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Correlation and Inequality in Weighted Majority Voting Games

Bhattacherjee, Sanjay and Sarkar, Palash (2019) Correlation and Inequality in Weighted Majority Voting Games. In: Deprivation, Inequality and Polarization. Economic Studies in Inequality, Social Exclusion and Well-Being. Springer, Singapore, pp. 161-191. ISBN 978-981-13-7943-7. E-ISBN 978-981-13-7944-4. (doi:10.1007/978-981-13-7944-4_9) (KAR id:93927)

Abstract

In a weighted majority voting game, the weights of the players are determined based on some socio-economic parameter. A number of measures have been proposed to measure the voting powers of the different players. A basic question in this area is to what extent does the variation in the voting powers reflect the variation in the weights? The voting powers depend on the winning threshold. So, a second question is what is the appropriate value of the winning threshold? In this work, we propose two simple ideas to address these and related questions in a quantifiable manner. The first idea is to use Pearson's Correlation Coefficient between the weight vector and the power profile to measure the similarity between weight and power. The second idea is to use standard inequality measures to quantify the inequality in the weight vector as well as in the power profile. These two ideas answer the first question. Both the weight-power similarity and inequality scores of voting power profiles depend on the value of the winning threshold. For situations of practical interest, it turns out that it is possible to choose a value of the winning threshold which maximises the similarity score and also minimises the difference in the inequality scores of the weight vector and the power profile. This provides an answer to the second question. Using the above formalisation, we are able to quantitatively argue that it is sufficient to consider only the vector of swings for the players as the power measure. We apply our methodology to the voting games arising in the decision making processes of the International Monetary Fund (IMF) and the European Union (EU). In the case of IMF, we provide quantitative evidence that the actual winning threshold that is currently used is sub-optimal and instead propose a winning threshold which has a firm analytical backing. On the other hand, in the case of EU, we provide quantitative evidence that the presently used threshold is very close to the optimal.

Item Type: Book section
DOI/Identification number: 10.1007/978-981-13-7944-4_9
Uncontrolled keywords: Voting games, Weighted majority, Power measure, Correlation, Inequality, Gini index, Coefficient of variation
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Computing
University-wide institutes > Institute of Cyber Security for Society
Depositing User: Sanjay Bhattacherjee
Date Deposited: 06 Apr 2022 09:16 UTC
Last Modified: 05 Nov 2024 12:59 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/93927 (The current URI for this page, for reference purposes)

University of Kent Author Information

Bhattacherjee, Sanjay.

Creator's ORCID: https://orcid.org/0000-0002-3367-6192
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