Social inequality refers to the graduated dimensions (Blau 1977), vertical classifications (Ossowski 1963: Schwartz 1981) and bounded categories (Tilly 1998), or hierarchical relations (Burt 1982) by which human populations at varying levels of aggregation are differentiated. This concept is among the oldest and most diversely defined in sociology, extending back at least as far as Plato's conception of the republic and developed subsequently in the social theories of Marx  1976–1978, Mosca (1939), Weber  1978, Simmel (1896), Sorokin (1941), Eisenstadt (1971), Merton (1968), and others. The construct often is used interchangeably with related (though relatively more specific) concepts such as social class, social stratification, socioeconomic status, power, privilege, cumulative advantage, dependence, and dominance. It is relevant for the study of social systems that range in size from the dyad (Simmel 1896) to the modern world system (Wallerstein 1974).
SOCIAL INEQUALITY AS A GRADUATED DIMENSION
When social inequality is conceptualized as a graduated dimension, it is treated as a distributional phenomenon. Here the approach is to define inequality in terms of the distribution of socially valued attributes such as education, income, information, health, and influence in a population. However, distributional phenomena can be examined from one of two very different assumptions. The first assumption views inequality as being an outcome of or generated by the underlying distribution of valued traits among individuals. In this sense, it refers to "regular differences in power, goods, services, and privileges among defined sets" of actors (Granovetter and Tilly 1988). The second assumption views inequality strictly as a system-level property with individual-level differences that are defined as derivative rather than generative (Blau 1977). Distributions such as the size of the system and its total volume of resources are examined as higher levels of aggregation, with the goal of determining the overall level of inequality (oligarchy) across systems and without reference to individual differences (e.g., Lenski 1966; Mayhew 1973; Mayhew and Schollaert 1980).
Both approaches operationalize inequality along criteria that usually are measurable at the level of individual actors (persons, races, gender categories, organizations, nation-states) in a system. Early applications of the first assumption can be found in Pareto's ( 1980) examinations of income distributions and the circulation of elites. Pareto proposed that economic and political inequality emerged from the distribution and redistribution of "congenital abilities" that were valued within social systems. Sorokin (1941) proposed similar arguments to explain social and cultural processes of mobility and inequality.
Among the most influential and controversial conceptualizations of inequality as a graduated dimension emerging from individual differences was Davis and Moore's (1945) functionalist statement of the principles of stratification. Those authors argued that social inequality results from the differential distribution of societal rewards to individuals on the basis of their relative achievement of ranked social positions. This achievement process, with its implications for social mobility, was formally specified by Blau and Duncan (1967), who established that educational attainment mediated the process of intergenerational social mobility among men. Those researchers defined social inequality as socioeconomic status based on the economic and prestige rewards accorded to achieved occupational positions in American society. The strong parallel between this model of inequality and the neoclassical model of human capital (see Becker 1964) is well established (Wright 1978).
The most prominent distributional theories of inequality, however, are founded on macrosocial views of the division of labor, the rationalization of authority, and the distribution of social and economic rewards in industrial societies. Weber's ( 1978) theory of economic organization proposed that capitalist systems of property, power, and prestige developed out of the conjunction of changing systems of economic exchange (money economies) and accounting (double-entry bookkeeping) with rationalized systems of social control (rational-legal authority). Thus, social inequality in industrial society developed along economic and political dimensions to produce the multidimensional bases of inequality: class, status, and party. Lenski's (1966) comparative study of the evolution of inequality attempted to test Weber's rationalization thesis that inequality evolves necessarily (functionally) with increasing differentiation in the direction of systems of privilege based on rational authority and away from socially illegitimate systems of force or economic dominance.
Accordingly, distributional inequality can be concerned with more than the single dimension of individual socioeconomic outcomes. It also addresses macrosocial patterns of inequality (Eisenstadt 1971). According to Blau (1977), the parameters of social structure include inequality and heterogeneity—or graduated and nominal dimensions, respectively—which intersect to constrain and differentiate individuals' opportunities as well as their motivations and outcomes. The intersection of graduated and nominal parameters creates diverse systems or populations with differing distributional properties that cannot be reduced to an original individual source. Blau's distributional theory is "macrosocial in the sense that the 'cases' are populations or communities and the 'variables' measure some aspect (a rate or a distributional property) of these populations" (Skvoretz and Fararo 1986, p. 30). Following this approach, indicators of inequality can be defined in terms such as Lorenz curves (e.g., Gini indices, Theil coefficients), social welfare functions, or similar distributional properties (see Allison 1978; Wolfson 1997).
The emergence of the new global economy over the last two decades of the twentieth century has been associated with what has been characterized as a "surge" in wage and household income inequality (Gottschalk and Smeeding 1997) and a "winner-take-all income market" (Levy 1998) in advanced industrial countries. By and large, the growth of very high incomes in some sectors and the stagnation of wages in selected labor markets have produced a widening distribution of income. Distributional measures of economic inequality such as Gini and Theil coefficients reveal growing inequality among employed workers across advanced industrial societies with some of the highest inequality observed in the United States.
Economic inequality also may intersect with the nominal category of race, for example, and produce more diverse outcomes than traditional functional or neoclassical economic theories would predict. Examinations of patterns of interracial/interethnic marriage, for example, indicate that the association between occupational achievement and race is mediated by the extent of interracial/interethnic marriage in a community (see Blum 1984; Blau et al. 1982). This treatment of inequality, which is based on notions of dispersion and association, departs from the simple reduction of unequal outcomes to individual attributes and embeds the process in extended distributional contexts.
Other distributional approaches introduce constructs to explain inequality at levels above individual attributes, although individuals usually remain the units of analysis. Spatial and temporal contexts, for example, define and constrain distributions of individual outcomes. The examination of occupational mobility within organizational or labor-market contexts attempts to nest the process of inequality in the workplace within organizational and occupational boundaries. The availability of occupational positions within a system is seen as being independent of the motivations and other attributes of workers. White's (1970) influential notion of "vacancy chains" exemplifies this approach with its argument that job vacancies produce opportunity structures for individual mobility and define the mobility chances, and thus distributional outcomes, of individuals. Vacancy-chain models have been particularly useful for examining closed opportunity systems, such as internal labor markets (Sorensen 1977).
Distributions of individuals in systems of inequality also are influenced by temporal factors. Merton's (1968) provocative discussion of the "Matthew effect" in scientific career systems argues that over time, initial inequalities in a system bias distributional outcomes in favor of initial advantage. Formal extensions and applications of Merton's notion of accumulative advantage have been applied across contexts (Cole and Cole 1973; Allison and Stewart 1974) to establish patterns of temporal regulation of distributional outcomes over and above the attributes of individuals over time. The cumulative advantage hypothesis has received considerable attention in research on the relationship between age and inequality within cohorts (Dannefer 1987; O'Rand and Henretta 1999). Succeeding cohorts of U.S. populations display growing inequality across the age span, with higher coefficients of inequality at older ages within cohorts and (in recent decades) increased inequality among the aged in successive cohorts (Crystal 1995).
SOCIAL INEQUALITY AS A VERTICAL CLASSIFICATION OR BOUNDED CATEGORY
When social inequality is conceptualized as a vertical classification system, it is treated as an oppositional phenomenon. Here the approach is to define inequality in terms of "the relative position in a matrix of oppositions" (Schwartz 1981, p. 94) of social categories that determine relations of dominance, such as class, race, and gender. Vertical classifications grow out of antagonistic and contradictory interests in the relations of "objective" positions in the social division of labor, not out of the dispersed motivations and interests of individuals. Dominance and subordination emerge from the objective opposition of social categories. Dichotomous, binary, and polar conceptions of inequality (e.g., ruler–ruled, rich–poor, white–black, masculine–feminine) generally are informed by an oppositional framework. Some researchers have argued that this approach to inequality may be the most ancient in human social consciousness (Ossowski 1963; Schwartz 1981).
Class theories that follow Marxian frameworks dominate this approach (Braverman 1974; Wright 1985). Marx's theory of class proposes that class relations in capitalist systems are inevitably in conflict. Since all value is ultimately produced by labor, all (capitalist) profit must be at the expense of labor. The objective positions of the owning class (bourgeoisie) and the laboring class (proletariat) therefore are necessarily antagonistic. Advanced capitalist systems sustain the exploitation of labor through rationalized job-definition systems and the degradation of work (Braverman 1974). Wright (1978) has argued, furthermore, that in advanced capitalist societies, the elaborate differentiation of functions originally embodied in entrepreneurial capitalism into many different categories has not overcome the fundamental oppositional inequality of its origins; contradictory class positions continue to exist as a result of the underlying structure of capitalist relations.
Oppositional frameworks lend themselves to the examination of classlike relations such as those observable in race- and gender-centered systems of inequality. Oppositional approaches to the examination of race inequality can be traced to Myrdal's (1944) pioneering analysis of racial exploitation in the U.S. context. These approaches argue that race is an invariant principle of vertical classification that is masked by ideologies of economic progress and attainment (Pinkney 1984). Debates regarding the inevitability of racial opposition as the basis of inequality center on the substitutability of race and class as categories in the recent history of U.S. inequality. Wilson (1980) has proposed the controversial argument that class inequality has superseded race inequality as the basis of cross-race differences in economic and social outcomes.
Theories of gender inequality extend back to Mill's libertarian essay on the subjection of women (Mill 1859) and Engels's Marxian analysis two decades later (Engels  1942) of the relationship between private property and the stratification of family (gender) roles. However, contemporary feminist theories provide the strongest argument for gender inequality as an oppositional, vertical classification system. The sex/gender system, it is argued, subordinates women in patriarchal relations that exist over and above class relations ( Jaggar 1984), since male dominance over women's productive and reproductive roles predates the emergence of capitalism (Harding 1983). This system of inequality leads inevitably to a conflict of interests and to the emergence of competing ideologies.
Since the notion of dominance is central to vertical-classification approaches to inequality, these approaches are readily applied to the analysis of large-scale systems of inequality, such as the state (Skocpol 1979) and the modern world system (Wallerstein 1974). Mechanisms of domination extend beyond class (or classlike) interests and are observable in the historical relations of nation-states (Reddy 1987) and multistate sectors of the modern world system (Wallerstein 1974). Asymmetrical relations of exchange and dependence between states and geopolitical state sectors create relations of dominance, which define global inequalities. Those inequalities can be formulated as distributional phenomena by following a functional framework; however, the historical analysis of dominance systems lends itself more readily to oppositional analysis. The classification of the world system into core and periphery sectors that resulted from historically contingent factors introduces notions of centrality and dominance that suggest more than an underlying distribution of resources (Wallerstein 1974).
Tilly's (1998) statement on "durable inequalities" argues that persistent inequalities based on exploitation, opportunity hoarding, adaptation, and emulation largely take the form of bounded (usually dichotomous) categories (male–female, slave–owner, citizen–foreigner, white–black, etc.) that are resilient and readily generalizable across time and social systems. Relationships of inequality persist because participants in paired categories adapt to and participate in the perpetuation of those arrangements.
SOCIAL INEQUALITY AS HIERARCHICAL RELATIONS
When social inequality is conceptualized as hierarchical relations, it is treated as a system of interactions or interdependencies characterized by relative symmetry (equality) and asymmetry (inequality) among relations. Here the approach usually is to define the form of social relations rather than the attributes of individuals in those relations and to account for patterns of unequal relations without referring to oppositions. Inequality or dominance stems from positions in hierarchical relations, not from the a priori possession or control of resources or power by individuals, groups, or categories (Marsden 1983). This relational approach to inequality can be traced to Simmel (1896), whose studies of the structures of superordination–subordination by persons, groups, and principles continue to inform research on hierarchical relations and social networks in modern life (Coleman 1982).
Because social relationships have formal properties such as connectedness, transitivity, reciprocity, and multiplexity, they are measurable units of analysis in the study of social inequality within populations at all levels, from siblings to communities to transnational trading systems (Lin and Marsden 1982). These social units make up complex configurations of social relations within which distinctive positions of relative equivalence or centrality can be revealed (Burt 1982). Thus, in their study of coalitions and elite structures in the German community of Altneustadt, Laumann and Pappi (1976) determined the relational bases of influence between natives and newcomers by using network techniques that emphasized associational patterns rather than personal attributes. Patterns of social distance and connectedness among corporate actors, not the preexisting distribution of resources, defined the influence process in that community.
A study by Granovetter (1974) of the job-search process clearly demonstrates the relative utility of relational over distributional approaches to inequality. Granovetter demonstrates that weak ties, rather than strong ties, in a community prevail in a successful job search. The "strength of weak ties" hypothesis (related to Simmel's tertius gaudens, or the third who enjoys) provides the counterintuitive argument that weaker (secondary) social contacts increase individuals' access to jobs more than stronger (primary) ties do. These ties operate independently of the attributes of individual job seekers.
The "strength of weak ties" phenomenon can be extended beyond the job-search process to examine structures of relational inequality in different contexts. Studies of interlocking directorates and informational brokerage systems, for example, demonstrate that loosely coupled relational systems of different forms produce different systems of social inequality (Burt 1982). The network of ties constitutes a social-constraint context within which actors are "captured." Burt's (1983) study of corporate philanthropy as a cooptive relation is a specific example of the relational bases of inequality in a market context. Using Internal Revenue Service data on firm expenditures for advertising and philanthropy, Burt demonstrates that firm philanthropy co-opts the household sector by legitimizing the firm to the public as a protector and by improving the ability of specific classes to purchase the firm's products (Burt 1983, p. 424). The strength of this approach is that advertising, which is more blatantly co-optive, does not escape public suspicion, whereas philanthropy does so more easily. Firms in an economic sector perform unequally as a result of their relative co-optive relations with the public, and the public has a co-optive relationship as consumers in that context.
Finally, it should be mentioned that despite the rationale provided above for the bulk of sociological research on relational inequality, the relational approach has been used to examine the importance of individual resources for social inequality. Indeed, early experimental efforts to study small group processes of inequality demonstrated that both individual resources and social relations can create systems of inequality, whether measured as leadership processes or as communication networks (Thibaut and Kelley 1959). More recently, studies of what Burt (1982) has termed "ego-centered" networks examine network position itself as an individual resource with implications for social inequality.
APPROACHES TO SOCIAL INEQUALITY
The three major approaches to the study of social inequality outlined above have different implications for theory as well as for method. The distributional approach that examines social inequality as a graduated dimension depends primarily on sample data and can be directed toward individual as well as structural explanations of inequality. The oppositional approach to vertical classifications and bounded categories may use sample data but has tended to adopt historical and qualitative approaches to study the institutionalization of dominance in various forms, such as class, race, and gender, as well as other forms of domination/subordination. The relational approach, which provides a direct method for examining the social context of inequality, may use sample or case data to map the configurations of the relations of inequality with implications for explanation at both the individual and structural levels.
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