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Abstract

Two families of indices are defined which may be used to characterize the effective number of components in systems with unequal component sizes. A general formula is staled relating size, effective size, and effective number of components. Special cases of this formula are considered which yield formulae identical or closely related to a variety of other expressions including entropy, the Greehberg-Lieberson index of diversity (also known as the Rae-Taylor fractionalization index), the Herfindahl-Hirschman concentration index, the coefficient of variation, the ordinary mean, the weighted mean and the harmonic mean. Applications of these formulae are considered for a variety of problems, including measurement of population and GNP concentrations, distinguishing between density and crowding, and reconciling differing student and faculty perceptions of average class size.

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References

Allison

P. D.

(1978) “Measures of inequality.” Amer. Soc. Rev. 43 (December): 865–880.

Blau

P. M.

(1977) Inequality and Heterogeneity. Sage CA: Los Angeles, CA: SAGE Publications. CBS (1978) The CBS Almanac 1978.

Feld

Grofman

(1980) “The class size paradox and conflict of interest among faculty, students, and administration.” Frontiers of Economics 3.

Feld

Grofman

(1977) “Variation in class size, the class size paradox and some consequences for students.” Research in Higher Education 6: 215–222.

Gibbs

J. P.

Martin

W. T.

(1962) “Urbanization, technology, and division of labor: international patterns.” Amer. Soc. Rev. 27 (October): 667–677.

Greenberg

(1956) “The measurement of linguistic diversity.” Language 32: 109–115.

Grofman

(1974) “Indices of representation and distortion.” SUNY, Stony Brook, (unpublished)

Herfindahl

O. C.

(1950) “Concentration in the steel industry.” Ph.D. dissertation, Columbia University.

Hirschman

A. O.

(1945) National Power and Structure of Foreign Trade. Sage CA: Los Angeles, CA: SAGE Publications.

10.

Kittel

(1958) Elementary Statistical Physics. Sage CA: Los Angeles, CA: SAGE Publications.

11.

Laakso

Taagepera

(1979) “’Effective’ number of parties: a measure with application to West Europe.” Comparative Pol. Studies 12 (April): 3–27.

12.

Laakso

Taagepera

(1978) “Proportional representation in Scandinavia: implications for Finland.” Scandinavian Pol. Studies 1: 43–60.

13.

Lieberson

(1969) “Measuring population diversity.” Amer. Soc. Rev. 34 (December): 850–862.

14.

Rae

D. W.

Taylor

(1970) The Analysis of Political Cleavages. Sage CA: Los Angeles, CA: SAGE Publications.

15.

Taagepera

(1979) “Inequality, concentration, imbalance.” Pol. Methodology 6: 275–291.

16.

Taagepera

Ray

J. L.

(1977) “A generalized index of concentration.” Soc. Methods & Research 5 (February): 367–384.

17.

Taylor

C. L.

Hudson

M. C.

(1972) World Handbook of Political and Social Indicators. Sage CA: Los Angeles, CA: SAGE Publications.

18.

Theil

(1967) Economics and Information Theory. Sage CA: Los Angeles, CA: SAGE Publications.

Effective Size and Number of Components

Abstract

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References