Unambiguous Ranking Research Articles

Toxic Kidney Damage in Rats Following Subchronic Intraperitoneal Exposure to Element Oxide Nanoparticles.

Chronic diseases of the urogenital tract, such as bladder cancer, prostate cancer, reproductive disorders, and nephropathies, can develop under the effects of chemical hazards in the working environment. In this respect, nanosized particles generated as by-products in many industrial processes seem to be particularly dangerous to organs such as the testes and the kidneys. Nephrotoxicity of element oxide particles has been studied in animal experiments with repeated intraperitoneal injections of Al2O3, TiO2, SiO2, PbO, CdO, CuO, and SeO nanoparticles (NPs) in total doses ranging from 4.5 to 45 mg/kg body weight of rats. NPs were synthesized by laser ablation. After cessation of exposure, we measured kidney weight and analyzed selected biochemical parameters in blood and urine, characterizing the state of the excretory system. We also examined histological sections of kidneys and estimated proportions of different cells in imprint smears of this organ. All element oxide NPs under investigation demonstrated a nephrotoxic effect following subchronic exposure. Following the exposure to SeO and SiO2 NPs, we observed a decrease in serum creatinine and urea, respectively. Exposure to Al2O3 NPs caused an increase in urinary creatinine and urea, while changes in total protein were controversial, as it increased under the effect of Al2O3 NPs and was reduced after exposure to CuO NPs. Histomorphological changes in kidneys are associated with desquamation of the epithelium (following the exposure to all NPs except those of Al2O3 and SiO2) and loss of the brush border (following the exposure to all NPs, except those of Al2O3, TiO2, and SiO2). The cytomorphological evaluation showed greater destruction of proximal sections of renal tubules. Compared to the controls, we observed statistically significant alterations in 42.1% (8 of 19) of parameters following the exposure to PbO, CuO, and SeO NPs in 21.1% (4 of 19)-following that, to CdO and Al2O3 NPs-and in 15.8% (3 of 19) and 10.5% (2 of 19) of indicators, following the exposure to TiO2 and SiO2 nanoparticles, respectively. Histomorphological changes in kidneys are associated with desquamation of epithelium and loss of the brush border. The cytomorphological evaluation showed greater destruction of proximal sections of renal tubules. The severity of cyto- and histological structural changes in kidneys depends on the chemical nature of NPs. These alterations are not always consistent with biochemical ones, thus impeding early clinical diagnosis of renal damage. Unambiguous ranking of the NPs examined by the degree of their nephrotoxicity is difficult. Additional studies are necessary to establish key indicators of the nephrotoxic effect, which can facilitate early diagnosis of occupational and nonoccupational nephropathies.

Ranking intersecting distribution functions

SummarySecond‐degree dominance has become a widely accepted criterion for ordering distribution functions according to social welfare. However, it provides only a partial ordering, and it may fail to rank distributions that intersect. To rank intersecting distribution functions, we propose a general approach based on rank‐dependent theory. This approach avoids making arbitrary restrictions or parametric assumptions about social welfare functions and allows researchers to identify the weakest set of assumptions needed to rank distributions according to social welfare. Our approach is based on two complementary sequences of nested dominance criteria. The first (second) sequence extends second‐degree stochastic dominance by placing more emphasis on differences that occur in the lower (upper) part of the distribution. The sequences characterize two separate systems of nested subfamilies of rank‐dependent social welfare functions. This allows us to identify the least restrictive rank‐dependent social preferences that give an unambiguous ranking of a given set of distribution functions. We also provide an axiomatization of the sequences of dominance criteria and the corresponding subfamilies of social welfare functions. We show the usefulness of our approach using two empirical applications; the first assesses the welfare implications of changes in household income distributions over the business cycle, while the second performs a social welfare comparison of the actual and counterfactual outcome distributions from a policy experiment.

Aggregating Multidimensional Criteria in Audit Decision Making

Measuring total performance of prospective alternatives in decision making (DM) needs aggregation of their noncomparable properties which often have different scales of measure. In order to address this, scale transformations and normalization are applied, but problems of validation of such additive models and interpretation of the physical sense of the result arise. In this paper, a multiplicative performance aggregation of properties' values is suggested for DM. Application of the approach enables consistent and unambiguous ranking of the alternatives allowing values of all their properties of interest. A realistic example of DM related to audit activity planning is considered where several competing control areas should be selected into an audit plan. Beyond audit planning, the approach is generalizable to other DM problems in corporate management and governance where one needs to rank alternatives compared in multiple dimensions.

Quality of life in chronic conditions using patient-reported measures and biomarkers: a DEA analysis in type 1 diabetes

BackgroundA chronic disease impacts a patient’s daily life, with the burden of symptoms and managing the condition, and concerns of progression and disease complications. Such aspects are captured by Patient-Reported Outcomes Measures (PROM), assessments of e.g. wellbeing. Patient-Reported Experience Measures (PREM) assess patients’ experiences of healthcare and address patient preferences. Biomarkers are useful for monitoring disease activity and treatment effect and determining risks of progression and complications, and they provide information on current and future health. Individuals may differ in which among these aspects they consider important. We aimed to develop a measure of quality of life using biomarkers, PROM and PREM, that would provide an unambiguous ranking of individuals, without presuming any specific set of importance weights. We anticipated it would be useful for studying needs and room for improvement, estimating the effects of interventions and comparing alternatives, and for developing healthcare with a broad focus on the individual. We wished to examine if efficiency analysis could be used for this purpose, in an application to individuals with type 1 diabetes.ResultsWe used PROM and PREM data linked to registry data on risk factors, in a large sample selected from the National Diabetes Registry in Sweden. Efficiency analysis appears useful for evaluating the situation of individuals with type 1 diabetes. Quality of life was estimated as efficiency, which differed by age. The contribution of different components to quality of life was heterogeneous, and differed by gender, age and duration of diabetes. Observed quality of life shortfall was mainly due to inefficiency, and to some extent due to the level of available inputs.ConclusionsThe efficiency analysis approach can use patient-reported outcomes measures, patient-reported experience measures and comorbidity risk factors to estimate quality of life with a broad focus on the individual, in individuals with type 1 diabetes. The approach enables ranking and comparisons using all these aspects in parallel, and allows each individual to express their own view of which aspects are important to them. The approach can be used for policy regarding interventions on inefficiency as well as healthcare resource allocation, although currently limited to type 1 diabetes.

Pairwise growth competitions identify relative fitness relationships among artemisinin resistant Plasmodium falciparum field isolates

BackgroundCompetitive outcomes between co-infecting malaria parasite lines can reveal fitness disparities in blood stage growth. Blood stage fitness costs often accompany the evolution of drug resistance, with the expectation that relatively fitter parasites will be more likely to spread in populations. With the recent emergence of artemisinin resistance, it is important to understand the relative competitive fitness of the metabolically active asexual blood stage parasites. Genetically distinct drug resistant parasite clones with independently evolved sets of mutations are likely to vary in asexual proliferation rate, contributing to their chance of transmission to the mosquito vector.MethodsAn optimized in vitro 96-well plate-based protocol was used to quantitatively measure-head-to-head competitive fitness during blood stage development between seven genetically distinct field isolates from a hotspot of emerging artemisinin resistance and the laboratory strain, NF54. These field isolates were isolated from patients in Southeast Asia carrying different alleles of kelch13 and included both artemisinin-sensitive and artemisinin-resistant isolates. Fluorescent labeled microsatellite markers were used to track the relative densities of each parasite throughout the co-growth period of 14–60 days. All-on-all competitions were conducted for the panel of eight parasite lines (28 pairwise competitions) to determine their quantitative competitive fitness relationships.ResultsTwenty-eight pairwise competitive growth outcomes allowed for an unambiguous ranking among a set of seven genetically distinct parasite lines isolated from patients in Southeast Asia displaying a range of both kelch13 alleles and clinical clearance times and a laboratory strain, NF54. This comprehensive series of assays established the growth relationships among the eight parasite lines. Interestingly, a clinically artemisinin resistant parasite line that carries the wild-type form of kelch13 outcompeted all other parasites in this study. Furthermore, a kelch13 mutant line (E252Q) was competitively more fit without drug than lines with other resistance-associated kelch13 alleles, including the C580Y allele that has expanded to high frequencies under drug pressure in Southeast Asian resistant populations.ConclusionsThis optimized competitive growth assay can be employed for assessment of relative growth as an index of fitness during the asexual blood stage growth between natural lines carrying different genetic variants associated with artemisinin resistance. Improved understanding of the fitness costs of different parasites proliferating in human blood and the role different resistance mutations play in the context of specific genetic backgrounds will contribute to an understanding of the potential for specific mutations to spread in populations, with the potential to inform targeted strategies for malaria therapy.

Modelling methods and cross-validation variants in QSAR: a multi-level analysis$

ABSTRACTPrediction performance often depends on the cross- and test validation protocols applied. Several combinations of different cross-validation variants and model-building techniques were used to reveal their complexity. Two case studies (acute toxicity data) were examined, applying five-fold cross-validation (with random, contiguous and Venetian blind forms) and leave-one-out cross-validation (CV). External test sets showed the effects and differences between the validation protocols. The models were generated with multiple linear regression (MLR), principal component regression (PCR), partial least squares (PLS) regression, artificial neural networks (ANN) and support vector machines (SVM). The comparisons were made by the sum of ranking differences (SRD) and factorial analysis of variance (ANOVA). The largest bias and variance could be assigned to the MLR method and contiguous block cross-validation. SRD can provide a unique and unambiguous ranking of methods and CV variants. Venetian blind cross-validation is a promising tool. The generated models were also compared based on their basic performance parameters (r2 and Q2). MLR produced the largest gap, while PCR gave the smallest. Although PCR is the best validated and balanced technique, SVM always outperformed the other methods, when experimental values were the benchmark. Variable selection was advantageous, and the modelling had a larger influence than CV variants.

Regular Consistent Preferences

In a dynamic choice environment, an agent's tastes may change over time, leading to a conflict between plans made today and choices made in the future. In response, a consistent planner restricts herself to plans that she will actually follow, by anticipating today how she will rank continuation plans in the future. Since the agent's expected future rankings often play an important role in policy analysis, they need to be elicited from observable choices. In this paper, we provide a method to elicit expected future rankings by considering the agent's preferences today over dynamic decision problems. Our identification strategy exploits that, in many applications of the consistent planning model, future rankings are monotone with respect to a partial order, which provides an unambiguous ranking of some alternatives. Our results are developed in a general framework, and can therefore be used to elicit expected future rankings in many applications of the consistent planning model. To illustrate our findings, we consider a dynamic consumption problem with quasi-hyperbolic discounting, and show how the agent's expectations about her present-bias in the future can be elicited from simple choice experiments today.

Urbanization between compactness and dispersion: designing a spatial model for measuring 2D binary settlement landscape configurations

ABSTRACTMeasuring spatial patterns is a crucial task in spatial sciences. Multiple indicators have been developed to measure patterns in a quantitative manner. However, most comparative studies rely on relative comparisons, limiting their explanatory power to specific case studies. Motivated by advancements in earth observation providing unprecedented resolutions of settlement patterns, this paper suggests a measurement technique for spatial patterns to overcome the limits of relative comparisons. We design a model spanning a feature space based on two metrics – largest patch index and number of patches. The feature space is defined as ‘dispersion index’ and covers the entire spectrum of possible two-dimensional binary (settlement) patterns. The model configuration allows for an unambiguous ranking of each possible pattern with respect to spatial dispersion. As spatial resolutions of input data as well as selected areas of interest influence measurement results, we test dependencies within the model. Beyond, common other spatial metrics are selected for testing whether they allow unambiguous rankings. For scenarios, we apply the model to artificially generated patterns representing all possible configurations as well as to real-world settlement classifications differing in growth dynamics and patterns.

Effective Clusters as Territorial Performance Engines in a Regional Development Strategy - A Triple-Layer DEA Assessment of the Aviation Valley in Poland

Regional development policy aims to cope with the challenge of spatial disparities. It is based on a smart combination of various critical capital assets in a region which functionally and spatially interact and which yield synergetic economic opportunities and promising challenges for innovation and progress. The present study regards sustainable territorial performance – as a manifestation of regional development – as the overarching principle for competitive advantages and economic growth in a system of regions, which is particularly induced by territorial capital, comprising human capital, infrastructural capital and social capital. In the long-standing tradition of regional development policy a wide variety of effective facilitators or drivers of accelerated spatial growth has been distinguished, for instance, industrial districts, growth poles, growth centers, industrial complexes, special economic zones, communication axes, and so forth. In the past decades, a new concept has been introduced, viz. economic-technological clusters. An avalanche of literature has been published on the conceptual, operational and policy foundation and relevance of this concept, especially in relation to previously developed regional growth concepts. In this paper, clusters will be regarded as the spatial foci of sustainable territorial performance strategies and synergetic actions by both public and private actors. The present paper aims to address the relevance of cluster concepts for an effective regional development policy, based on the above notion of territorial capital. It does so by introducing a new concept, viz. effective cluster, in which spatial-economic synergy, local/regional concentration of industry, and the supporting role of territorial capital are regarded as the main determinants of a highly performing cluster in a given territory. The effective cluster concept will be tested on the basis of a field study on the aviation and aerospace cluster ‘Dolina Lotnicza’ in the Podkarpackie region in South-East Poland. This is one of the most vibrant high-tech clusters in thecountry. A new approach based on a triple-layer architecture will be adopted here, viz.: a quantitative comparative analysis of the 16 Polish ‘voivodships’ (main administrative regions in the country, at a NUTS-2 level), a benchmark analysis of the 25 counties (‘powiats’) within the Podkarpackie voivodship (at a NUTS-4 level), and an effective industrial cluster analysis on the basis of the individual aviation firms located in the Podkarpackie region. In each step an extended Data Envelopment Analysis (DEA), characterised by a merger of a Slack-Based Measure (SMB) and a super-efficiency (SE) DEA, will be used in order to achieve an unambiguous ranking of the various regions or Decision Making Units (DMUs). The study will employ an extensive database on individual actors in the cluster, in combination with a broadly composed territorial-capital database for the areas under study. The paper will be concluded with some strategic policy lessons.

Tracing high-sustainability performers among world cities - design and application of a multi-temporal data envelopment analysis

Sustainability performance is nowadays a major challenge for many cities in the world. Sustainable development refers to the achievement of both ecological and socio-economic objectives over a relevant time period. The present study aims to trace the relative sustainability status of 39 world cities included in the so-called Global City Power Index (GPCI) of the Mori Memorial Foundation in Japan. This is a unique large-scale and detailed multi-temporal data base containing approx. 80 systematically collected urban indicators for the cities concerned. This paper presents and applies a novel and advanced assessment methodology for sustainable and efficient performance strategies of these 39 global cities, by means of an extended and multi-temporal version of a Data Envelopment Analysis (DEA). Using this novel approach, our study seeks to arrive at an unambiguous ranking of the highest performers among ‘urban sustainability champions’, during the time period 2012–2015. Based on the DEA efficiency assessment by regarding the urban input-output ratio as a performance indicator, we examine here one input indicator (Total Employees) and four sustainability output indicators (CO2 Emissions, Nominal GDP, Level of Satisfaction of Employees with their Lives, and Percentage of Renewable Energy Used). Our empirical results provide a global sustainability ranking of the cities concerned. We also show that many European cities have a relatively high performance score on the human and urban environment. We present next more detailed information on a selection of a few interesting cities. Our approach appears to be able to address realistic and transparant priorities and complex policy choices aiming at an improvement of relatively inefficient world cities.

Cost-efficient reductions in nutrient loads; identifying optimal spatially specific policy measures

Abstract Nitrogen leakage from agriculture contributes significantly to eutrophication of freshwater and marine ecosystems, and numerous studies have focused on finding cost-effective ways to mitigate this effect. This article utilizes high-resolution data to identify a spatially targeted cost-effective reduction of nitrogen leakage, optimizing over measures as well as over locations. The use of discrete optimization techniques ensure that mutually exclusive measures are not applied on the same plot of land. The analysis is based on a case study of Odense Fjord, where spatially explicit data capture the spatial heterogeneity of the effects and costs of abatement measures. The differences in retention capacity; soil types; and current land use are particularly important factors for the spatial variation in costs and effects. The analysis highlights the importance of applying discrete optimization techniques in spatially specific analyses. We find that no unambiguous ranking of measures or spatial pattern of abatement effort can be given. Hence, landscape scale models are needed to identify optimal abatement effort. The results show that spatial targeting offers substantial improvements in cost-effectiveness compared to a uniform regulation.

Bayesian Inference of Natural Rankings in Incomplete Competition Networks

Competition between a complex system's constituents and a corresponding reward mechanism based on it have profound influence on the functioning, stability, and evolution of the system. But determining the dominance hierarchy or ranking among the constituent parts from the strongest to the weakest – essential in determining reward and penalty – is frequently an ambiguous task due to the incomplete (partially filled) nature of competition networks. Here we introduce the “Natural Ranking,” an unambiguous ranking method applicable to a round robin tournament, and formulate an analytical model based on the Bayesian formula for inferring the expected mean and error of the natural ranking of nodes from an incomplete network. We investigate its potential and uses in resolving important issues of ranking by applying it to real-world competition networks.

Regulating a monopoly with universal service obligations: The role of flexible tariff schemes

This paper's purpose is to study the problem of a utility monopoly's regulator, which has a universal service goal that is binding, in the sense that there is no two-part tariff that can induce efficient consumption, self-finance the firm, and guarantee universal access at the same time.The optimal two-part tariffs that the regulator should set under the following three regulatory rules are derived: no flexibility (the monopolist only offers the regulated plan), partial flexibility (the monopolist can offer alternative plans, but these—and the regulated one—must be available to all customers), and full flexibility (the regulated plan must be available to all customers, but the alternative ones could be offered to specific clients).The solutions under the three schemes are characterized, and they provide an unambiguous ranking of regulatory rules: total flexibility is weakly better than partial flexibility, and partial flexibility is strictly better than no flexibility. As the regulatory scheme becomes more flexible, the optimally regulated two-part tariff increases its fixed component and decreases the variable one.

A Theory for Ranking Distribution Functions

When is one distribution (of income, consumption, or some other economic variable) more equal or better than another? This question has proven difficult to answer in situations where distribution functions intersect and no unambiguous ranking can be attained without introducing weaker criteria than second-degree stochastic dominance. The conventional approach in empirical work is to adopt some summary statistics, with no explicit reason being given for preferring one measure rather than another. In this paper, we develop a theory for ranking distribution functions. Our theory offers a general framework to unambiguously rank any set of distribution functions and quantify the social welfare level of a dominating distribution as compared to a dominated distribution. The framework is based on two complementary sequences of nested dominance criteria. The first (second) sequence extends second-degree stochastic dominance by placing more emphasis on differences that occur in the lower (upper) part of the distribution. These sequences of dominance criteria characterize two separate systems of nested subfamilies of social welfare functions. This allows us to identify the least restrictive social preferences that give an unambiguous ranking of any set of distribution functions. We also provide an axiomatization of the sequences of dominance criteria and the corresponding subfamilies of social welfare functions. To perform inference, we develop asymptotic distribution theory for empirical dominance criteria where it is demonstrated that the associated empirical processes converge in distribution to Gaussian processes. The usefulness of our framework is illustrated with two empirical applications; the first assesses the social welfare implications of changes in household income distributions over the business cycle, while the second ranks the actual and counterfactual outcome distributions from a policy experiment.

Inequality of Happiness in the U.S.: 1972–2010

It is well accepted that a country's GDP may not fully reflect its level of well‐being. In recent years, happiness has emerged as an alternative indicator of well‐being, and research has mainly focused on determining the level of happiness. While it is important to look at the level, the distribution of happiness is also a salient aspect in any evaluation of inequality. There has been a growing interest in the distribution of happiness, although the ordinal nature of the data makes the use of standard inequality measures problematic. Our paper contributes to the literature by exploring the distributions for the U.S. from 1972 to 2010. Based on new methods developed for ordinal data, we are able to overcome the problems associated with ordinality and obtain unambiguous rankings of happiness distributions. We also compute the level of happiness inequality using existing measures based on median centred approaches. Further, we decompose the median based inequality measures of happiness by gender, race, and region.

Comparisons of heterogeneous distributions and dominance criteria

We are interested in the comparisons of standard-of-living across societies when observations of both income and household structure are available. We generalise the approach of A.B. Atkinson and F. Bourguignon (1987) [3] to the case where the marginal distributions of needs can vary across the household populations under comparison. We assume that a sympathetic observer uses a utilitarian social welfare function in order to rank heterogeneous income distributions. Insofar as any individual can play the role of the observer, we take the unanimity point of view according to which the plannerʼs judgements have to comply with a certain number of basic normative principles. We impose increasingly restrictive conditions on the householdʼs utility function and we investigate their effects on the resulting rankings of the distributions. This leads us to propose four dominance criteria that can be used for providing an unambiguous ranking of income distributions for heterogeneous populations.

Robust inequality comparisons

This paper is concerned with the problem of ranking Lorenz curves in situations where the Lorenz curves intersect and no unambiguous ranking can be attained without introducing weaker ranking criteria than first-degree Lorenz dominance. To deal with such situations, Aaberge (Soc Choice Welf 33:235-259, 2009) introduced two alternative sequences of nested dominance criteria for Lorenz curves, which proved to characterize two separate systems of nested subfamilies of inequality measures. This paper uses the obtained characterization results to arrange the members of two different generalized Gini families of inequality measures into subfamilies according to their relationship to Lorenz dominance of various degrees. Since the various criteria of higher degree Lorenz dominance provide convenient computational methods, these results can be used to identify the largest subfamily of the generalized Gini families, and thus the least restrictive social preferences, required to reach unambiguous ranking of a set of Lorenz curves. We further show that the weight-functions of the members of the generalized Gini families offer intuitive interpretations of higher degree Lorenz dominance, which generally has been viewed as difficult to interpret because they involve assumptions about third and higher derivatives. To demonstrate the usefulness of these methods for empirical applications, we examine the time trend in income and earnings inequality of Norwegian males during the period 1967-2005.

Specific Climate Impact of Passenger and Freight Transport

Emissions of short-lived species contribute significantly to the climate impact of transportation. The magnitude of the effects varies over time for each transport mode. This paper compares first the absolute climate impacts of current passenger and freight transportation. Second, the impacts are normalized with the transport work performed and modes are compared. Calculations are performed for the integrated radiative forcing and mean temperature change, for different time horizons and various measures of transport work. An unambiguous ranking of the specific climate impact can be established for freight transportation, with shipping and rail having lowest and light trucks and air transport having highest specific impact for all cases calculated. Passenger travel with rail, coach or two- and three-wheelers has on average the lowest specific climate impact also on short time horizons. Air travel has the highest specific impact on short-term warming, while on long-term warming car travel has an equal or higher impact per passenger-kilometer.

Robust Inequality Comparisons

This paper is concerned with the problem of ranking Lorenz curves in situations where the Lorenz curves intersect and no unambiguous ranking can be attained without introducing weaker ranking criteria than first-degree Lorenz dominance. To deal with such situations Aaberge (2009) introduced two alternative sequences of nested dominance criteria for Lorenz curves which was proved to characterize two separate systems of nested subfamilies of inequality measures. This paper uses the obtained characterization results to arrange the members of two different generalized Gini families of inequality measures into subfamilies according to their relationship to Lorenz dominance of various degrees. Since the various criteria of higher degree Lorenz dominance provide convenient computational methods, these results can be used to identify the largest subfamily of the generalized Gini families and thus the least restrictive social preferences required to reach unambiguous ranking of a set of Lorenz curves. From the weight-functions of these inequality measures we obtain intuitive interpretations of higher degree Lorenz dominance, which generally has been viewed as difficult to interpret because they involve assumptions about third and higher derivatives. To demonstrate the usefulness of these methods for empirical applications, we examine the time trend in income and earnings inequality of Norwegian males during the period 1967-2005.

Ranking intersecting Lorenz curves

This paper is concerned with the problem of ranking Lorenz curves in situations where the Lorenz curves intersect and no unambiguous ranking can be attained without introducing weaker ranking criteria than first-degree Lorenz dominance. To deal with such situations two alternative sequences of nested dominance criteria between Lorenz curves are introduced. At the limit the systems of dominance criteria appear to depend solely on the income share of either the worst-off or the best-off income recipient. This result suggests two alternative strategies for increasing the number of Lorenz curves that can be strictly ordered; one that places more emphasis on changes that occur in the lower part of the income distribution and the other that places more emphasis on changes that occur in the upper part of the income distribution. Both strategies turn out to depart from the Gini coefficient; one requires higher degree of downside and the other higher degree of upside inequality aversion than what is exhibited by the Gini coefficient. Furthermore, it is demonstrated that the sequences of dominance criteria characterize two separate systems of nested subfamilies of inequality measures and thus provide a method for identifying the least restrictive social preferences required to reach an unambiguous ranking of a given set of Lorenz curves. Moreover, it is demonstrated that the introduction of successively more general transfer principles than the Pigou–Dalton principle of transfers forms a helpful basis for judging the normative significance of higher degrees of Lorenz dominance. The dominance results for Lorenz curves do also apply to generalized Lorenz curves and thus provide convenient characterizations of the corresponding social welfare orderings.