Application of Hamilton's and Divisor Methods to Degressively Proportional Allocation Functions

Cegiełka, Katarzyna; Łyko, Janusz

doi:10.1016/j.sbspro.2013.12.852

Cited by 3 publications

(3 citation statements)

References 4 publications

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“…The literature on the subject includes both proposed methods dealing with division of seats in the European Parliament [for example: (Pukelsheim, 2007;Ramírez-González, 2007;Martínez-Aroza and Ramírez-González, 2008;Słomczyński and Życzkowski, 2010;Pukelsheim, 2010;Słomczyński and Życzkowski, 2010;Grimmett et al, 2011;Florek, 2012;Ramírez-González et al, 2012;Słomczyński and Życzkowski, 2012;Łyko and Rudek, 2013;Dniestrzański and Łyko, 2014;Łyko and Rudek, 2017;Cegiełka et al, 2019), as well as theoretical analyses to be applied regardless of what type of goods are divided (Słomczyński and Życzkowski, 2012;Cegiełka and Łyko, 2014;Haman, 2017;Dniestrzański and Łyko, 2020;Cegiełka et al, 2021a;Cegiełka et al, 2021b. The discussion around indicating a single rule to form the composition of the European Parliament has been ongoing for more than fifteen years. The best-known proposal is the so-called Cambridge Compromise (Grimmett et al, 2011).…”

Section: Introductionmentioning

confidence: 99%

The Implications of Possible Enlargements of the European Union for the Configuration of Power in the European Parliament

Cegiełka¹,

Dniestrzański²,

Maciuk³

et al. 2022

ERSJ

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Purpose:The paper aims at simulating the composition of the European Parliament (EP) after possible impending enlargements of the European Union. To this end, a number of scenarios are considered to this end including the accession of the four countries with current candidate status and the three countries which applied for admission to the Community as of March 2022. Approach/Methodology/Design: The analyzed simulations of EP composition were developed using the methods most frequently proposed in the literature, i.e. the parabolic method, the base+prop method and r-DP methods. These methods allocate the seats in concordance with the condition of degressive proportionality. Findings: All the scenarios of the EU enlargement discussed imply an increased total EP representation of the group of countries with low income in terms of GDP per capita, hence their role in the EP increases. This result complies with the idea of the harmonious development of European countries based on cooperation as promoted by the Community. Practical Implications: Eight different scenarios of possible enlargements of the EuropeanUnion were applied to determine the divisions of seats in the European Parliament. These simulations can underlie the choice of a concrete method of finding the allocation of mandates as an alternative to the current practice of determining the composition of seats by negotiations. Grouping states according to GDP per capita makes it possible to compare the methods employed in the context of their influence on the total quantity of the representation of countries with different levels of affluence. Originality/Value: The added value of this paper is the comparison of results from selected methods in view of possible enlargements of the Community. In particular, it turns out that the base+prop method is the most "neutral" for the countries with the highest GDP per capita, as in the case of Ukraine's accession.

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Section: Introductionmentioning

confidence: 99%

The Implications of Possible Enlargements of the European Union for the Configuration of Power in the European Parliament

Cegiełka¹,

Dniestrzański²,

Maciuk³

et al. 2022

ERSJ

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“…This lack of uniqueness is studied in papers dealing with the so-called unrounded degressive proportionality (UDP), which examine the non-integer degressively proportional allocations (see for example [10][11][12][13]). In this paper, the authors mainly draw on the approach of degressively proportional allocations of divisible goods.…”

Section: Introductionmentioning

confidence: 99%

Relative Entropy in Determining Degressive Proportional Allocations

Cegiełka

Dniestrzański

Łyko

et al. 2021

Entropy

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The principle of degressively proportional apportionment of goods, being a compromise between equality and proportionality, facilitates the application of many different allocation rules. Agents with smaller entitlements are more interested in an allocation that is as close to equality as possible, while those with greater entitlements prefer an allocation as close to proportionality as possible. Using relative entropy to quantify the inequity of allocation, this paper indicates an allocation that neutralizes these two contradictory approaches by symmetrizing the inequities perceived by the smallest and largest agents participating in the apportionment. First, based on some selected properties, the set of potential allocation rules was reduced to those generated by power functions. Then, the existence of the power function whose exponent is determined so as to generate the allocation that symmetrizes the relative entropy with respect to equal and proportional allocations was shown. As a result, all agents of the apportionment are more inclined to accept the proposed allocation regardless of the size of their entitlements. The exponent found in this way shows the significant relationship between the problem under study and the well-known Theil indices of inequality. The problem may also be seen from this viewpoint.

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“…The design of most bodies of an international character obliges their members to create a system of methods to take common, usually compromise, decisions. Due to the increasing importance of the European Parliament and the expanding group of its countries -members of the European Union -more attention has been paid to the system of distribution of seats in the European Parliament (see, among others, [Ramirez et al 2006;Pukelsheim 2007;Łyko et al 2010;Cegiełka 2011;Cegiełka, Łyko 2014;Misztal 2014]).…”

Section: Introductionmentioning

confidence: 99%

The allocation of seats in the European Parliament and the principle of degressive proportionality

Peternek¹,

Kośny²

2015

Mathematical Economics

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One of the key issues in the process of preparing for an election to the European Parliament is to determine the number of seats for each country. The Treaty of Lisbon, signed by Member States of the European Union, has obliged the European Parliament to establish rules guaranteeing that the distribution of seats should be done according to, inter alia, the principle of degressive proportionality. The purpose of this paper is to explore how the principle of degressive proportionality is actually implemented, and to propose a compromise -a mathematical solution, guaranteeing that the distribution of seats is consistent with the requirements of the Lisbon Treaty.

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Application of Hamilton's and Divisor Methods to Degressively Proportional Allocation Functions

Cited by 3 publications

References 4 publications

The Implications of Possible Enlargements of the European Union for the Configuration of Power in the European Parliament

The Implications of Possible Enlargements of the European Union for the Configuration of Power in the European Parliament

Relative Entropy in Determining Degressive Proportional Allocations

The allocation of seats in the European Parliament and the principle of degressive proportionality

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