INTRODUCTION

This chapter reviews the basic conceptual foundations for the measurement of polariza­tion, the origins of those foundations, how polarization is distinct from inequality and other ways of considering distances and differences across individuals, and how polariza­tion can be measured in an economic, a social, and in a hybrid socioeconomic perspective.

It is useful to stress at the outset that the term polarization means different things to different people. First, some people view polarization as important for ethical reasons and others consider polarization as instrumental toward generating tensions and conflicts. Second, there are different “types” of polarization. This chapter distinguishes five such types: income polarization, income bipolarization, social polarization, socioeconomic polarization, and multidimensional polarization. They are listed in Table 5.1, along with their main distinguishing features—how they form groups and how they measure distances. Some of the relevant indices are also listed.

Table 5.1 A categorization of polarization indices

5.1.1 Income Polarization

The chapter first discusses income polarization, understood as polarization over the uni­variate distribution of a cardinal variable of interest. This regards polarization as a clus­tering of that variable around an arbitrary number of local means. Variables of interest in that context usually measure welfare; income polarization is then polarization over the distribution of a measure of welfare. This measure of welfare is often income, which explains why the term “income polarization” is chosen to denote this class of polarization measures. The variable of interest can also be unrelated to welfare. One can think, for instance, of income polarization over a distribution of political attitudes or over a distri­bution of geographical locations. As long as these variables have cardinal value, polari­zation over them will be referred to as income polarization.

The formalization of income polarization has mostly relied in the literature on an identification/alienation framework. Members of the same group identify with each other; members of different groups feel alienation with respect to one another. Income polarization is assumed to be increasing in both aspects: the greater the level of group identification or the greater the level of alienation, the greater the level of polarization.

5.1.2 Bipolarization

An alternative notion of polarization across a cardinal variable of interest is bipolarization. Bipolarization captures distances across two groups. These two groups have usually been defined as lying on either side of a median, thus taken as the middle of a distribution; for this reason, the bipolarization literature is closely linked to the literature on the size of the middle class. But one can also think of bipolarization as being concerned with the distance between two other separate income groups, such as the poor and the nonpoor or the bourgeois and the proletarians. (Those two groups cannot, however, be defined by a var­iable other than the variable interest; using a variable other than the variable of interest to define groups would generate a measure of socioeconomic polarization—see later discussion.)

Two notions are intrinsic to the nature of bipolarization: the notion of changes in spreads from the middle and the notion of variations in “bipolarity.” An increase in the spreads of incomes from a middle position increases bipolarization. An increase in bipolarity—smaller income distances either among those below or among those above the middle—raises bipolarization. Equivalently, a reduction in the income gaps between any two incomes, both above or below the median, increases bipolarization.

The discussion until now already makes clear that the measurement of polarization generally involves both inequality- and equality-like constituents. The equality-like con­stituent is the basis of the fundamental conceptual difference between inequality and polarization. Polarization differs from inequality in that the importance ofpole (or group) homogeneity carries weight in addition to the importance of heterogeneity across indi­viduals. Increased distances across individuals of different groups increase both inequality and polarization; increased bunching (for income polarization) or increased equality (for bipolarization) across individuals of the same group decreases inequality but raises polarization.

Much of the debate on the differences between inequality and polarization—and on the possible relevance of each in explaining conflict—effectively rests on the nature of the effects of Pigou-Dalton transfers on each of these measures of the income distribution. A regressive Pigou-Dalton transfer increases bipolarization if the transfer takes place across the median; however, such a transfer increases inequal­ity but decreases bipolarization if it occurs entirely on one side of the median.^[171] Whether either (or both) of these transfers increases conflict is a matter of debate; the polarization literature generally supports the view that a regressive same-side-of- the-median transfer actually reduces conflict.^[172]

5.1.3 Social Polarization

The chapter then turns to social polarization. Social polarization is concerned with polar­ization over variables that are qualitative or have no particular cardinal content. Social polarization does not use information on distances between individuals or groups; it only takes into account the size of the groups and sets distances between them to a constant. This is not to say that social polarization cannot measure tensions or distances across groups; it does this by focusing on the distribution of group sizes.

What matters for social polarization is not only how many groups there are, but also how salient their sizes are. The social polarization literature argues that, ceteris paribus, the larger the size of another group, the greater the threat felt by a given group (proportionally to the size of the other group). This introduces a fundamental distinction between inequality of 0/1 group membership (also called group fractionalization) and social polarization. Frac- tionalization increases when two identical groups split into two because there is then greater group membership inequality; social polarization falls following such a change.

5.1.4 Socioeconomic and Multidimensional Polarization

Social polarization bases group identity on social characteristics; it sets distances to a binary 0/1 variable and thus does not make use of cardinal distance information.

Socioeconomic polarization makes an asymmetric use of these dimensions. One set of social variables is used for group identification; a second set of economic variables fixes distances.^[173] Because of this, the usual properties of the income polarization and income bipolarization settings do not apply. In particular, bipolarization properties of increasing spread and of increasing bipolarity do not hold in a socioeconomic polarization context.

Multidimensional polarization measures can also be designed.^[174] Group membership can be based on the entire set of social and economic characteristics; so can the measurement of distances across individuals. When this is done, a multidimensional ana­logue of unidimensional income polarization is obtained. Multidimensional polarization can also be of a socioeconomic type; this is achieved by defining social membership by social characteristics (as is usual) and by measuring distances on the basis of a multivariate distribution of welfare indicators.

5.2.