Classes of Complete Simple Games that are All Weighted

Important decisions are likely made by groups of agents. Thus group decision making is very common in practice. Very transparent group aggregating rules are given by weighted voting, where each agent is assigned a weight. Here a proposal is accepted if the sum of the weights of the supporting agents meets or exceeds a given quota. We study a more general class of binary voting systems -- complete simple games -- and propose an algorithm to determine which sub classes, parameterized by the agent's type composition, are weighted.