- Weighted Voting Systems and Voting Power

2014 ◽  
pp. 442-459
Keyword(s):  
Voting Systems ◽  
Weighted Voting ◽  
Voting Power

scholarly journals Standard Voting Power Indexes Do Not Work: An Empirical Analysis

2004 ◽  
Vol 34 (4) ◽  
pp. 657-674 ◽  
Author(s):  
ANDREW GELMAN ◽  
JONATHAN N. KATZ ◽  
JOSEPH BAFUMI
Keyword(s):  
Empirical Analysis ◽  
Square Root ◽  
Voting Systems ◽  
Political Implication ◽  
Weighted Voting ◽  
Voting Power ◽  
European Elections ◽  
Using Data ◽  
Decisive Vote ◽  
Voting Model

Voting power indexes such as that of Banzhaf are derived, explicitly or implicitly, from the assumption that all votes are equally likely (i.e., random voting). That assumption implies that the probability of a vote being decisive in a jurisdiction with n voters is proportional to 1/√n. In this article the authors show how this hypothesis has been empirically tested and rejected using data from various US and European elections. They find that the probability of a decisive vote is approximately proportional to 1/n. The random voting model (and, more generally, the square-root rule) overestimates the probability of close elections in larger jurisdictions. As a result, classical voting power indexes make voters in large jurisdictions appear more powerful than they really are. The most important political implication of their result is that proportionally weighted voting systems (that is, each jurisdiction gets a number of votes proportional to n) are basically fair. This contradicts the claim in the voting power literature that weights should be approximately proportional to √n.

New issues in voting power analysis

2000 ◽  
Vol 9 (2) ◽  
Author(s):  
František Turnovec
Keyword(s):  
Simple Model ◽  
Power Analysis ◽  
Power Indices ◽  
Weighted Voting ◽  
Voting Power ◽  
Voting Game ◽  
Weighted Voting Game

The paper introduces concept of power indices with constraints on voting configuration formation, so called constrained power indices. It is shown in the paper that some of most frequently used power indices based on extremely simple model of weighted voting game can be extended for more sophisticated models of voting situations.

scholarly journals An Empirical Comparison of the Performance of Classical Power Indices

2002 ◽  
Vol 50 (1) ◽  
pp. 1-22 ◽  
Author(s):  
Dennis Leech
Keyword(s):  
A Priori ◽  
Power Indices ◽  
Power Structures ◽  
Empirical Comparison ◽  
Shareholder Voting ◽  
Banzhaf Index ◽  
Weighted Voting ◽  
Voting Power ◽  
Relative A Priori ◽  
New Algorithms

Power indices are general measures of the relative a priori voting power of individual members of a voting body. They are useful for both positive and normative analysis of voting bodies particularly those using weighted voting. This paper applies new algorithms for computing the rival Shapley-Shubik and Banzhaf indices for large voting bodies to shareholder voting power in a cross section of British companies. Each company is a separate voting body and there is much variation in ownership between them resulting in different power structures. Because the data are incomplete, both finite and ‘oceanic’ games of shareholder voting are analysed. The indices are appraised, using reasonable criteria, from the literature on corporate control. The results are unfavourable to the Shapley-Shubik index and suggest that the Banzhaf index much better reflects the variations in the power of shareholders between companies as the weights of shareholder blocs vary.

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