Weighted majority games and the matrix of homogeneity

Easy weighted majority games

In a weighted majority game each player has a positive integer weight and there is a positive integer quota. A coalition of players is winning (losing) if the sum of the weights of its members exceeds (does not exceed) the quota. A player is pivotal for a coalition if her omission changes it from a winning to a losing one. Most game theoretic measures of the power of a player involve the comput...

Directed and weighted majority games

In this paper we deal with several classes of simple games; the first class is the one of ordered simple games (i.e. they admit of a complete desirability relation). The second class consists of all zero-sum games in the first one. First of all we introduce a "natural" partial order on both classes respectively and prove that this order relation admits a rank function. Also the first class turn...

Power in Weighted Majority Games

This paper suggests an indicator of power in weighted majority games. An indicator of power determines the ability of a voter to influence the outcomes of the voting bodies he belongs to. In a weighted majority game each voter is assigned a certain nonnegative real number weight and there is a positive real number quota satisfying a boundedness condition such that a group of voters can pass a r...

The Modified Nucleolus as Canonical Representation of Weighted Majority Games

On the likelihood of dummy players in weighted majority games

When the number of players is small in a weighted majority voting game, it can occur that one of the players has no influence on the result of the vote, in spite of a strictly positive weight. Such a player is called a “dummy” player in game theory. The purpose of this paper is to investigate the conditions that give rise to such a phenomenon and to compute its likelihood. It is shown that the ...