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An Equivalent Formulation for the Shapley Value Read chapter Read first chapter

2018 | OriginalPaper | Chapter

Remarks on Unrounded Degressively Proportional Allocation

Authors : Katarzyna Cegiełka, Piotr Dniestrzański, Janusz Łyko, Arkadiusz Maciuk

Published in: Transactions on Computational Collective Intelligence XXXI

Publisher: Springer Berlin Heidelberg

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Abstract

The Lisbon Treaty has legally endorsed degressiveness as a principle of distributing indivisible goods. Yet the principle has been implemented in executive acts with insufficient precision. As a result, it cannot be unambiguously applied in practice. Therefore many theoretical studies have been conducted aiming at a more precisely defined formulation of the principle so that resulting allocations could be explicitly derived from primary rules. This paper belongs to such research stream. It aims at submitting a formal definition of unrounded degressively proportional distribution.

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Footnotes
1
Detailed mathematical analysis of the allocation functions the reader will find in [9].
 
2
Haman argues that the value of parameter u can be then interpreted as a measure of degression of allocations. A smaller value of this parameter indicates more degression of the allocation. The smaller the value u, the more degressive allocation (closer to equal division). A given allocation is less degressive (closer to a proportional allocation), as u approaches unity. Haman continues the research into degressive proportionality in a weak case (UDP) and in a strong case (RDP) [11].
 
Literature
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Lamassoure, A., Severin, A.: Report on the composition of the European Parliament. Committee on Constitutional Affairs, A6-0351 (2007)
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Maciuk, A.: Przykłady podziałów mandatów do Parlamentu Europejskiego spełniających warunki Traktatu Lizbońskiego [Examples of the divisions of seats to the European Parliament that meet the conditions of the Treaty of Lisbon]. Prace Naukowe Uniwersytetu Ekonomicznego we Wrocławiu. Ekonometria 33(198), 85–96 (2011)
4.
Florek, J.: A numerical method to determine a degressive proportional distribution of seats in the European Parliament. Math. Soc. Sci. 63(2), 121–129 (2012)MathSciNetCrossRef
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Łyko, J., Rudek, R.: A fast exact algorithm for the allocation of seats for the EU Parliament. Expert Syst. Appl. 40, 5284–5291 (2013)CrossRef
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Pukelsheim, F.: A parliament of degressive representativeness? Institut für Mathematik, Universität Augsburg, Preprint Nr 015/2007 (2007)
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Pukelsheim, F.: Putting citizens first: representation and power in the European Union. In: Cichocki, M., Życzkowski, K. (eds.) Institutional Design and Voting Power in the European Union, pp. 235–253. Ashgate, London (2010)
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Słomczyński, W., Życzkowski, K.: Mathematical aspects of degressive proportionality. Math. Soc. Sci. 63(2), 94–101 (2012)MathSciNetCrossRef
10.
Haman, J.: Degresywnie proporcjonalny podział mandatów w Parlamencie Europejskim [Degressively proportional division of seats in the European Parliament]. Decyzje 8, 53–78 (2007)
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Gualtieri, R., Trzaskowski, R.: Report on the composition of the European Parliament with a view to the 2014 elections. A7-0041/2013 (2013)
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Pukelsheim, F.: Proportional Representation. Apportionment Methods and Their Applications. Springer, Cham (2014)CrossRef
Metadata
Title
Remarks on Unrounded Degressively Proportional Allocation
Authors
Katarzyna Cegiełka
Piotr Dniestrzański
Janusz Łyko
Arkadiusz Maciuk
Copyright Year
2018
Publisher
Springer Berlin Heidelberg
Book
Transactions on Computational Collective Intelligence XXXI

Print ISBN: 978-3-662-58463-7

Electronic ISBN: 978-3-662-58464-4

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-662-58464-4_6

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