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a consequence of the party's selective appeal or whether the party merely mirrors the underlying social structure.

Attraction, Concentration, and Reflection Measures Compared

As conceptualized, our measures of social attraction, social concentration, and social reflection pertain to distinctly different perspectives from which to evaluate the bases of party support. Under certain conditions, however, these different perspectives converge, offering the viewer essentially the same picture from each vantage point. This can be seen by examining some logical interrelationships among the formulas underlying the measures.

Let us first compare social attraction with social reflection. Upon first thought, one correctly imagines that a party which draws its support equally from the various subgroups of a cleavage dimension would be perfectly reflective of the composition of society on that dimension. It may also seem that social reflection deteriorates to the extent that the party fluctuates in its attractiveness. But this line of thinking does not adequately provide for possible differences in the proportions of the subgroups within the society. When the subgroups are grossly different in size, slight shifts in the party's attractiveness across the groups may result in improved or impaired reflection.

Our measures capture and express these subtleties. When the k subgroups are all equal in proportion within the society, the attraction and reflection measures are mathematically equivalent, producing identical values. But when the k subgroups are not equal in proportion (which is usually the case), the measures are free to vary within constraints of the extent of the departure of the k subgroups from equality. For societies divided into unequal subgroups along any cleavage dimension, a party's social attraction may vary widely from its social reflection. The extent to which this occurs depends on the characteristics of the society and the appeals of its parties. This is a matter for empirical analysis of the observed attraction and reflection scores.

Let us next compare social attraction with social concentration. According to party theory, we expect the concepts of social attraction and social concentration to be inversely related: highly attractive parties being low on concentration and vice versa. This is again a matter for empirical test and verification. Mathematically, however, there is a built-in inverse relationship at the extremes of low attraction and high concentration--that is, when the party attracts support from only one group, all its support is necessarily concentrated within that group. This situation yields an attraction score of 0 and a concentration score of 1. But perfect attraction (1.0) does not imply an absence of concentration (0)--except under the special condition that the k subgroups involved in the analysis are equal in size.2 If the subgroups are not equal in size within the society, which is most apt to be the case, the measures can vary widely from each other within constraints introduced by the relative proportions of society embraced by each of the k subgroups. In general, if the k subgroups are grossly disproportionate in size, it is possible to obtain both high attraction and high concentration (or alternatively, low attraction and low concentration) simultaneously.

From the preceding discussion, it follows that the concentration and reflection are also related to each other, but the relationship is more tenuous. Only under the very special condition of two subgroups of equal size are the measures mathematically determined (see footnote 2). To the extent that the subgroups depart from equality, social concentration and social reflection can vary widely. Even the extreme conditions of perfect attraction or perfect concentration can produce different degrees of reflection when the subgroups are of different size. Because the student of comparative politics typically analyzes societies composed of majorities and minorities, each of these Concepts offers its own contributions to understanding the social bases of party support.

Attraction, Concentration, and Reflection Measures Applied

Note that these measures apply to individual parties, not party systems. Note also that they apply to specific social variables--such as occupation, religion, or race--and not to attraction or concentration reflection in general, overall aspects of society. More encompassing measures, if they are desired, will have to be constructed later from the several specific measures that we generate for the major social variables within a given country.

The determination of a "major social variable" varies considerably across countries. Anderson et al. (1967) identify four categories of "cultural differentiators" that are significant for developing nations: race, ethnicity and language, religion and caste, and regionalism. Rose and Urwin, who are concerned primarily with developed Western nations, select religion, regionalism, and communalism (ethnicity and language) as significant for politics in modern societies, and they cite urban-rural and occupation as two other significant social groupings (1969, pp. 12-14). Although they list some

2. Under the very special condition of only two subgroups of equal size (i.e., each claiming .5 of the population), the square root of the concentration formula is equivalent to 1 - social attraction. Because, in this case, social attraction is also equal to social reflection, the same equivalence holds for social reflection. But this relationship applies only to the condition of society divided into two subgroups of equal size; it does not hold true for any number of k equal subgroups.

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