRONG if for every coalition that is losing, its complement is not. In most cases, a mechanism designer wants games that are both PROPER and STRONG. To this end, we first show that the problem of determining whether a game is PROPER or STRONG is, in general, NP-hard. Then we determine those conditions (that can be evaluated in polynomial time) under which a given WVG is PROPER and those under which it is STRONG. Finally, for the general NP-hard case, we discuss two different approaches for overcoming the complexity: a deterministic approximation scheme and a randomized approximation method