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Modern democratic political systems are hardly conceivable without political representation. This also applies to the European Union, a unique political system with a directly elected and fully-fledged assembly representing the EU citizens, with the European Parliament being the first international parliamentary assembly to strive for democratic political representation. The case study addresses the composition of the European Parliament, or more specifically, it focuses on methods of apportioning the European Parliamentary seats among the EU Member States according to the degressive proportionality principle as codified by the Lisbon Treaty. First, the paper discusses the principle of degressive proportionality, both from a theoretical and empirical perspective, in the latter case taking into account the composition of the European Parliament since the first popular elections in 1979. Subsequently, the study discusses the most relevant proposed European Parliamentary seat apportionment methods, i.e. the Cambridge Compromise, the Power Compromise and the 0,5-DPL method, and seeks to analyse their consequences on the representation of the EU Member States in the European Parliament. The paper concludes that the Cambridge compromise is the most appropriate of the methods discussed as it best meets the requirements of the Lisbon Treaty and related documents for the composition of the European Parliament. [ABSTRACT FROM AUTHOR]

An apportionment paradox occurs when the rules for apportionment in a political system or distribution system produce results which seem to violate common sense. For example, The Alabama paradox occurs when the total number of seats increases but decreases the allocated number of a state and the population paradox occurs when the population of a state increases but its allocated number of seats decreases. The Balinski-Young impossibility theorem showed that there is no deterministic apportionment method that can avoid the violation of the quota rule and doesn’t have both the Alabama and the population paradoxes. In this paper, we propose a randomized apportionment method as a stochastic solution to the Balinski-Young impossibility. [ABSTRACT FROM AUTHOR]

This paper examines state interest in the nine bases of congressional seat apportionment considered for the House of Representatives as part of the Fourteenth Amendment to the US Constitution. We ask, what if voters preferred apportionments that delivered larger vote shares to their state? We then show that among all states, one basis of apportionment was a weak Condorcet winner, while the others were in a vote cycle. In both chambers of Congress, however, pure majority voting created orderings of the nine bases and a different Condorcet winner. Ironically, Congress did not select either Condorcet winner. Instead, a population-based apportionment was reported out of committee and passed both chambers as a consequence of agenda control and lack of pairwise voting. Our analysis provides an example of how agenda setting with incomplete information unintentionally can produce undesirable outcomes for a legislature. [ABSTRACT FROM AUTHOR]

What model of voter enrolment is appropriate for states with nomadic minority populations? The present paper examines this question with reference to an equality-based, moral right to vote and considers four models that track some of the different institutional strategies that have been developed by states with transient populations. The paper shows that the right to vote is compatible neither with a model that makes permanent residence in a constituency an absolute condition for voter enrolment and so excludes nomads from the electoral process, nor with a model that enables nomadic voter enrolment but restricts the number of nomads that can enrol in a single constituency. But the right is, subject to certain caveats, consistent with a model that enables nomads to enrol in a constituency of their choice and, as well, with a model that enables nomads to enrol and vote in a distinct, non-territorial constituency. [ABSTRACT FROM AUTHOR]

Abstract: Particulate matter (PM) is one of the primary pollutants produced from mining operations. This paper summarizes the existing techniques used to identify sources of PM and their contribution to ambient air pollution. Human health studies indicate that there is an association between airborne PM and adverse health effects. Particularly in coal mining areas, the burning of coal and PM from machinery operations cause low air quality that is physically harmful. Thus, the sources of smoldering combustion, that are typical in coal mine burns, increase the risk to mine workers who are exposed to high concentrations of known toxicity associated with PM. Recent studies on the modeling of PM concentration profiles across various sources were reviewed for this paper. [ABSTRACT FROM AUTHOR]

Electoral authoritarian regimes usually preserve the dominance of the ruling party through electoral fraud, violence and intimidation. This paper focuses on the subtler forms of manipulation that undermine the electoral integrity and democratic outcomes. Specifically, we examine how an unusual electoral rule, involving multimember districts elected through plurality bloc voting for party slates, exaggerates the legislative seat shares of the People’s Action Party (PAP) in Singapore. This rule, used also by other electoral authoritarian regimes, facilitates the manipulation of district magnitude and gerrymandering, especially the ‘stacking’ form, to produce a large disproportionality which distorts the seats-votes linkage. It operates in an undemocratic fashion by precluding the opposition from gaining anything but token seats as long as the PAP remains the plurality-winning party. The importance of this electoral rule and its manipulation has been overlooked in current work that emphasises redistributive strategies or coercion to repress electoral competition. [ABSTRACT FROM AUTHOR]

Serendipity, curiosity, and lived experience shaped my career as a social demographer and my interests in social policy. I transitioned from the humanities to sociology and demography as a graduate student at the University of Texas at Austin, where I discovered my affinity for quantitative research. My interest in Latin American demography gave way to domestic concerns as new opportunities arose at each of the three institutions where I have had the privilege to work—the University of Wisconsin-Madison, the University of Chicago, and Princeton University. That all three institutions hosted vibrant demography and policy programs facilitated my research about the Hispanic population, family structure, urban poverty, college access, and myriad aspects of socioeconomic inequality and immigrant integration. Superb colleagues and talented graduate student collaborators deserve major credit for my career accomplishments. I attribute numerous opportunities to serve on philanthropic and corporate boards to the strength of weak ties. [ABSTRACT FROM AUTHOR]

Given a real number α ∈ (0 , 1) , we define the Webster sequence of density α to be W α = (⌈ (n − 1 / 2) / α ⌉) n ∈ N , where ⌈ x ⌉ is the ceiling function. It is known that if α and β are irrational with α + β = 1 , then W α and W β partition N. On the other hand, an analogous result for three-part partitions does not hold: There does not exist a partition of N into sequences W α , W β , W γ with α , β , γ irrational. In this paper, we consider the question of how close one can come to a three-part partition of N into Webster sequences with prescribed densities α , β , γ. We show that if α , β , γ are irrational with α + β + γ = 1 , there exists a partition of N into sequences of densities α , β , γ , in which one of the sequences is a Webster sequence and the other two are "almost" Webster sequences that are obtained from Webster sequences by perturbing some elements by at most 1. We also provide two efficient algorithms to construct such partitions. The first algorithm outputs the n th element of each sequence in O (1) time and the second algorithm gives the assignment of the m th positive integer to a sequence in O (1) time. We show that the results are best-possible in several respects. Moreover, we describe applications of these results to apportionment and optimal scheduling problems. [ABSTRACT FROM AUTHOR]

Psychologists serving as Qualified Medical Examiners (QMEs) in settings where mental and emotional damage claims (i.e., psychological disability stemming from psychological injury) are involved typically must comment not only upon the impact of the injury on the individual's functioning and quality of life, but also on the causality of the psychological disability. This is a highly specialized endeavor for which little guidance exists. The disparate conceptualizations of causality in the fields of psychology and law and the unavoidable complexities associated with determining causality, especially the apportionment of causality across industrial and non-industrial factors, are discussed. The questions at the core of the present paper are: 1) What are the ethical challenges facing psychologists working as QMEs who are tasked with determining causality of psychological disability in the ways currently required by the law, and 2) What considerations should guide ethically-minded psychologists in such settings? The authors argue that, although some level of subjectivity is unavoidable, psychologists working within the legal system can take the lead in bringing an evidence-based approach and greater scientific rigor to the high-stakes causal evaluations required as a basis for determining compensation for injured workers. [ABSTRACT FROM AUTHOR]

Let $${\mathcal {M}}$$ be the space of all the $$\tau \times n$$ matrices with pairwise distinct entries and with both rows and columns sorted in descending order. If $$X=(x_{ij})\in {\mathcal {M}}$$ and $$X_{n}$$ is the set of the $$n$$ greatest entries of $$X$$ , we denote by $$\psi _{j}$$ the number of elements of $$X_{n}$$ in the column $$j$$ of $$X$$ and by $$\psi ^{i}$$ the number of elements of $$X_{n}$$ in the row $$i$$ of $$X$$ . If a new matrix $$X^{\prime }=(x_{ij}^{\prime })\in {\mathcal {M}}$$ is obtained from $$X$$ in such a way that $$X^{\prime }$$ yields to $$X$$ (as defined in the paper), then there is a relation of majorization between $$(\psi ^{1},\psi ^{2},\ldots ,\psi ^{\tau })$$ and the corresponding $$(\psi ^{\prime 1},\psi ^{\prime 2},\ldots ,\psi ^{\prime \tau })$$ of $$X^{\prime }$$ , and between $$(\psi _{1}^{\prime },\psi _{2}^{\prime },\ldots ,\psi _{n}^{\prime })$$ of $$X^{\prime }$$ and $$(\psi _{1},\psi _{2},\ldots ,\psi _{n})$$ . This result can be applied to the comparison of closed list electoral systems, providing a unified proof of the standard hierarchy of these electoral systems according to whether they are more or less favourable to larger parties. [ABSTRACT FROM AUTHOR]

There are a variety of methods that state legislatures can use to pass legislation which relates to municipalities. This paper explores why, how and when states changed their constitutions from allowing special legislation for municipalities to requiring general laws which would apply to all municipalities. Historians have put forward several explanations for why special legislation was harder to maintain as the nineteenth century progressed. A new way of framing the story is presented here by considering how the passage of special legislation was maintained through a logroll; legislators formed a coalition to vote on each other's local legislation. As the size of the legislature expanded and the composition of the legislature changed, it may have been harder for legislators to maintain a coalition in order to logroll each other's proposed local legislation. The previous theories along with the new one presented here are empirically tested. Evidence suggests a link between the size of the state legislature and the probability of instituting general legislation for municipalities, indicating that one motivation for adopting general laws was the dissolution of a stable logroll. [ABSTRACT FROM AUTHOR]

In the classic apportionment problem, the goal is to decide how many seats of a parliament should be allocated to each party as a result of an election. The divisor methods solve this problem by defining a notion of proportionality guided by some rounding rule. Motivated by recent challenges in the context of electoral apportionment, we consider the question of how to allocate the seats of a parliament under parity constraints between candidate types (e.g., an equal number of men and women elected) while at the same time satisfying party proportionality. We study two different approaches to solve this question. We first provide a theoretical analysis of a recently devised mechanism based on a greedy approach. We then propose and analyze a mechanism that follows the idea of biproportionality introduced by Balinski and Demange. In contrast with the classic biproportional method by Balinski and Demange, this mechanism is ruled by two levels of proportionality: Proportionality is satisfied at the level of parties by means of a divisor method, and then biproportionality is used to decide the number of candidates allocated to each type and party. A typical benchmark used in the context of two-dimensional apportionment is the fair share (a.k.a matrix scaling), which corresponds to an ideal fractional biproportional solution. We provide lower bounds on the distance between these two types of solutions, and we explore their consequences in the context of two-dimensional apportionment. [ABSTRACT FROM AUTHOR]

Several different arguments support the use of Webster's method when seats in a parliament are to be apportioned proportionally according to populations. This note—instigated by a new property—summarizes the reasons. [ABSTRACT FROM AUTHOR]

This paper formulates a new criterion that distinguishes the set of parametric methods within the set of all the divisor methods of apportionment. The criterion-that a method transfer seats as it 'should'-asks that as population (or the votes of parties in a PR system) is shifted more and more from one state to another state (from one party to another party) at some point the first state (or party) is apportioned one less seat, the second state (or party) one more seat, and the remaining apportionments are as they were. It goes on to examine several properties of parametric methods. [ABSTRACT FROM AUTHOR]

Hamilton's method is a natural and common method to distribute seats proportionally between states (or parties) in a parliament. In the USA it has been abandoned due to some drawbacks, in particular the possibility of the Alabama paradox, but it is still in use in many other countries. In this paper we give, under certain assumptions, a closed formula for the asymptotic probability, as the number of seats tends to infinity, that the Alabama paradox occurs given the vector p1,…, pm of relative sizes of the states. From the formula we deduce a number of consequences. For example, the expected number of states that will suffer from the Alabama paradox is asymptotically bounded above by 1/e and on average approximately 0.123. [ABSTRACT FROM AUTHOR]

In this paper, the sum deviation just-in-time (JIT) sequencing problem in mixed-model production systems is studied relating with the discrete apportionment problem together with their respective mathematical formulations. The assignment formulation for the first problem is briefly discussed followed by the existence of JIT cyclic sequences. Presenting the concise discussion on divisor methods for the discrete apportionment problem, we have proposed two mean-based divisor functions for this problem claiming that they are better than the existing divisors; hence, we found a better bound for the JIT sequencing problem. The linkage of both the problems is characterized in terms of similar type of objective functions. The problems are shown equivalent via suitable transformations and similar properties. The joint approaches for the two problems are discussed in terms of global and local deviations proposing equitably efficient solution. [ABSTRACT FROM AUTHOR]

This paper first discusses two methods for apportioning the US House of Representatives, Equal Proportions and Major Fractions. The method of Equal Proportions will be used in the 2000 apportionment, but it is biased in favor of smaller states. The method of Major Fractions is a mathematically unbiased method, but will not be used in 2000. However, we show that apportionments for 2000 would not differ much according to these two methods. We also consider different definitions of the apportionment population, mainly based on including or excluding legal and illegal immigrants from the apportionment process. We show that the apportionment results for 2000 will not differ if illegal immigrants who entered the USA in the 1990s are kept in, or removed from, the apportionment population. But the apportionment results will differ in a major way if all persons immigrating to the USA in the 1990s are kept in, or removed. [ABSTRACT FROM AUTHOR]

The U.S. apportions congressional districts both across states and within states based upon population. Scholars have long focused on the electoral implications of redistricting within states, but there has been less consideration of the electoral implications of apportionment across states. In this paper, I analyze congressional elections from 2002 to 2014 and theorize that the limited number of political opportunities in states with few congressional districts will lead to higher levels of quality candidate emergence and electoral competition in these states. I find support for this theory; specifically, as the number of political opportunities in a state increases, the number of quality candidates running for office decreases. [ABSTRACT FROM AUTHOR]

A heuristic for decomposing traffic matrices in TDMA satellite communication. With the time-division multiple access (TDMA) technique in satellite communication the problem arises to decompose a given n×n traffic matrix into a weighted sum of a small number of permutation matrices such that the sum of the weights becomes minimal. There are polynomial algorithms when the number of permutation matrices in a decomposition is allowed to be as large as n. When the number of matrices is restricted to n, the problem is NP-hard. In this paper we propose a heuristic based on a scaling technique which for each number of allowed matrices in the range from n to n allows to give a performance guarantee with respect to the total weight of the solution. As a subroutine we use new heuristic methods for decomposing a matrix of small integers into as few matrices as possible without exceeding the lower bound on the total weight. Computational results indicate that the method might also be practical. [ABSTRACT FROM AUTHOR]

Chemical contamination from point source discharges in developed (resource‐rich) countries has been widely regulated and studied for decades; however, diffuse sources are largely unregulated and widespread. In the European Union (EU), large dischargers report releases of some chemicals, yet little is known of total emissions (point and diffuse) and their relative significance. We estimated copper loadings from all significant sources including industry, sewage treatment plants, surface runoff (from traffic, architecture, and atmospheric deposition), septic tanks, agriculture, mariculture, marine transport (antifoulant leaching), and natural processes. A combination of European datasets, literature, and industry data were used to generate export coefficients. These were then multiplied by activity rates to derive loads. A total of approximately 8 kt of copper per annum (ktpa) is estimated to enter freshwaters in the EU, and another 3.5 ktpa enters transitional and coastal waters. The main inputs to freshwater are natural processes (3.7 ktpa), agriculture (1.8 ktpa), and runoff (1.8 ktpa). Agricultural emissions are dominated by copper‐based plant protection products and farmyard manure. Urban runoff is influenced by copper use in architecture and by vehicle brake linings. Antifoulant leaching from boats (3.2 ktpa) dominates saline water loads of copper. It is noteworthy that most of the emissions originate in a limited number of copper uses where environmental exposure and pathways exist, compared with the bulk of copper use within electrical and electronic equipment and infrastructure that has no environmental pathway during its use. A sensitivity analysis indicated significant uncertainty in data from abandoned mines and urban runoff load estimates. This study provided for the first time a methodology and comprehensive metal load apportionment to European aquatic systems, identifying data gaps and uncertainties, which may be refined over time. Source apportionments using this methodology can inform more cost‐effective environmental risk assessment and management. Integr Environ Assess Manag 2023;19:1031–1047. © 2022 The Authors. Integrated Environmental Assessment and Management published by Wiley Periodicals LLC on behalf of Society of Environmental Toxicology & Chemistry (SETAC). Key Points: For the first time, a source apportionment of copper to the aquatic environment has been achieved for all significant point and diffuse sources of copper.A total of approximately 8 kt of copper per annum (ktpa) is estimated to enter freshwaters in the European Union, and another 3.5 ktpa enters transitional and coastal waters.The main inputs to freshwater are natural processes (3.7 ktpa), agriculture (1.8 ktpa), and runoff (1.8 ktpa), with agricultural emissions dominated by copper‐based plant protection products and farmyard manure and urban runoff by architecture and brake lining wear.Antifoulant leaching from boats (3.2 ktpa) dominates saline water loads of copper. [ABSTRACT FROM AUTHOR]

Admissible measures of diversity allow specification of the number of types (species, alleles, etc.) that are “effectively” involved in producing the diversity (the “diversity effective number”, also referred to as “true diversity”) of a community or population. In metacommunities, effective numbers additionally serve in partitioning the total diversity (symbolized by γ ) into one component summarizing the diversity within communities (symbolized by α ) and an independent component summarizing the differences between communities (symbolized by β ). There is growing consensus that the β -component should be treated in terms of an effective number of “distinct” communities in the metacommunity. Yet, the notion of distinctness is shown in the present paper to remain conceptually ambiguous at least with respect to the diversity within the “distinct” communities. To overcome this ambiguity and to provide the means for designing further desirable effective numbers, a new approach is taken that involves a generalized concept of effective number. The approach relies on first specifying the distributional characteristics of partitioning diversity among communities (among which are differentiation, where the same types tend to occur in the same communities, and apportionment, where different types tend to occur in different communities), then developing the indices which measure these characteristics, and finally inferring the effective numbers from these indices. Major results: (1) The β -component reflects apportionment characteristics of metacommunity structure and is quantified by the “apportionment effective number” of communities (number of effectively monomorphic communities). Since differentiation between communities arises only as a side effect of apportionment, the common interpretation of the β -component in terms of differentiation is unwarranted. (2) Multiplicative as well as additive methods of partitioning the total type diversity ( γ ) involve apportionment effective numbers of communities that are based on different apportionment indices. (3) “Differentiation effective numbers” of communities exist but do not conform with the classical concept of partitioning total type diversity into components within and between communities. (4) Differentiation characteristics are measured as effective numbers of distinct types (rather than communities) from the dual perspective, in which the roles of type and community membership are exchanged. This is relevant e.g. in studies of endemism and competitive exclusion. (5) For Shannon-Wiener diversity, all of the differentiation and apportionment effective numbers are equal, with the exception of those representing additive partitioning. (6) Under either perspective, that is dual or non-dual, measures of compositional differentiation (as originally suggested for the assessment of β -diversity) do not figure in the partitioning of total diversity into components, since they do not build on the intrinsic concept of diversity. [ABSTRACT FROM AUTHOR]

Ideally, a representative democracy awards a genuine vote to each adult. We study this issue in competitive democracies with an election model combining district apportionment and proportional representation. Four classic seat allocation rules, including d'Hondt, are reframed as Dutch auctions, allowing important properties to be easily derived. The pros and cons of these methods are stated in terms of economic inequality; Sainte Laguë's is shown to best carry the genuine vote ideal, both for elections and for apportionment. We next expound the interplay between these two components in generating an inequitable treatment of voters and develop the scale-free index of inequity best fitted to their concern. We apply it to 40 countries for the apportionment of electoral districts. Lastly, we compute the same inequity index for recent parliamentary elections in 80 countries, finding that the majority system mistreats electors, thus putting a 'price' on government stability. [ABSTRACT FROM AUTHOR]

(1) Background: Is variation among the communities of a metacommunity higher than within the communities? Community ecologists and population geneticists often characterize the structure of metacommunities by partitioning variation (diversity) into the two following components using measures such as F S T or G S T and α - and β -diversity. The within-communities component is usually some average of (type, species, genetic) diversities within the communities, and the among-communities component is the additive or multiplicative complement of the overall diversity. Such an among-communities component lacks independent conceptual specification, a matter of long-standing dispute. Only if the two components are independently and commensurably specified can the central question of comparability be answered meaningfully. (2) Methods: A novel approach to overcoming this conceptual weakness identifies two principles of the partitioning of variation among communities (concentration and division) then relates these principles to the common notions of variation (diversity) within and among communities, distinguishes primary indicators to quantify the partitioning principles, transforms the indicators into conceptually independent measures (indices) of variation within and among communities, and by this attains their commensurability and thus comparability. The application of the methods to quantifying the effects of evolutionary mechanisms is outlined. (3) Results: Common approaches are corrected and extended. (a) Analyses of metacommunity/metapopulation structures that rely on apportionment or related indices and take its complement to be differentiation yield incomparable measures of variation within and among communities. (b) The common practice of partitioning the total diversity into additive or multiplicative components produces the inconsistent ranking of the two components. (c) Community concentration and division can result from elementary processes of adaptive differentiation and migration (gene flow) among communities, where the (commensurable) amounts of community concentration and division reflect the relative participation of these processes in metacommunity structuring and translate directly into the measures of diversity within and among communities. (d) The modelling of the contributions of the two partitioning principles to the metacommunity structure is restricted by the marginal distributions of types and community affiliation. (e) The model demonstrates the degree to which adaptational processes at the metacommunity level are mixtures of adaptational events within and among communities. [ABSTRACT FROM AUTHOR]

In 1998 a long-lost proposal for an election law by Gottlob Frege (1848–1925) was rediscovered in the Thüringer Universitäts- und Landesbibliothek in Jena, Germany. The method that Frege proposed for the election of representatives of a constituency features a remarkable concern for the representation of minorities. Its core idea is that votes cast for unelected candidates are carried over to the next election, while elected candidates incur a cost of winning. We prove that this sensitivity to past elections guarantees a proportional representation of political opinions in the long run. We find that through a slight modification of Frege's original method even stronger proportionality guarantees can be achieved. This modified version of Frege's method also provides a novel solution to the apportionment problem, which is distinct from all of the best-known apportionment methods, while still possessing noteworthy proportionality properties. [ABSTRACT FROM AUTHOR]

The apportionment process that precedes redistricting is generally a staid American political ritual. Recent debates about who should be included in the apportionment basis, however, have raised new questions about representation in the apportionment process. To estimate the effects of excluding non-citizens and children from apportionment, we describe an algorithm to simulate drawing of state legislative districts, based on a previously published algorithm, Seed-Fill-Shift-Repair (SFSR), designed to draw congressional districts. To account for the larger number of districts to draw we implement an adapted search heuristic that is able to efficiently create contiguous and population-balanced maps for state legislative districts, which we call SFSR-G. We use SFSR-G to simulate 1000 maps of upper and lower legislative chambers in 12 states to demonstrate that a shift from total population to citizen voting age population as the apportionment basis will reduce minority–majority and minority-opportunity districts. The paper presents findings for all 12 states investigated, and discusses the important case of Texas at greater length. [ABSTRACT FROM AUTHOR]