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Power indices as an aid to institutional design: the generalised apportionment problem

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Leech, Dennis (2002) Power indices as an aid to institutional design: the generalised apportionment problem. Working Paper. University of Warwick, Department of Economics, Coventry.

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Abstract

A priori voting power analysis can be useful in helping to design a weighted voting system that has certain intended properties. Power indices can help determine how many weighted votes each member should be allocated and what the decision rule should be. These choices can be made in the light of a requirement that there be a given distribution of power and/or a desired division of powers between individual members and the collective institution. This paper focuses on the former problem: choosing the weights given that the power indices and the decision rule are fixed exogenously.

Item Type: Working or Discussion Paper (Working Paper)
Subjects: H Social Sciences > HB Economic Theory
Divisions: Faculty of Social Sciences > Economics
Library of Congress Subject Headings (LCSH): Voting research, Decision making, Power (Social sciences), Choice (Psychology)
Series Name: Warwick economic research papers
Publisher: University of Warwick, Department of Economics
Place of Publication: Coventry
Date: August 2002
Number: No.648
Number of Pages: 27
Status: Not Peer Reviewed
Access rights to Published version: Open Access
Description: Paper prepared for the workshop on Voting Power Analysis, LSE 9-11 August 2002.
References: Arrow, Kenneth J. and F. H. Hahn (1971), "General Competitive Analysis, San Francisco, Holden Day. Balinski, M.L. and H. P. Young (1982), Fair Representation: Meeting the Ideal of One Man, One Vote, Yale University Press. Banzhaf, John F (1965), “Weighted Voting Doesn’t Work: A Mathematical Analysis”, Rutgers Law Review, 19: 317-343 Brams, Steve P. and J. Affuso (1976), “Power and Size: a New Paradox,” Theory and Decision, 7: 29-56. Coleman, James S (1971) "Control of Collectivities and the Power of a Collectivity to Act," in B.Lieberman (ed), Social Choice, New York, Gordon and Breach; reprinted in J.S. Coleman, 1986, Individual Interests and Collective Action, Cambridge University Press. Dubey, Pradeep. and Lloyd.S. Shapley (1979), "Mathematical Properties of the Banzhaf Value," Mathematics of Operational Research, 4: 99-131. Felsenthal, Dan S. and Moshé Machover, (1998),The Measurement of Voting Power, Cheltenham, Edward Elgar. Gambarelli, Gianfranco (1999), "Minimax Apportionments" Group Decision and Negotiation, 8:441-61. Holler, Manfred (1982), "An Introduction to the Analysis of Power, Voting and Voting Power, in Manfred Holler (Ed.), Power, Voting and Voting Power, Physica-Verlag, Wurtzburg. --------------------(1987), "Paradox Proof Decision Rules in Weighted Voting", in The Logic of Multiparty Systems, Dordrecht:Martinus Nijhoff Publishers, 425-36. Laruelle, Annick and Federico Valenciano (2001), “Shapley-Shubik and Banzhaf Indices Revisited”, Mathematics of Operations Research, 26, 89-104. Laruelle, Annick and Mika Widgren (1998), "Is the Allocation of Voting Power among EU Member States Fair?", Public Choice, 94, 317-39. Leech, Dennis (2002a), "An Empirical Comparison of the Performance of Classical Power Indices", Political Studies, 50: 1- 22. ----------------- (2002b), "Voting Power in the Governance of the International Monetary Fund", Annals of Operations Research, 109, 373-395. ----------------- (2002c), "The Use of Coleman's Power Indices to Inform the Choice of Voting Rule with Reference to the IMF Governing Body and the EU Council of Ministers", Warwick Economic Research Papers, Number 645, (Available for download from www.warwick.ac.uk/fac/soc/Economics/research/twerps.html) --------------- (forthcoming), “Designing the Voting System for the Council of the European Union,” Public Choice, in press. (Available for download from www.warwick.ac.uk/fac/soc/Economics/leech.) Lucas, William F. (1983), “Measuring Power in Weighted Voting Systems,” in S. Brams, W. Lucas and P. Straffin (eds.), Political and Related Models, Springer. Nurmi, Hannu.(1978),."Power and Support: the Problem of Representational Democracy", Munich Social Science Review, 4:5-24. -------------------(1982), "The Problem of the Right Distribution of Voting Power" in Manfred Holler (Ed.), Power, Voting and Voting Power, Physica-Verlag, Wurtzburg. Penrose, L.S. (1946), "The Elementary Statistics of Majority Voting," Journal of the Royal Statistical Society, 109, 53-57. Shapley, Lloyd and Martin Shubik (1954), “A Method for Evaluation the Distribution of Power in a Committee System”, American Political Science Review, 48, 787-92. Sutter, Matthias (2000), "Fair Allocation and Re-weighting of Votes and Voting Power in the EU Before and After the Next Enlargement", Journal of Theoretical Politics, 12:433-49.
URI: http://wrap.warwick.ac.uk/id/eprint/1538

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