Power Indices and Minimal Winning Coalitions for Simple Games in Partition Function Form
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...
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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...
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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...
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ژورنال
عنوان ژورنال: Group Decision and Negotiation
سال: 2017
ISSN: 0926-2644,1572-9907
DOI: 10.1007/s10726-017-9542-x