Fractionalization Index 175 Essay ⋆ Political Science Essay Examples ⋆ EssayEmpire

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The concept of fractionalization denotes the fragmentation and indirectly also the concentration of a set of elements (a population) into subsets (or components) along certain criteria. In the social sciences, such sets of elements used as the unit of analysis are commonly social systems, such as a legislative body, a party system, or a society as a whole. An index of fractionalization measures the degree of such fragmentation or concentration characterizing a system. Fractionalization becomes a relevant feature of political life in the context of social and political cleavages, that is, where circumstances that have the potential for conflict among members of a population force those members to take sides. Among the criteria, on which the division of elements or individuals into relevant subgroups might be based, are attitudes toward political issues, voting behavior, membership in parties or other politically relevant organizations, or social characteristics, such as mother tongue, religion, caste membership, and other self-inscriptive identity markers.

A commonly used index of fractionalization (F) is computed as the complement of the Herfindahl-Hirschman index of concentration, Hj= , that is, by subtracting the values of that index from 1. The formula for F can thus be stated as Fj = 1 , where s is the share of group i (i = 1 . . . N) in the unit of analysis j. The value of this index indicates the likelihood that two randomly drawn elements of a given set belong to different subsets within that set, with higher likelihoods indicating a higher degree of fragmentation. The values of the fractionalization index range from 0 to 1. The larger the number of subsets of the total population, and the more evenly the elements are distributed among those subsets, the larger will be the value of the fragmentation index. In political science, Douglas Rae first proposed the use of this index to measure the fragmentation of party systems in 1967.

To illustrate the results of the fractionalization index, demonstration of a few hypothetical constellations based on a frequently encountered example drawn from political sociology appears useful. If a population is divided along religious lines, the different preferences over the issues at hand might conceivably be condensed into subgroups along religious affiliation. If the population consisted of four religious subgroups of equal size, this would yield an H-value of 0.25 and an F-value of 0.75. If, hypothetically, the population consisted of only one religious affiliation, this would yield an H-value of 1.00 and an F-value of 0.00, indicating maximum concentration and conversely minimum fragmentation. If ten subgroups of equal size (0.10) existed, the Hand F-values would be 0.10 and 0.90, respectively, indicating a high level of fractionalization. If, however, the raw number of religious subgroups were three, of which one group’s share was 0.80, while the other two groups were of equal size (0.10), the H-value would be 0.66 and the F-value, 0.34. If, on the other hand, the groups were of equal size, the H-value would be around 0.33, and the F-value would be around 0.67. Thus, due to the fact that the formula provides for a weighting of each component’s weighting by its own share, the relative weight depends heavily on the distribution of group sizes.

To provide for a more intuitive interpretation regarding the relative strength of contending parties to a conflict, the “effective number” indices have been proposed and found acceptance as alternatives in research on party systems as well as ethnic politics. They were first suggested by Laakso and Taagepera in 1979 to measure the number of “relevant” parties (Sartori) in a competitive party system. The most commonly found formulation for its calculation, related to the party systems literature, is

However, in a generalized form it can also be stated as . A population divided into four equally strong groups would thus yield an effective number value of 4. This is more in accordance with intuition than an F-value of 0.75 for the same constellation. Due to this more intuitive appeal, this index has become relatively more popular than Rae’s index when measuring the level of concentration or fragmentation of size or relevance of a system of elements in political science. Since, however, this index also has a number of mathematical properties that produce counterintuitive results, especially in situations wherein one component is comparatively large in relation to the others, criticisms and suggestions for its modification have frequently been made.

Bibliography:

Dunleavy, Patrick, and Francoise Boucek. “Constructing the Number of Parties.” Party Politics 9, no. 3 (2003): 291–315.
Laakso, Markku, and Rein Taagepera. “‘Effective’ Number of Parties: A Measure with Applications to Western Europe.” Comparative Political Studies 12 (1979): 3–27.
Nohlen, Dieter. Wahlrecht und Parteiensystem. 4th ed. Opladen, Germany: Leske and Budrich, 2004.
Rae, Douglas. The Political Consequences of Electoral Laws. New Haven, Conn.: Yale University Press, 1967.