scholarly journals A generalization of Condorcet’s Jury Theorem to weighted voting games with many small voters

2007 ◽  
Vol 35 (3) ◽  
pp. 607-611 ◽  
Author(s):  
Ines Lindner
Keyword(s):  
Weighted Voting ◽  
Weighted Voting Games ◽  
Condorcet’S Jury Theorem ◽  
Voting Games ◽  
Jury Theorem

Human-computer Coalition Formation in Weighted Voting Games

2020 ◽  
Vol 11 (6) ◽  
pp. 1-20
Author(s):  
Moshe Mash ◽  
Roy Fairstein ◽  
Yoram Bachrach ◽  
Kobi Gal ◽  
Yair Zick
Keyword(s):  
Coalition Formation ◽  
Weighted Voting ◽  
Weighted Voting Games ◽  
Voting Games

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.

Monotonicity of power in weighted voting games with restricted communication

2012 ◽  
Vol 64 (3) ◽  
pp. 247-257 ◽  
Author(s):  
Stefan Napel ◽  
Andreas Nohn ◽  
José Maria Alonso-Meijide
Keyword(s):  
Weighted Voting ◽  
Weighted Voting Games ◽  
Voting Games

Analyzing Power in Weighted Voting Games with Super-Increasing Weights

2018 ◽  
Vol 63 (1) ◽  
pp. 150-174 ◽  
Author(s):  
Yuval Filmus ◽  
Joel Oren ◽  
Yair Zick ◽  
Yoram Bachrach
Keyword(s):  
Weighted Voting ◽  
Weighted Voting Games ◽  
Voting Games ◽  
Analyzing Power

scholarly journals Computing power indices for weighted voting games via dynamic programming

2021 ◽  
Vol 31 (2) ◽  
Author(s):  
Jochen Staudacher ◽  
László Á. Kóczy ◽  
Izabella Stach ◽  
Jan Filipp ◽  
Marcus Kramer ◽  
...  
Keyword(s):  
Dynamic Programming ◽  
Power Indices ◽  
Efficient Computation ◽  
Unified Framework ◽  
Weighted Voting ◽  
Weighted Voting Games ◽  
The Public ◽  
Voting Games ◽  
Carry Over ◽  
Minimal Winning Coalitions

We study the efficient computation of power indices for weighted voting games using the paradigm of dynamic programming. We survey the state-of-the-art algorithms for computing the Banzhaf and Shapley-Shubik indices and point out how these approaches carry over to related power indices. Within a unified framework, we present new efficient algorithms for the Public Good index and a recently proposed power index based on minimal winning coalitions of smallest size, as well as a very first method for computing Johnston indices for weighted voting games efficiently. We introduce a software package providing fast C++ implementations of all the power indices mentioned in this article, discuss computing times, as well as storage requirements.

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