Multiple indicators, partially ordered sets, and linear extensions: Multi-criterion ranking and prioritization

This paper is concerned with the question of ranking a finite collection of objects when a suite of indicator values is available for each member of the collection. The objects can be represented as a cloud of points in indicator space, but the different indicators (coordinate axes) typically convey different comparative messages and there is no unique way to rank the objects while taking all indicators into account. A conventional solution is to assign a composite numerical score to each object by combining the indicator information in some fashion. Consciously or otherwise, every such composite involves judgments (often arbitrary or controversial) about tradeoffs or substitutability among indicators. Rather than trying to combine indicators, we take the view that the relative positions in indicator space determine only a partial ordering and that a given pair of objects may not be inherently comparable. Working with Hasse diagrams of the partial order, we study the collection of all rankings that are compatible with the partial order (linear extensions). In this way, an interval of possible ranks is assigned to each object. The intervals can be very wide, however. Noting that ranks near the ends of each interval are usually infrequent under linear extensions, a probability distribution is obtained over the interval of possible ranks. This distribution, called the rank-frequency distribution, turns out to be unimodal (in fact, log-concave) and represents the degree of ambiguity involved in attempting to assign a rank to the corresponding object. Stochastic ordering of probability distributions imposes a partial order on the collection of rank-frequency distributions. This collection of distributions is in one-to-one correspondence with the original collection of objects and the induced ordering on these objects is called the cumulative rank-frequency (CRF) ordering; it extends the original partial order. Although the CRF ordering need not be linear, it can be iterated to yield a fixed point of the CRF operator. We hypothesize that the fixed points of the CRF operator are exactly the linear orderings. The CRF operator treats each linear extension as an equal voter in determining the CRF ranking. It is possible to generalize to a weighted CRF operator by giving linear extensions differential weights either on mathematical grounds (e.g., number of jumps) or empirical grounds (e.g., indicator concordance). Explicit enumeration of all possible linear extensions is computationally impractical unless the number of objects is quite small. In such cases, the rank-frequencies can be estimated using discrete Markov chain Monte Carlo (MCMC) methods.     

Different ranking methods: potentialities and pitfalls for the case of European opinion poll

Prioritization and ranking of objects are primary needs in various substantive fields. It might be said that ranking and comparison are the first step in every risk assessment procedure, whatever the ‘risk’ is intended as: social, environmental, political or economic. Often objects to be ranked are valued by a multi-dimensional attribute which is usually transformed into a composite numerical score. In spite of conventional solutions, the author agrees with recent recommendations of performing multiple ranking, keeping indicators separated. Different innovative methods are analyzed and compared: Hasse diagrams method, POSAC and Nonlinear PCA. The first one stems directly from partial order theory, the second one may be seen as an approximation of Hasse representation in a two dimensional space, whilst the third one belongs to the wide set of non-linear multivariate techniques and it is particularly suitable in handling data of categorical type. Among them, the first two methods compare objects on the basis only on order property of data, whilst the last one simultaneously performs an optimal scale of qualitative attributes and a ranking of objects. The case study is based on the Eurobarometer survey carried out in 2002, at the request of the European Commission, which collects Europeans opinion about various political and social issues. The analysis is focused on users’ level of satisfaction about access easiness, cost, quality, information received and contracts of various services of general interest, such as telephone services, power (gas and electricity) providers, water and postal utilities, urban and rail transports. Separate indicators are set up for each facet of each service within different European regions. Eventually, the ranking of European regions is performed on the basis of the overall performance of services of general interest, as perceived by users. Selected methods lead to almost alike results, still with some differentiations due to different approaches used. As it frequently occurs, each method has its own advantages and pitfalls which are here explored and compared.     

Preliminary prioritization based on partial order theory and R software for compositional complexes in landscape ecology,with applications to restoration,remediation, and enhancement

The present purpose is to provide convenient computational capability and visualizations for preliminary partial or progressive prioritization based largely on concepts of partial order theory and implemented in R software as illustrated in a context of conservation and sustainable stewardship across landscapes with ecosystem services as a complex multidimensional domain that must be placed in public and private perspective in pursuit of multi-resource management. Practical perspective is promoted by graphic visualization with local partial order modeling (LPOM) methods for screening of settings and scenarios involving interactions of ecosystem elements as evidenced by environmental indicators. ORDIT ordering and precedence plots arise from ascribed advantage as an outcome of a rating regime. Representative ranks constitute criteria drawn from the rank distribution for the case in question. Distal data are determined with regard to remediation and retention. Median mismatches reflect interplay of indicators appearing as isolated instances in plotting patterns. A suggested strategy to circumvent computational constraints is partitioning the pool of cases into collectives by clustering, pursuing classes of partitions, and then prioritizing in particular partitions. When prime prospects have been obtained, detailed determinations can be done with partial ordering procedures involving Hasse diagrams and similarly complex constructs that are difficult to apply with many cases and/or indicator criteria.     

Application of partial order to stream channel assessment at bridge infrastructure for mitigation management

Many environmental systems and infrastructure systems are monitored using a set of indicator values that assess several aspects of site condition. The values of different indicators often convey different comparative messages for the study sites. The comparability between sites is analyzed within the theory of partially-ordered sets and visualized with Hasse diagrams. This paper demonstrates that properties of partially-ordered sets and the conversion of indicator scores into a rank matrix provide a manager or decision-maker with valuable information that would be lost if the monitored indicator data were aggregated only into a single index. Stream stability assessment data from 49 bridge crossing sites in the United States are used to demonstrate these techniques in prioritization and identification of restoration and maintenance needs of stream channels at bridge crossings.     

国际企业环境绩效评估指标体系差异分析

随着人类社会经济活动的不断发展,环境问题日益突出,为顺应可持续发展战略,企业环境绩效评估被提上日程。对国际上两种企业环境绩效评估指标体系(ISO14031指标体系和生态效益指标体系)进行了差异分析,为我国企业环境绩效评估指标体系的建立和完善起到借鉴作用。     

Infant mortality and social environment in Georgia: an application of hotspot detection and prioritization

Recent years have witnessed the growth of new information technologies and their applications to various disciplines. The goal of this paper is to demonstrate how the two innovative methods, upper level set scan (ULS) hotspot detection and the multicriteria prioritization scheme, facilitate population health and break new ground in public health surveillance. It is believed that the social environment (i.e. social conditions and social capital) is one of the determinants of human health. Using infant health data and 10 additional indicators of social environment in the 159 counties of Georgia, ULS identified 52 counties that are in double jeopardy (high infant mortality and a high rate of low infant birth weight). The multicriteria ranking scheme suggested that there was no conspicuous spatial cluster of ranking orders, which improved the traditional decision making by visual geographic cluster. Both hotspot detection and ranking methods provided an empirical basis for re-allocating limited resources and several policy implications could be drawn from these analytic results.     

The 2010 Biodiversity Indicators: Challenges for Science and Policy

Abstract:  The 2010 biodiversity target adopted globally and in Europe is an important political commitment for improved biodiversity conservation and management. Whether or not it is achieved will be judged by a set of biodiversity indicators now under development. We reviewed the development of these indicators in Europe and globally, paying particular attention to the need to make the indicators relevant to the purpose; to distinguish between measures of pressure, state, and response; to design and validate the indicators in context; to ensure effective communication with relevant audiences; to turn lists of measures into simple or composite indicators; and to maximize the cost-effectiveness of the indicator process. We conclude that urgent steps are needed to complete the indicator set, reduce and refine the agreed measures, ensure that work is started soon so that reliable reporting occurs in 2010, and start soon on planning for subsequent assessments.     

城市生态可持续发展指标的进展

建设生态城市是一种国际趋势,也在中国受到关注。为了监测评估城市的生态可持续发展,要有一套科学的指标体系。文章讨论了生态城市的特点;评述了国外的3类指标体系和国内采用世界银行“真实储蓄率”指标在城市一应用研究,提出了建立这类指标的一些原则与方法。     

城市人居环境评价体系的研究及应用

在国内外人居环境理论研究及实践的基础上,提出了由系统层、子系统层和指标层构成的城市人居环境评价指标体系,其中系统层由社会经济环境、自然生态环境、公共设施建设、环境资源保护和环境管理能力五部分组成,子系统层由16个指标组成,指标层由43个具体指标组成。利用统计分析法(Delphi)确定各指标的权值。同时,针对本指标体系结构提出了单项评价和综合评价相结合的评价模式,并设置了城市人居环境质量指数和系统协调度两个综合性指标来全面评价城市人居环境质量。通过对重庆市渝北城区的综合评价,评价结果较客观地反映了该城区的实际。     

Aktuelle Entwicklungen bei Umweltindikatorensystemen

The current monitoring of the status of the environment and natural resources is a substantial basis for the implementation of a sustainable development as a model of the environmental policy in the terms of Agenda 21. For the 90s, in particular by the mandate of Rio 1992, both the international institutions (international level), e.g. the OECD, the United Nation Commission of Sustainable Development and the European Environmental Agency, and the environmental protection authorities of the different countries (national level) e.g. Germany, and of the federal states of Germany (regional level) are developing environmental indicator systems. In the context of the Local Agenda 21, indicators for the ecological, economic, social and institutional categories are set up on a communal level. In the environmental indicator systems different issues, e.g. climate change, ozone layer depletion, water quality and water resources, waste, toxic contamination, biodiversity, landscape protection, soil resources, forest resources, etc., are described. Concepts with driving forces, pressure, state, impact and/or response indicators are applied. The German Council of Environmental Advisors (SRU) requires that the selection and aggregation of indicators must be transparent and comprehensibly documented and that the chosen indicators must be oriented at political targets. The following article gives an overview of relevant actual environmental indicator systems, their concepts and structuring, and points to the further research and developmental requirements within this area.     

A Global Indicator for Biological Invasion

Abstract:  "Trends in invasive alien species" is one of only two indicators of threat to biodiversity that form part of the Convention on Biological Diversity's (CBD) framework for monitoring progress toward its "2010 target" (i.e., the commitment to achieve by 2010 a significant reduction in the current rate of biodiversity loss). To date, however, there is no fully developed indicator for invasive alien species (IAS) that combines trends, derived from a standard set of methods, across species groups, ecosystems, and regions. Here we provide a rationale for the form and characteristics of an indicator of trends in IAS that will meet the 2010 framework goal and targets for this indicator. We suggest single and composite indicators that include problem-status and management-status measures that are designed to be flexible, readily disaggregated, and as far as possible draw on existing data. The single indicators at national and global scales are number of IAS and numbers of operational management plans for IAS. Global trends in IAS are measured as the progress of nations toward the targets of stabilizing IAS numbers and the implementation of IAS management plans. The proposed global indicator thus represents a minimum information set that most directly addresses the indicator objective and simultaneously aims to maximize national participation. This global indicator now requires testing to assess its accuracy, sensitivity, and tractability. Although it may not be possible to achieve the desired objective for a global indicator of biological invasion by 2010 as comprehensively as desired, it seems possible to obtain trend estimates for a component of the taxa, ecosystems, and regions involved. Importantly, current indicator development initiatives will also contribute to developing the mechanisms necessary for monitoring global trends in IAS beyond 2010.     

PICABUE: a methodological framework for the development of indicators of sustainable development

SUMMARY

Significant interest in the concept of sustainable development exists amongst scientists, planners, policy makers and the public, and considerable effort and expenditure is made or envisaged at local, national and international levels to promote a more sustainable society. Until ‘green accounting’ and similar systems are made available and are implemented, the sustainability indicator will be the most effective tool available for monitoring progress towards a more sustainable society. Sustainability indicators are already available but are characterized by a poor or absent theoretical underpinning. This paper addresses this problem by proposing a methodological framework that can be applied to the construction of indicators of sustainable development. In order to be consistent with widely accepted definitions of sustainable development, considerations relating to the measurement of quality of life and ecological integrity are central to the methodology. The methodological framework has relevance to a variety of spatial scales and to geographically diverse areas (urban or rural, developed or developing countries) so that a suite of sustainability indicators can be produced that is tailored to the needs and resources of the indicator user, but which remains rooted firmly in the fundamental principles of sustainable development.     

循环经济和工业生态效率指标体系

首先介绍了在OECD国家应用较多的生态效率的概念，并提出目前大力推行的循环经济的本质就是提高生态效率。为了衡量和评价循环经济的发展，有必要研究探索循环经济评价指标体系，本文借鉴生态效率指标体系的内容，对循环经济的评价指标体系进行了初步研究和设计。     

唐山生态城市建设核心指标体系与评价

以我国东部沿海重工业城市—唐山市为例,通过分析其背景及发展特色,应用层次分析法结合专家评价法构建了一套唐山生态城市建设核心指标体系。体系主要包括4类1级指标、13类2级指标和49类3级指标,同时采用线性加权法计算得出唐山生态城市建设过程中不同发展阶段的生态化水平。结果表明,唐山市现阶段已经处于较高的生态化水平;2015年综合指数值可望处于Ⅰ级生态化水平,基本达到生态城市标准;且有望在2020—2030年建成中等发达国家水平的生态化城市。     

Measuring impacts on species with models and metrics of varying ecological and computational complexity

Approaches to assess the impacts of landscape disturbance scenarios on species range from metrics based on patterns of occurrence or habitat to comprehensive models that explicitly include ecological processes. The choice of metrics and models affects how impacts are interpreted and conservation decisions. We explored the impacts of 3 realistic disturbance scenarios on 4 species with different ecological and taxonomic traits. We used progressively more complex models and metrics to evaluate relative impact and rank of scenarios on the species. Models ranged from species distribution models that relied on implicit assumptions about environmental factors and species presence to highly parameterized spatially explicit population models that explicitly included ecological processes and stochasticity. Metrics performed consistently in ranking different scenarios in order of severity primarily when variation in impact was driven by habitat amount. However, they differed in rank for cases where dispersal dynamics were critical in influencing metapopulation persistence. Impacts of scenarios on species with low dispersal ability were better characterized using models that explicitly captured these processes. Metapopulation capacity provided rank orders that most consistently correlated with those from highly parameterized and data-rich models and incorporated information about dispersal with little additional computational and data cost. Our results highlight the importance of explicitly considering species’ ecology, spatial configuration of habitat, and disturbance when choosing indicators of species persistence. We suggest using hybrid approaches that are a mixture of simple and complex models to improve multispecies assessments.     

Electricity consumption: The growth pattern as an ecological indicator

Ecological problems are mainly caused by growth processes. The energy input is a key indicator for ecosystems. In this context, the use of the most valuable kind of energy is of special importance. Economic systems may be considered as special ecosystems. The most valuable kind of energy used in economic systems of industrialised countries is electricity. For some industrialised countries the growth pattern of electricity consumption and its relation to the gross domestic product is considered in this contribution. A linear relation between both indicators for about 3 decades after the Second World War and a coupling of these indicators starting at 1973 has been found. The aim of the contribution is to present this relation and to initiate a discussion about its reason and its interpretation.     

Priority-Setting Tool Applied to Canada's Landbirds Based on Concern and Responsibility for Species

Abstract: As a contribution to Partners in Flight–Canada, the Canadian Wildlife Service developed a ranking system to help set priorities for landbird species. Two complementary species lists were generated: one with scores for "concern" representing vulnerability and population trend, and one for "responsibility" for regionally characteristic fauna. The concern score gave equal weight to vulnerability, a composite score based on abundance and breadth of range, and population trend, because its purpose was to give early warning of potential problems. Responsibility scores were scale-free and were assigned for the season in which the species is most abundant. Other systems for identifying species of concern may be more appropriate for other jurisdictions or organisms, but the responsibility ranking is widely applicable. This system is a coarse filter that generates preliminary ranks; additional information should be considered in deciding how to allocate scarce resources for conservation. Unrefined results are nonetheless useful for a variety of purposes, as illustrated by the scores for Canadian landbirds. About 25% of Canada's high-responsibility species are also of high concern. These high-concern species are not associated with specific habitats or migration patterns. Conservation of species ranking high on concern and responsibility merits cooperation with the United States and Mexico in particular. The scores identified improved monitoring as a priority conservation activity for Canada.     

Determining Decision Thresholds and Evaluating Indicators when Conservation Status is Measured as a Continuum

Categorization of the status of populations, species, and ecosystems underpins most conservation activities. Status is often based on how a system's current indicator value (e.g., change in abundance) relates to some threshold of conservation concern. Receiver operating characteristic (ROC) curves can be used to quantify the statistical reliability of indicators of conservation status and evaluate trade‐offs between correct (true positive) and incorrect (false positive) classifications across a range of decision thresholds. However, ROC curves assume a discrete, binary relationship between an indicator and the conservation status it is meant to track, which is a simplification of the more realistic continuum of conservation status, and may limit the applicability of ROC curves in conservation science. We describe a modified ROC curve that treats conservation status as a continuum rather than a discrete state. We explored the influence of this continuum and typical sources of variation in abundance that can lead to classification errors (i.e., random variation and measurement error) on the true and false positive rates corresponding to varying decision thresholds and the reliability of change in abundance as an indicator of conservation status, respectively. We applied our modified ROC approach to an indicator of endangerment in Pacific salmon (Oncorhynchus nerka) (i.e., percent decline in geometric mean abundance) and an indicator of marine ecosystem structure and function (i.e., detritivore biomass). Failure to treat conservation status as a continuum when choosing thresholds for indicators resulted in the misidentification of trade‐offs between true and false positive rates and the overestimation of an indicator's reliability. We argue for treating conservation status as a continuum when ROC curves are used to evaluate decision thresholds in indicators for the assessment of conservation status. Determinación de Umbrales de Decisiones y Evaluación delos Indicadores cuando se Mide el Estado de de Conservación como un Continuo