scholarly journals Characterizations of power indices based on null player free winning coalitions

Optimization ◽  
2013 ◽  
pp. 1-12 ◽  
Author(s):  
M. Alvarez-Mozos ◽  
F. Ferreira ◽  
J.M. Alonso-Meijide ◽  
A.A. Pinto
Keyword(s):  
Power Indices ◽  
Null Player

scholarly journals An Axiomatization for Two Power Indices for (3,2)-Simple Games

2019 ◽  
Vol 21 (01) ◽  
pp. 1940001 ◽  
Author(s):  
Giulia Bernardi ◽  
Josep Freixas
Keyword(s):  
Power Index ◽  
Power Indices ◽  
Simple Games ◽  
Banzhaf Index ◽  
Null Player

The aim of this work is to give a characterization of the Shapley–Shubik and the Banzhaf power indices for (3,2)-simple games. We generalize to the set of (3,2)-simple games the classical axioms for power indices on simple games: transfer, anonymity, null player property and efficiency. However, these four axioms are not enough to uniquely characterize the Shapley–Shubik index for (3,2)-simple games. Thus, we introduce a new axiom to prove the uniqueness of the extension of the Shapley–Shubik power index in this context. Moreover, we provide an analogous characterization for the Banzhaf index for (3,2)-simple games, generalizing the four axioms for simple games and adding another property.

Using equations from power indices to analyze figure skating teams

Public Choice ◽  
2017 ◽  
Vol 170 (3-4) ◽  
pp. 231-251 ◽  
Author(s):  
Diana Cheng ◽  
Peter Coughlin
Keyword(s):  
Power Indices ◽  
Figure Skating

Dynamic Programming for Computing Power Indices for Weighted Voting Games with Precoalitions

Games ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 6
Author(s):  
Jochen Staudacher ◽  
Felix Wagner ◽  
Jan Filipp
Keyword(s):  
Dynamic Programming ◽  
Power Indices ◽  
Efficient Computation ◽  
Banzhaf Index ◽  
Weighted Voting ◽  
Computing Power ◽  
Weighted Voting Games ◽  
Voting Games ◽  
Large Numbers ◽  
New Algorithms

We study the efficient computation of power indices for weighted voting games with precoalitions amongst subsets of players (reflecting, e.g., ideological proximity) using the paradigm of dynamic programming. Starting from the state-of-the-art algorithms for computing the Banzhaf and Shapley–Shubik indices for weighted voting games, we present a framework for fast algorithms for the three most common power indices with precoalitions, i.e., the Owen index, the Banzhaf–Owen index and the symmetric coalitional Banzhaf index, and point out why our new algorithms are applicable for large numbers of players. We discuss implementations of our algorithms for the three power indices with precoalitions in C++ and review computing times, as well as storage requirements.

The Owen and Shapley spatial power indices: A comparison and a generalization

2017 ◽  
Vol 89 ◽  
pp. 10-19 ◽  
Author(s):  
Mathieu Martin ◽  
Zephirin Nganmeni ◽  
Bertrand Tchantcho
Keyword(s):  
Power Indices
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