tary literature has developed within comparative politics over the measurement of social fragmentation--the counterpart of concentration (Rae 1968; Rae and Taylor 1970; Mayer 1972). The concentration measure used in the ICPP project was independently derived, but it has links with both bodies of literature. In contrast to our social attraction measure, our concentration measure expresses unevenness of a percentage pattern. Because of the special quality of the percentage score ingredients for the concentration variable (the percentages must total to 100), we can take advantage of a different approach in measuring that pattern.
Our approach is similar to that used in economics to measure the concentration of firms in the marketplace. We square and sum the proportions of each group's contribution to the total set of party supporters. In the limiting case of perfect concentration--when all the party's support comes from only one of several existing groups--the concentration score is 1. A simple summing of squared proportions of support components, however, does not allow for comparison across parties or countries when the number of existing groups varies. For example, when there are only two significant groups within a social category (e.g., religion divided into Catholic and Protestant) and the two groups contribute equally to the party's composition, the sum of the squared proportions (.502 + .502) is .50. But, when there are three groups also equally divided (.332 + .332+ .332), the value is .33. Thus, a correction must be introduced to allow for the number of groups and to render the concentration scores comparable in the two cases. This correction factor is included in our formula for measuring social concentration:
where k is the number of subgroups within the cleavage dimension included in the analysis and Yj is the proportion of the party's support coming from" the jth subgroup of k groups.
This formula ranges from 0--when the party's support comes equally from the competing groups--to 1.0, when one of the groups contributes all its supporters. The scores are comparable across parties and countries, regardless of the number of groups included in the analysis.
"Social reflection" is defined as the extent to which the composition of the party's supporters accurately reflects the social composition of the population along any given dimension of social cleavage. A party which is high on social reflection for a given variable mirrors in its own composition the proportional distribution of social groups in the society. Take the religion variable for example. If a society is 40 percent Protestant and 60 percent Catholic, the supporters of a perfectly reflective party would also display a division of 40 percent Protestant and 60 percent Catholic. Our concept of social reflection, in contrast to the concepts of attraction and concentration, uses the distribution of groups in society as a touchstone for comparison. It is operationalized by measuring the deviations of the proportional composition of the party (percentages computed across rows in Table 5.1) from the proportional composition of society. The formula for computing social reflection is
where k is the number of subgroups within the cleavage dimension included in the analysis; Yj is the proportion of the party's support coming from the jth of k subgroups; and Gj is the proportion of the jth group in the society as a whole.
This formula produces scores ranging from 0 to 1 only when the population is equally distributed along the k groupings for the social variable. When the population distribution is unequal, the formula can produce negative values. These negative values represent situations of extreme inequality, for example, social groupings with very small percentages of the total population furnishing most or all of a party's supporters. Because there is no limit to poor social reflection at the extreme, one cannot "norm" a measure of reflection so that 0 reflects the "worst" degree. In our measure, the baseline of 0 is defined for the situation which obtains when the population is equally distributed along the k groupings of a social variable and a party derives all of its support from any one of the k subgroups--for example, a 100 percent Catholic party in a society that is 50 percent Catholic and 50 percent Protestant.
The measure of social reflection is important in itself for evaluating the social bases of party support. It is also complementary to the previous measure of social concentration. A party composed of 90 percent Catholics and 10 percent Protestants would score very high on religious concentration according to our formula. But, if the society itself were 90 percent Catholic and 10 percent Protestant, the party's concentration of Catholic interests would be viewed differently from that if both groups were of equal strength. Our reflection score therefore indicates whether a high concentration score is