Power Indices and minimal winning Coalitions
نویسندگان
چکیده
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 minimal winning coalitions.
منابع مشابه
2 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...
متن کامل2 00 9 Power indices and minimal winning coalitions Werner Kirsch and Jessica Langner June 21 , 2009
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...
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 کاملPower Indices and Minimal Winning Coalitions in Simple Games with Externalities
We propose a generalization of simple games to situations with coalitional externalities. The main novelty of our generalization is a monotonicity property that we define for games in partition function form. This property allows us to properly speak about minimal winning embedded coalitions. We propose and characterize two power indices based on these kind of coalitions. We provide methods bas...
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 ...
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ورودعنوان ژورنال:
- Social Choice and Welfare
دوره 34 شماره
صفحات -
تاریخ انتشار 2010