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1

Degressively proportional functions using the example of seat distribution in the European Parliament

100%
Dniestrzański P.
Didactics of Mathematics
|
2012
|
issue 9(13)
35-42
EN
This article presents an example of the current problem from the borders of economics and politics, which can be used in mathematics courses for economics majors. This problem is the distribution of seats in the European Parliament among the member states of the European Union, and the principle of degressive proportionality formulated for this purpose in the legislation.
2

Adjustment function as a tool for distribution of seats in the European Parliament

80%
Misztal A.
Mathematical Economics
|
2011
|
issue 7 (14)
137-154
EN
The article points out the concept of degressive proportionality, which is defined in the Lisbon Treaty and concerns allotment of seats in the European Parliament. The article introduces the concept of adjustment functions that allows the execution of the transition from the proportional division to degressively proportional. It reminds us of the four methods based on adjustment functions leading to degressively proportional divisions in the weak sense. Methods that are listed are: “shifted proportionality” (by Pukelsheim), parabolic method (by Ramirez), power-type method (by Ramirez), and power-type method (by Haman). The article contains a proposition of a special form of an adjustment function, which is dependent on an increasing, strictly concave function and several parameters. These are the population of the least and most populous country of the European Union (now Malta and Germany), the minimum and maximum number of seats to be allocated (now 6 and 96) and the additional parameter c. It is chosen in such a way that, with a fixed method of rounding of the adjustment function (and thus calculating the number of seats per country), the total number of seats does not exceed a certain fixed value (target 750).
3
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The allocation of seats in the European Parliament and the principle of degressive proportionality

80%
Peternek P., Kośny M.
Mathematical Economics
|
2015
|
issue 11(18)
99-113
EN
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.
4

Degressive proportionality – source, findings and discussion of the cambridge compromise

80%
Dniestrzański P.
Mathematical Economics
|
2011
|
issue 7 (14)
39-50
EN
The principle of degressive proportionality in relation to the division of indivisible goods in the past few years – especially since the signing of the Treaty of Lisbon – has been one of the topics frequently appearing in studies of economists, mathematicians, lawyers and people involved in politics. It combines a purely theoretical and easily definable question with a very important practical problem that concerns primarily members of the European Union and countries aspiring to become one. The article shall include a debate and discussion of the findings of the Cambridge Compromise concerning proposals to solve the problem of allocating seats in the European Parliament.
5
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Degressive proportionality – notes on the ambiguity of the concept

80%
Dniestrzański P.
Mathematical Economics
|
2013
|
issue 9 (16)
21-28
EN
This article discusses the problem of the definition of degressive proportionality. This term is used in many areas of economics but its meaning is not standardized. It is understood differently when related to tax issues compared to distribution of seats in the European Parliament. The differences are small but significant. The article provides and analyzes the different meanings of the concept of degressive proportionality and proposes to introduce two new concepts – concave degressive proportionality and convex degressive proportionality.
6
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Axiomatization of divisor methods and weakly degressive proportionality

80%
Dniestrzański P.
Didactics of Mathematics
|
2017
|
issue 14(18)
19-26
EN
The paper analyzes the differences between weakly degressive proportionality and proportional allocations represented by divisor methods. The analysis is accomplished by the axiomatization of divisor methods in line with Balinski and Young.
7
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Sprawiedliwość podziału degresywnie proporcjonalnego

80%
Łyko J.
Ekonomia - Uniwersytet Ekonomiczny we Wroclawiu
|
2013
|
issue 2 (23)
180-189
EN
The principle of degressively proportional distribution of seats in the European Parliament has been legally sanctioned under the terms of the Lisbon Treaty. Thus there appeared a solution which defied the perception of justice of distribution according to culturally shaped proportional allocation rules. Previous methods of determining the composition of collegiate bodies generally used the rule of proportional to the population of each constituency, composition of the legal body representing the society. On this basis, there are many socially accepted methods which have been tried and tested. In the field of electoral law regulations the rule of degressive proportionality is a new solution, and as such it still lacks tradition and already shaped approval that may justify its use. This article aims to find justification for this solution as opposed to the socially accep- table methods of distribution of goods and debts. In order to arrive at this argument the article reaches back to Aristotle’s philosophical concept, as well as solutions taken from the Talmud. It turns out that the degressive proportionality falls within the accepted concepts of equitable distribution. It offers an intermediate solution between equal and proportional allocation. There are also legitimate reasons for the use of degressively proportional rule in the process of allocating seats in the European Parliament. The problem is only the lack of unambiguity of the rule and the lack of precise reasoning to determine the boundary conditions at the level set in the Lisbon Treaty. This creates a very high degree of freedom of interpretation, leaving room for political negotiations on the acceptance of specific proposals. This situation has led to the point that, since the legal acceptance of the principle of degressive proportionality, the rule has not been applied in practice. Proposals for the composition of the European Parliament presented at the beginning of 2013 for the term 2014-2019 indicate that over the next five years exceptions to this rule will be approved. The second part of the paper presents proposals on solving the problem that can be found in the literature, as well as two other directions for seeking fair allocation. They cannot be deprived of discretion, as, of course, it is not possible to obtain conclusive decisions without the introduction of additional postulates. These postulates aim at clarifying the determination of the boundary conditions in such a way as to reduce the number of possible solutions or introduce an additional rule that will allow for an unambiguous (for a given population) specification of composition of the European Parliament. This is possible thanks to, inter alia, the ability to generate all feasible solutions. In this situation the solution of the problem is to select one out of a finite number of known divisions according to an established criterion. This frees the process of selecting the composition of the European Parliament from political considerations, and moves the weight of the debate to the ground of determining the said additional criterion. The current problem concerning the distribution of seats in the European Parliament is of course more general. The conditions that caused sanctioning of such a solution are of economic and social origin. It is expected that in the future the number of problems associated with allocation of goods, that are solved in this way, will be greater than they are currently. Undoubtedly, inequalities in various aspects of social existence favor the issue.
8
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Disproportions in proportional distributions

80%
Misztal A.
Mathematical Economics
|
2013
|
issue 9 (16)
89-104
EN
In the case of degressive proportionality, a large over-representation of small countries is a deliberate concession of larger countries to ensure that less populated states are adequately represented (the principle of European solidarity). It is worth emphasizing how important is the role played by election thresholds, which prevent excessive fragmentation of the parliament. Thus, they act as a stabilizing factor in the political scene, which in Polish conditions cannot be overestimated. A weakness of the thresholds is the fact that they distort the proportionality of the results and cause over-representation of certain parties. In extreme cases they can lead to the dictatorship of one party even if it is provided with low popularl support.
9

Degressive proportionality in the European Parliament

70%
Cegiełka K.
Mathematical Economics
|
2011
|
issue 7 (14)
31-38
EN
The division of mandates to the European Parliament has posed difficulties since the beginning of its operation. The introduction of the degressive proportionality principle to legal acts intensified further discussion on this subject. The researchers propose different solutions in the form of algorithms or functions with which it is possible to determine the composition of the European Parliament.
10

Composition of the European Parliament in the 2014-2019 term

70%
Cegiełka K.
Didactics of Mathematics
|
2012
|
issue 9(13)
25-34
EN
Currently, representatives of 28 countries form the European Parliament. Their populations are characterized by a large disparity which leads to the need to seek methods of allocating the seats which are not based on proportional methods. They should have fulfilled the conditions of degressive proportionality by 2009. Although scientists have so far offered various solutions in line with the assumptions, MEPs did not take any of them. Furthermore, they changed the interpretation of the new rule in subsequent terms of office. At the same time, they have not determined a composition of the European Parliament which meets the conditions of degressive proportionality. In the paper, the author presents the degressive proportionality principle and analyzes the composition of the European Parliament in 2014-2019 term proposed by MEPs.
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