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Voting power and voting blocs

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  • Dennis Leech

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  • Robert Leech

Abstract

We investigate the method of power indices to study voting power of members of a legislature that has voting blocs. Our analysis is theoretical, intended to contribute to a theory of positive political science in which social actors are motivated by the pursuit of power as measured by objective power indices. Our starting points are the papers by Riker (Behavioural Science, 1959, “A test of the adequacy of the power index”) and Coleman (American Sociological Review, 1973, “Loss of Power”). We argue against the Shapley–Shubik index and show that anyway the Shapley–Shubik index per head is inappropriate for voting blocs. We apply the Penrose index (the absolute Banzhaf index) to a hypothetical voting body with 100 members. We show how the power indices of individual bloc members can be used to study the implications of the formation of blocs and how voting power varies as bloc size varies. We briefly consider incentives to migrate between blocs. This technique of analysis has many real world applications to legislatures and international bodies. It can be generalised in many ways: our analysis is a priori (assuming formal voting and ignoring actual voting behaviour) but can be made empirical with voting data reflecting behaviour; it examines the consequences of two blocs but can easily be extended to more. Copyright Springer Science + Business Media, Inc. 2006

Suggested Citation

  • Dennis Leech & Robert Leech, 2006. "Voting power and voting blocs," Public Choice, Springer, vol. 127(3), pages 285-303, June.
  • Handle: RePEc:kap:pubcho:v:127:y:2006:i:3:p:285-303 DOI: 10.1007/s11127-006-1914-8
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    References listed on IDEAS

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    1. Dan S. Felsenthal & Moshé Machover, 1998. "The Measurement of Voting Power," Books, Edward Elgar Publishing, number 1489, April.
    2. Dennis Leech, 2002. "An Empirical Comparison of the Performance of Classical Power Indices," Political Studies, Political Studies Association, vol. 50(1), pages 1-22, March.
    3. Pradeep Dubey & Lloyd S. Shapley, 1979. "Mathematical Properties of the Banzhaf Power Index," Mathematics of Operations Research, INFORMS, vol. 4(2), pages 99-131, May.
    4. repec:cup:apsrev:v:48:y:1954:i:03:p:787-792_00 is not listed on IDEAS
    5. James Coleman, 1970. "The benefits of coalition," Public Choice, Springer, vol. 8(1), pages 45-61, March.
    6. Leech, Dennis & Leech, Robert, 2004. "Voting Power in the Bretton Woods Institutions," The Warwick Economics Research Paper Series (TWERPS) 718, University of Warwick, Department of Economics.
    7. Straffin, Philip Jr., 1994. "Power and stability in politics," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 32, pages 1127-1151 Elsevier.
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    Cited by:

    1. Matthew Gould & Matthew D. Rablen, 2016. "Equitable representation in councils: theory and an application to the United Nations Security Council," Public Choice, Springer, vol. 169(1), pages 19-51, October.
    2. Claus Beisbart, 2010. "Groups can make a difference: voting power measures extended," Theory and Decision, Springer, vol. 69(3), pages 469-488, September.
    3. Leech, Dennis & Leech, Robert, 2012. "A New Analysis of A Priori Voting Power in the IMF: Recent Quota Reforms Give Little Cause for Celebration," The Warwick Economics Research Paper Series (TWERPS) 1001, University of Warwick, Department of Economics.
    4. Alonso-Meijide, J.M. & Bilbao, J.M. & Casas-Méndez, B. & Fernández, J.R., 2009. "Weighted multiple majority games with unions: Generating functions and applications to the European Union," European Journal of Operational Research, Elsevier, vol. 198(2), pages 530-544, October.
    5. Serguei Kaniovski, 2008. "The exact bias of the Banzhaf measure of power when votes are neither equiprobable nor independent," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(2), pages 281-300, August.

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