Abstract
A class of allocation rules is introduced for allocating votes in a parliament to parties based on population. A unique feature of the class is that a well-defined objective function is associated with each allocation rule in the class. It is shown that the objective function corresponding to the “square root” allocation rule is of particular interest. This rule attempts to give each party a number of votes proportional to the square root of its size. Also described is an allocation procedure which takes care of the typical situation when the allocation rule results in fractional votes being allocated whereas in fact one allows only whole number votes to be allocated. Allocations for the European Parliament using the above class of rules are compared with the currently proposed allocations for that body.
This article first appeared in the European Economic Review, 9 (1977), 247–263. Reprinted with the permission of Elsevier Science Publishers B.V. (North-Holland). Research supported in part by NSF Grant GS-41319X.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Balinski, M.L. and H.P. Young: 1976, “A Problem of Fair Division: Apportioning the European Parliament,” Research Memorandum RM-76–55, International Institute for Applied Systems Analysis, Laxenburg, Austria.
Grosfeld, F.: 1967, “De kwadratuur van de democratische cirkelgang,” Vrij Nederland, December 30, 4.
Kendall, M.G. and A. Stuart: 1950, “The Law of Cubic Proportion in Election Results,” British Journal ofSociology 1, 183–196.
Lucas, W.F.: 1974, “Measuring Power in Weighted Voting Schemes,” Technical Report no. 227, Department of Operations Research, Cornell University, Ithaca, New York.
Penrose, L.S.: 1946, “The Elementary Statistics of Majority Voting,” Journal ofthe Royal Statistical Society 109, 53–57.
Penrose, L.S.: 1952, On the Objective Study of Crowd Behaviour, H.K. Lewis, London.
Theil, H.: 1969, “The Desired Political Entropy,” The American Political Science Review 63, 521–525.
Theil, H.: 1971, “The Allocation of Power that Minimizes Tension,” Operations Research 19, 977–982.
Theil, H.: 1972, Statistical Decomposition Analysis with Applications in the Social and Administrative Sciences, North-Holland, Amsterdam.
Theil, H.: 1975/6, Theory and Measurement of Consumer Demand, (2 vols.), North Holland, Amsterdam.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Theil, H., Schrage, L. (1992). The Apportionment Problem and the European Parliament. In: Raj, B., Koerts, J. (eds) Henri Theil’s Contributions to Economics and Econometrics. Advanced Studies in Theoretical and Applied Econometrics, vol 24. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2410-2_20
Download citation
DOI: https://doi.org/10.1007/978-94-011-2410-2_20
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5063-0
Online ISBN: 978-94-011-2410-2
eBook Packages: Springer Book Archive