Measures of Multigroup Segregation

In this paper we derive and evaluate measures of multigroup segregation. After describing four ways to conceptualize the measurement of multigroup segregation—as the disproportionality in group (e.g., race) proportions across organizational units (e.g., schools or census tracts), as the strength of association between nominal variables indexing group and organizational unit membership, as the ratio of between–unit diversity to total diversity, and as the weighted average of two–group segregation indices—we derive six multigroup segregation indices: a dissimilarity index (D), a Gini index (G), an information theory index (H), a squared coefficient of variation index (C), a relative diversity index (R), and a normalized exposure index (P). We evaluate these six indices against a set of seven desirable properties of segregation indices. We conclude that the information theory index H is the most conceptually and mathematically satisfactory index, since it alone obeys the principle of transfers in the multigroup case. Moreover, H is the only multigroup index that can be decomposed into a sum of between– and within–group components.     

Ethnic Integration and Spatial Segregation of the Chinese Population

Because of the overwhelming numerical dominance of the Han within the Chinese population and the highly localised distributions of most minority groups, it is difficult to assess the level of either segregation or ethnic integration in China in a systematic or meaningful manner. Previous studies have either been limited to mapping the locations of minority groups or have been based on provincial data, which for analytical purposes are too coarse to characterise the geographical distribution of minority populations at the sub-provincial level. In this paper, county-level data were used to calculate a diversity index for each county to illustrate the level of ethnic diversity. The results of these analyses indicate that high levels of diversity for a particular province are limited to a specific geographic region within it (especially along the international boundary and in some mountainous areas), rather than characterising the province as a whole. The approach used in this paper also employs a new measure based upon the idea of a standard deviational ellipse—a measure that is used to evaluate the level of spatial segregation between ethnic groups. An index illustrating the degree of spatial correlation between ethnic groups was derived for each province using county-level data. The results indicate that, although major population groups in southern and western China display a low level of spatial correlation (i.e. they are highly segregated), these same areas nevertheless exhibit relatively high levels of ethnic diversity.     

RESIDENTIAL INTERRACIAL EXPOSURE AND ISOLATION INDICES: Mean versus Median Indices, and the Difference It Makes

Interracial exposure and isolation ( p *) indices have been widely used in studies of residential racial segregation. However, a recent pilot study raised serious issues about the use of these indices, because they are based on the mean statistic, which may yield misleading results in the case of skewed distributions, as is often the case with census tract racial compositions. An alternative median exposure index ( p *- md ) is proposed, and mean and median indices of white-to-African-American and African-American-to-white exposure, as well as white and African-American isolation, are compared for the 50 largest metropolitan areas in the United States. The analysis shows that the mean and median measures produce different results, and that most of these differences are maximized in those areas that are most segregated and, especially for African-American-to-white exposure, in areas where the largest number of African Americans live. This creates significant problems in the interpretation and use of mean exposure and isolation indices, and in most cases, the median index yields a result more representative of the residential neighborhood situation of the majority of whites and African Americans. A particular problem with the mean exposure indices currently in common use is their tendency to overstate the degree of neighborhood-level interracial contact in U.S. metropolitan areas, and, in so doing, to understate the impact of racial housing discrimination.     

ON CAPITAL, TIME AND THE NEOCLASSICAL PARABLES

Many of the paradoxes in capital theory arise from seeking a purely 'physical' measure for the aggregate stock of capital. Several recent papers made it clear that heterogeneous capital outfits cannot be measured by a single aggregate index which is independent of the rate of interest. This paper defines and proves the general properties of an index of capital intensity — the degree of 'roundaboutnes'— which admits both the physical and the time dimensions of capital. A modified form of the neoclassical parables is defined and proved to be universally valid despite reswitching.     

Constructing indices of multivariate polarization

Multivariate indices of polarization are constructed to measure effects of non-income attributes like wealth and education. Polarization is considered as the presence of groups which are internally homogeneous, externally heterogeneous, and of similar size. We propose a class of polarization indices which is built from measures of relative groups size and from decomposable indices of socio-economic inequality. For the latter, we employ the special inequality indices of Maasoumi (Econometrica 54:991–997, 1986), Tsui (J Econ Theory 67:251–265, 1995; Soc Choice Welf 16:145–157, 1999) and Koshevoy and Mosler (J Multivar Anal 60:252–276, 1997). Then, postulates for multidimensional polarization measurement are stated and discussed. The approach is illustrated by an empirical application to the population of the East and West Germany with polarization defined on income and education.     

Emerging Patterns of Hispanic Residential Segregation: Lessons from Rural and Small‐Town America

The past two decades have ushered in a period of widespread spatial diffusion of Hispanics well beyond traditional metropolitan gateways. This article examines emerging patterns of racial and ethnic residential segregation in new Hispanic destinations over the 1990–2010 period, linking county, place, and block data from the 1990, 2000, and 2010 decennial censuses. Our multiscalar analyses of segregation are framed by classical models of immigrant assimilation and alternative models of place stratification. We ask whether Hispanics are integrating spatially with the native population and whether recent demographic and economic processes have eroded or perpetuated racial boundaries in nonmetropolitan areas. We show that Hispanic residential segregation from whites is often exceptionally high and declining slowly in rural counties and communities. New Hispanic destinations, on average, have higher Hispanic segregation levels than established gateway communities. The results also highlight microscale segregation patterns within rural places and in the open countryside (i.e., outside places), a result that is consistent with emerging patterns of “white flight.” Observed estimates of Hispanic‐white segregation across fast‐growing nonmetropolitan counties often hide substantial heterogeneity in residential segregation. Divergent patterns of rural segregation reflect local‐area differences in population dynamics, economic inequality, and the county employment base (using Economic Research Service functional specialization codes). Illustrative maps of Hispanic boom counties highlight spatially uneven patterns of racial diversity. They also provide an empirical basis for our multivariate analyses, which show that divergent patterns of local‐area segregation often reflect spatial variation in employment across different industrial sectors.     

Geodesic based centrality: Unifying the local and the global

A variety of node-level centrality measures, including purely structural measures (such as degree and closeness centrality) and measures incorporating characteristics of actors (such as the Blau's measure of heterogeneity) have been developed to measure a person's access to resources held by others. Each of these node-level measures can be placed on a continuum depending on whether they focus only on ego's direct contacts (e.g. degree centrality and Blau's measure of heterogeneity), or whether they also incorporate connections to others at longer distances in the network (e.g. closeness centrality or betweenness centrality). In this paper we propose generalized measures, where a tuning parameter δ regulates the relative impact of resources held by more close versus more distant others. We first show how, when a specific δ is chosen degree-centrality and reciprocal closeness centrality are two specific instances of this more general measure. We then demonstrate how a similar approach can be applied to node-level measures that incorporate attributes. When more or less weight is given to other nodes at longer distances with specific characteristics, a generalized measure of resource-richness and a generalized measure for diversity among one's connections can be obtained (following Blau's measure of heterogeneity). Finally, we show how this approach can also be applied to betweenness centrality to focus on more local (ego) betweenness or global (Freeman) betweenness. The importance of the choice of δ is illustrated on some classic network datasets.     

Age residential segregation in Canadian cities

Des indices de dissimilitude relativement a la distribution rCsidentielle de la population canadienne sont calculis ici pour les groupes d'ige de plus de 65 ans et de moins de 65 ans, ainsi que par sexe. Les donnPes de toutes les villes compris dans les programmes des secteurs de recensement de 1971 (30 villes), 1976 (32 villes), et 1981 (36 villes) sont utilisCes. L'analyse de I'annPe 1981 prksente un indice moyen de 27.5, pour des valeurs s'khelonnant entre 16.7 et 38.2. Les villes de I'ouest canadien presentent les indices de segregation les plus ClevPs, et les indices des femmes igCes sont plus PlevCs que ceux des hommes du mime ige. Depuis 1971, on note une augmentation de la segregation rksidentielle des personnes igCes, et aussi une augmentation de la difference sur la base du sexe. A partir de la thCorie Ccologique, une explication de la variation d'une ville a I'autre des degres de segrCgation est proposCe, puis est fortement appuyee par I'analyse.
Indexes of dissimilarity, measuring the dissimilarity of residential distribution between the population aged 65 years and over and the population aged under 65, were computed for all tracted cities in the 1971 (30 cities), 1976 (32 cities), and 1981 (36 cities) Censuses of Canada. Separate indexes were computed for elderly males and females. The results show an average index in 1981 of 27.5, and a range of 16.7 to 38.2; with cities in Western Canada having the highest segregation indexes. The indexes were higher for older women than for older men. Trends since 1971 indicate an increasing residential segregation of the aged as a group as well as a widening sex differential among them. An explanation of the variations in segregation levels among the cities based on ecological theory received strong support.     

Power indices expressed in terms of minimal winning coalitions

A voting situation is given by a set of voters and the rules of legislation that determine minimal requirements for a group of voters to pass a motion. A priori measures of voting power, such as the Shapley–Shubik index and the Banzhaf value, show the influence of the individual players in a voting situation and are calculated by looking at marginal contributions in a simple game consisting of winning and losing coalitions derived from the legislative rules. We introduce a new way to calculate these measures directly from the set of minimal winning coalitions and derive explicit formulae for the Shapley–Shubik and Banzhaf values. This new approach logically appealing as it writes measures as functions of the rules of the legislation. For certain classes of games that arise naturally in applications the logical shortcut drastically simplifies the numerical calculations to obtain the indices. The technique generalises directly to all semivalues.     

Social workers' conceptions of how the local living environment is related to social exclusion

The article is concerned with how community-based social workers conceptualize the relationship between the local living environment and social exclusion and inclusion processes. It provides a brief overview of general urban theory concerning the significance of the local living environment in a globalized world and looks at how social workers understand the mechanisms of spatial marginalization and urban segregation. In addition, the article examines social workers' views on sustainable living environments that support inclusion. It is argued that, through their daily work, social workers have a special yet restricted view on social exclusion and inclusion processes. Their knowledge could contribute to efforts to gain a deeper understanding of the phenomenon of spatial marginalization because they work in a position from which they can see the consequences and interdependencies of multiple issues between structural changes and individual survival in the context of the local living environment.     

A method for evaluating the behavior of power indices in weighted plurality games

In this paper, a systematic method to facilitate the comparison of a priori measures of power in an n-player r-candidate (n, r) weighted plurality game is proposed. This method, which exploits the notion of a structure of embedded winning coalitions (SEWC), enables the listing of all power profiles relevant to an (n, r) game under a given index and permits the computation of the probability of occurrence of each of these profiles. The vulnerability of an index to different paradoxes of power can also be systematically studied. For the purpose of illustration, we apply this method to the analysis of four well-known 2-candidate power indices namely the Shapley-Shubik index, the Banzhaf index, the Johnston index and the Deegan-Packel index. In each case, the set of power profiles and the likelihood of occurrence of each of these profiles are enumerated. The superadditivity property of these indices is also studied. Received: 20 October 1999/Accepted: 25 April 2001     

MEASURING AND ANALYZING CLASS INEQUALITY WITH THE GINI INDEX INFORMED BY MODEL-BASED CLUSTERING

The most widely used measure for studying social, economic, and health inequality is the Gini index/ratio. Whereas other measures of inequality possess certain useful characteristics, such as the straightforward decomposability of the generalized entropy measures, the Gini index has remained the most popular, at least in part due to its ease of interpretation. However, the Gini index has a limitation in measuring inequality. It is less sensitive to how the population is stratified than how individual values differ. The twin purposes of this paper are to explain the limitation and to propose a model-based method—latent class/clustering analysis for understanding and measuring inequality. The latent cluster approach has the major advantage of being able to identify potential "classes" of individuals who share similar levels of income or one or more other attributes and to assess the fit of the model-based classes to the empirical data, based on different cluster distributional assumptions and the number of latent classes. This paper distinguishes class inequality from individual inequality, the type that is better captured by the Gini. Once the classes are estimated, the membership of estimated classes obtained from the best fitting model facilitates the decomposition of the Gini index into individual and class inequality. Class inequality is then measured by two relative stratification indices based on either the relative size of the Gini between-class components or the relative number of stratified individuals. Therefore, the Gini index is extended and assisted by model-based clustering to measure class inequality, thereby realizing its great potential for studying inequality. Income data from France and Hungary are used to illustrate the application of the method.     

The measurement of occupational segregation and its component dimensions

The paper reviews different approaches to, and current knowledge of the measurement of occupational segregation, using the case of gender segregation. It shows that most popular segregation ‘indices’ are actually statistics of association in a 2x2 table, often with distorting weightings. The dimensions of segregation comprise a vertical dimension measuring inequality and an orthogonal horizontal one measuring difference without inequality. Together, the dimensions make up segregation as generally understood; so segregation and its dimensions require consistent measurements. Conditions for suitable measures are considered, and the limitations of the various measures noted. The alternative conception of segregation, where all occupations are treated as though they were the same size, is shown to be seriously flawed. The most useful measures are selected and shown to be related as Lorenz curves. Since all segregation measures vary with the number of occupations considered, standardisation on 200 occupations is introduced for the chosen measures.     

Segregation and Mortality: The Deadly Effects of Racism?

Elevated rates of mortality for African Americans compared to whites, coupled with the persistence of high levels of racial residential segregation, have directed attention to the structural manifestations of racism as potentially important pathogens for health. Using national mortality and census data for 1990 and a measure of black social isolation from whites, we examine the association between residential segregation and mortality in 107 major U.S. cities. Our analyses revealed that black social isolation tended to predict higher rates of mortality for African American males and females, although the strength of the association varied by cause of death. Socioeconomic deprivation explained a modest part of this association for black males but not for black females. Our analyses also found that a positive association between social isolation and mortality was more pronounced, for both blacks and whites, in cities that were also high on the index of dissimilarity. These findings highlight the need for research to identify the specific mechanisms and processes that link residential environments to adverse changes in health status.     

Lottery marketing in Québec and social deprivation: excessive exposure,insufficient protection?

In 2008, the Institut national de santé publique du Québec (INSPQ) undertook a research programme on lotteries. The preliminary qualitative exploratory component enabled us to observe the diversity and ubiquity of lottery advertising to which the vast majority of the population is exposed, including minors and non-players. The aim of a second component was to better comprehend the relationships between exposure to lottery marketing, lottery purchasing habits, attitudes towards gambling, and socio-economic vulnerability indicators. The study's data was collected by a polling firm from a representative sample of adults in the Québec population (n = 2001). Our survey revealed significant links between exposure, gambling behaviour and certain socio-economic indicators: for example, individuals with lower levels of education more often play the lotteries and spend the most on them. In addition, a greater number of people who are less educated and from a low-income household considered that lottery advertising was very or excessively present in their daily lives and that the amount of advertising has increased in recent years. From the perspective of creating healthy environments and protecting vulnerable populations, legislative measures to control the quantity, location and contents of gambling marketing would be promising preventive measures.     

Measuring residential segregation in multi-ethnic and unequal European cities

Immigration flows and social inequalities reflect increased social and multi-ethnic segregation in contemporary urban Europe. For a better understanding of these processes, the present study investigates the main strengths of the multi-group residential indices, testing sensitivity and reliability under different metropolitan contexts in five European countries. These indices focus on different research dimensions and approach multi-group residential segregation conceptually and mathematically in a different way. A multivariate exploratory data analysis was adopted to classify the observed segregation patterns into a few homogeneous types and to delineate the multivariate relationship between the indices. The results of principal component analysis demonstrate that the indices assessing uniformity and disproportionality of the social groups analysed (H and D) contribute largely to the diversification in today's multi-ethnic communities, clarifying the importance of the dimension of evenness. Our results highlight how segregation is more evident in economically disadvantaged metropolitan regions with high levels of social vulnerability.     

Inequality in voting power

This paper deals with the assessment of inequality in the distribution of voting power. Voting power is evaluated through a general concept of power measurement based on both the voting rule and the probability distribution over vote configurations. This general concept includes as particular cases the most usual power indices and other extensions of this traditional concept. Thus no particular power index is privileged in our approach. An inequality index over the class of all power profiles with a given number of voters generated by this general measure is then singled out by requiring reasonable properties. In order to compare profiles with different numbers of voters, two alternative principles are considered, which extend the said index consistently in two ways.Previous versions of this work were circulated under different titles. We gratefully acknowledge financial support from the Spanish Ministerio de Ciencia y Tecnología under the Ramón y Cajal programme and under projects PB96-0247 and BEC2000-0875; from the European Commission under the Training and Mobility of Researchers programme (contract FMRX - CT966-0055); and from the Instituto Valenciano de Investigaciones Económicas. We also thank two anonymous referees for their comments.2 October 2001     

Motion Picture Attendance and Social Isolation

It is hypothesized that a major cause of movie attendance is social isolation, which is measured by population increase, percentage of the population changing houses, and an urbanism index. Fairly high product-moment correlations are found between each of the two population mobility measures and movie attendance; the combined multiple correlation is even higher. Adding the urbanism index to this multiple correlation increases it only slightly. Significant regional differences in movie attendance are found to disappear when population increase is controlled.     

Blind Faith in the Free Market: Urban Poverty, Residential Segregation, and Federal Housing Retrenchment, 1970–1995

In recent years, research on poverty and segregation has been organized within a dominant discourse that centers on the relative salience of racial discrimination or macroeconomic change as a determinant of concentrated minority poverty. In contrast, little sociological research has focused on federal housing policies and programs as important factors shaping racial patterns of poverty and residential segregation in U.S. metropolitan areas. Drawing upon census data, public documents, housing reports, and interviews with local residents, I examine how federal and local housing initiatives in the 1980s and 1990s have interacted with the shift to a service-oriented economy to reinforce racial residential segregation and exacerbate urban poverty in Kansas City. I find that persistent racial residential segregation, including minority poverty concentration and the spatial isolation of inner-city neighborhoods, is due to post-1970 changes in the operation of the metropolitan housing market and retrenchment in federal and local housing policy. Rather than viewing racial discrimination and macroeconomic change as disconnected and separate "variables," I focus on the interconnectedness and mutually reinforcing character of both factors. Such an emphasis moves beyond separate-variables approaches and analyses to identify how concentrated minority poverty is sustained not only by racial discrimination and large-scale macroeconomic and demographic changes, but also by the market-centered orientation of federal housing programs and policies.