Beyond the Cambridge Compromise algorithm towards degressively proportional allocations

Cegiełka, Katarzyna; Łyko, Janusz; Rudek, Radosław

doi:10.1007/s12351-017-0292-y

Cited by 7 publications

(4 citation statements)

References 12 publications

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“…Again, it is impossible to calculate the PSI for this method, and there is no need to discuss the Relative-equality axiom. There are many other methods for the apportionment of the EP [13,[43][44][45][46][47]51,52,54,55]. None of these methods demonstrate a specific consideration for individual equality in their design (partly because the EP has not decided on a standard), except for proportionality, which cannot be applied to a subproportional context.…”

Section: On Existing Apportionment Methods For the Epmentioning

confidence: 99%

Axioms and Divisor Methods for a Generalized Apportionment Problem with Relative Equality

Wenruo

Zhao

2023

Mathematics

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The allocation of seats in a legislative body to groups based on their size is a crucial issue in legal and political studies. However, recent findings suggest that an optimal allocation of seats may not be proportional to the size of the groups. For instance, the European Parliament (EP) utilizes a subproportional system known as degressive proportionality. Unfortunately, current apportionment methods for the EP lack a rigorous axiomatic analysis and fail to adequately address equality. Building upon recent research on equality in subproportional settings, this paper proposed a novel generalization of existing axioms and divisor methods for proportionality to encompass subproportionality with relative equality. Specifically, we consider a function f(p)=a+bpγ on the standard number of seats for a group of size p, where a, b and γ are given non-negative constants, and a is an integer. This theory is exemplified through an empirical study focused on the EP.

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Section: On Existing Apportionment Methods For the Epmentioning

confidence: 99%

Axioms and Divisor Methods for a Generalized Apportionment Problem with Relative Equality

Wenruo

Zhao

2023

Mathematics

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“…A lot of research is also focused on one of the most important proposals developed in 2011 by the participants of the scientific meeting held at the instigation of the Committee on Constitutional Affairs of the European Parliament (AFCO) at the Centre for Mathematical Sciences, University of Cambridge. The papers such as Cegiełka et al (2019), Duff (2012), Grimmett (2012), Grimmett et al (2012), Habermas (2017, Haman (2017), Laslier (2012), Łyko and Rudek (2017), Macé and Treibich (2012), Moberg (2012), Grimmett (2018), Policy Department (2017) and Słomczyński and Życzkowski (2012) deal with this subject among other things.…”

Section: Review Of Literaturementioning

confidence: 99%

A neutral core of degressively proportional allocations under lexicographic preferences of agents

et al. 2021

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One of the main problems of practical applications of degressively proportional allocations of goods and burdens is lack of uniqueness of this principle. Even under given boundary conditions of allocation, i.e. determined minimal and maximal amounts of a good that can be assigned in a given allocation, there are usually many feasible solutions. The lack of formal rules of allocation is the reason why the allocation is typically a result of negotiations among its agents. A number of allocations favor some of agents or their groups, therefore other agents cannot accept them. The aim of this paper is to indicate a way of reducing the set of all feasible solutions exclusively to those that are neutral to all agents. As a result of the term of lexicographic preference of allocation agents defined on the basis of the relation theory followed by a numerical analysis of sets of all feasible solutions, it is possible to determine a core of this set in the form of a subset of all feasible solutions that are acceptable by all agents. In addition, this subset can be further divided into smaller subsets with regard to the degree of acceptance of their elements. Theoretical analysis is complemented by case studies, one of which is application of this idea to the allocation of seats in the European Parliament among the member states of the European Union.

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“…The first one draws on standard solutions applied in cases of proportional integer allocations [14]. One assumes that the condition of degressive proportionality has to be met before merely rounding to integers [15][16][17][18][19]. The second thread builds upon approaching the rule in its literal wording, and thereby it is assumed that the sequence which performs a given allocation must be degressively proportional [20][21][22][23].…”

Section: Case Studymentioning

confidence: 99%

Asymmetrization of a Set of Degressively Proportional Allocations with Respect to Lexicographic Order. An Algorithmic Approach

et al. 2021

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In the case of the proportional allocation of goods and burdens, the shares of all agents with respect to their values are equal, i.e., they form a constant sequence. In a degressively proportional allocation this sequence is nondecreasing when agents are increasingly ordered according to their values. The division performed according to this principle is ambiguous, and its selection requires many negotiations among participants. The aim of this paper is to limit the range of such negotiations when the problem is complex, i.e., the set of feasible solutions has high cardinality. It can be done thanks to a numerical analysis of the set of all feasible solutions, and eliminating allocations favoring or disfavoring some coalitions of agents. The problem is illustrated by the case study of allocating seats in the European Parliament in its 2019–2024 term.

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Beyond the Cambridge Compromise algorithm towards degressively proportional allocations

Cited by 7 publications

References 12 publications

Axioms and Divisor Methods for a Generalized Apportionment Problem with Relative Equality

Axioms and Divisor Methods for a Generalized Apportionment Problem with Relative Equality

A neutral core of degressively proportional allocations under lexicographic preferences of agents

Asymmetrization of a Set of Degressively Proportional Allocations with Respect to Lexicographic Order. An Algorithmic Approach

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