Proposal for Measure of Degressive Proportionality

AbstractDegressive proportionality is an intermediary solution between equality and proportionality. Taking this fact into account, the article proposes a measure of degression of the degressively proportional division. The defined measure was used, among other instances, in allocation based on classical proposals of seat distribution in European Parliament by Pukelsheim and Ramirez as well as the distribution of seats during the Parliamentary term of 2014- 2019. The outcome is confronted with other measures functioning in the literature

Mathematical aspects of degressive proportionality

We analyze properties of apportionment functions in context of the problem of allocating seats in the European Parliament. Necessary and sufficient conditions for apportionment functions are investigated. Some exemplary families of apportionment functions are specified and the corresponding partitions of the seats in the European Parliament among the Member States of the European Union are presented. Although the choice of the allocation functions is theoretically unlimited, we show that the constraints are so strong that the acceptable functions lead to rather similar solutions.Comment: several minor corrections, revised version 10 pages in two column style, one figure and two tables include

The implications of possible enlargements of the European Union for the configuration of power in the European parliament

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 European Union 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.peer-reviewe

Multi-Winner Voting with Approval Preferences

Approval-based committee (ABC) rules are voting rules that output a fixed-size subset of candidates, a so-called committee. ABC rules select committees based on dichotomous preferences, i.e., a voter either approves or disapproves a candidate. This simple type of preferences makes ABC rules widely suitable for practical use. In this book, we summarize the current understanding of ABC rules from the viewpoint of computational social choice. The main focus is on axiomatic analysis, algorithmic results, and relevant applications.Comment: This is a draft of the upcoming book "Multi-Winner Voting with Approval Preferences

Multi-Winner Voting with Approval Preferences

From fundamental concepts and results to recent advances in computational social choice, this open access book provides a thorough and in-depth look at multi-winner voting based on approval preferences. The main focus is on axiomatic analysis, algorithmic results and several applications that are relevant in artificial intelligence, computer science and elections of any kind. What is the best way to select a set of candidates for a shortlist, for an executive committee, or for product recommendations? Multi-winner voting is the process of selecting a fixed-size set of candidates based on the preferences expressed by the voters. A wide variety of decision processes in settings ranging from politics (parliamentary elections) to the design of modern computer applications (collaborative filtering, dynamic Q&A platforms, diversity in search results, etc.) share the problem of identifying a representative subset of alternatives. The study of multi-winner voting provides the principled analysis of this task. Approval-based committee voting rules (in short: ABC rules) are multi-winner voting rules particularly suitable for practical use. Their usability is founded on the straightforward form in which the voters can express preferences: voters simply have to differentiate between approved and disapproved candidates. Proposals for ABC rules are numerous, some dating back to the late 19th century while others have been introduced only very recently. This book explains and discusses these rules, highlighting their individual strengths and weaknesses. With the help of this book, the reader will be able to choose a suitable ABC voting rule in a principled fashion, participate in, and be up to date with the ongoing research on this topic

Equal representation in two-tier voting systems

The paper investigates how voting weights should be assigned to differently sized constituencies of an assembly. The one-person, one-vote principle is interpreted as calling for a priori equal indirect influence on decisions. The latter are elements of a one-dimensional convex policy space and may result from strategic behavior consistent with the median voter theorem. Numerous artificial constituency configurations, the EU and the US are investigated by Monte-Carlo simulations. Penrose’s square root rule, which originally applies to preference-free dichotomous decision environments and holds only under very specific conditions, comes close to ensuring equal representation. It is thus more robust than previously suggested

Equal or Not? : on the Material Aspect of Equality of European Parliament Elections in Poland

This article focuses on the issue of equality of elections, in the context of the 2014 European Parliament election in Poland. Most often the definition of principles of elections' equality comes down to emphasizing its two aspects: the formal one and the material one. The first of them refers to guaranteeing each person with the active voting right the same number of votes. The material aspect of the equality principle is connected with striving to guarantee the same "voting power" to the election participants. Most briefly, it means that a given number of people elect as many representatives as another group with the same numerical strength. The main aim of this article is focus on the material aspect of implementing the principle of equality in EP elections. In the article will be emphasized three issues decisive for the specific features of the electoral system (electoral districts, election threshold and electoral formula), at the same time influencing the range of implementation of the material equality of elections. General findings will be confronted with empirical data, which will allow to formulate conclusions about the degree to which the European Parliament election conducted in Poland on 25th May 2014 met the principle of material equality