Two new power indices based on winning coalitions
نویسندگان
چکیده
منابع مشابه
Power Indices and minimal winning Coalitions
The Penrose-Banzhaf index and the Shapley-Shubik index are the best-known and the most used tools to measure political power of voters in simple voting games. Most methods to calculate these power indices are based on counting winning coalitions, in particular those coalitions a voter is decisive for. We present a new combinatorial formula how to calculate both indices solely using the set of m...
متن کاملComplementary cooperation, minimal winning coalitions, and power indices
In this paper, we introduce a new family of simple games, which is referred to as the complementary weighted multiple majority game. For the two dimensional case, we prove that there are at most n+1 minimal winning coalitions (MWC for short), where n is the number of players. An algorithm for computing all the MWCs is presented, with a running time of O(n log n). Computing the main power indice...
متن کاملPower indices expressed in terms of minimal winning coalitions
A voting situation is given by a set of voters and the rules of legislation that determine minimal requirements for a group of voters to pass a motion. A priori measures of voting power, such as the Shapley-Shubik index and the Banzhaf value, show the influence of the individual players in a voting situation and are calculated by looking at marginal contributions in a simple game consisting of ...
متن کامل2 00 9 Power indices and minimal winning coalitions
The Penrose-Banzhaf index and the Shapley-Shubik index are the best-known and the most used tools to measure political power of voters in simple voting games. Most methods to calculate these power indices are based on counting winning coalitions, in particular those coalitions a voter is decisive for. We present a new combinatorial formula how to calculate both indices solely using the set of m...
متن کامل2 00 9 Power indices and minimal winning coalitions Werner Kirsch and Jessica Langner
The Banzhaf index and the Shapley-Shubik index are the best-known and the most used tools to measure political power of voters in a voting system. Most methods to calculate these power indices are based on counting winning coalitions, in particular those coalitions a voter is decisive for. We present a new combinatorial formula to calculate both indices solely using the set of minimal winning c...
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ژورنال
عنوان ژورنال: Journal of Difference Equations and Applications
سال: 2011
ISSN: 1023-6198,1563-5120
DOI: 10.1080/10236190903200677