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Probabilism and the Number of Units Affected: Measuring Influence Concentration1

Published online by Cambridge University Press:  01 August 2014

Bruce M. Russett
Bruce M. Russett*
Affiliation:
Yale University
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Extract

In suggesting a basis for operational indices of the concentration of power Steven Brams' creative article “Measuring the Concentration of Power in Political Systems” (see pp. 461–475) has performed an important service to the discipline in opening up a neglected area. It is very surprising that despite all the past efforts to devise summary measures of power bases (e.g., income or military strength) so little effort has gone into summary indices for rigorously gauging their dispersion or the absence of dispersion. Having acknowledged Brams' piece as an extremely valuable stimulus for further thought, I would like now to exercise a scientific prerogative to propose a variation in the approach that should, for some theoretical purposes, prove even more useful. As Brams notes appropriately, it is indeed true that the best index “for any particular study will depend on the nature and purposes of the study.”

All the versions of Brams' PC index are directed toward measuring the collective exercise of influence between different levels of decision-makers. This approach reflects an essentially deterministic point of view: the influence from any level on a mutual influence set or sets is determined by the exercise of influence on only one of its members. For example, if a has power over b, and b is in a mutual influence set with c, then c's actions vis-à-vis b are completely determined by a. As far as the PC index is concerned, this is no different from the case of a's directly influencing b and directly influencing c when b and c are not in an influence relationship. But if one takes a probabilistic viewpoint of indeterminacy, of a's predominance but less than complete control over b and c when they are in a mutual influence relationship, the relations among units at a subordinate level become interesting.

Type
Research Article
Information
American Political Science Review , Volume 62 , Issue 2 , June 1968 , pp. 476 - 480
Copyright
Copyright © American Political Science Association 1968

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Footnotes

1

I am grateful to the National Science Foundation and the Yale Political Data Program for general support, to Charles L. Taylor and Michael J. Taylor for our conversations on these points, and also to Steven J. Brams for a most productive further exchange.

References

2 The expression a→b means that a often influences b's actions, but with no implication that b always responds; a↔b would indicate mutual influence. The empirical meaning of “often” would of course have to be specified in the situation.

3 “Measuring the Concentration,” footnote 13.

4 See Alker, Hayward R. Jr., and Russett, Bruce M.; “Measures for Comparing Inequality,” in Merritt, Richard L. and Rokkan, Stein (eds.), Comparing Nations: The Use of Quantitative Data in Cross-National Research (New Haven: Yale University Press, 1966).Google Scholar

5 This is a case where Brams' PC index would differentiate the two, but by showing PC for 3b to be .75 and PC for 3a at the arbitrary value of zero (no minority control sets). Zero is of course an unsatisfactory value since there is in fact some concentration.

6 Formally, of course, the slope measures the rate of change in concentration, but similar measures with the Lorenz curve (e.g., the Schutz coefficient) are often used to suggest an aspect of concentration or inequality. See Alker and Russett, op. cit., p. 364. See also Goodman, Leo, “On Urbanization Indices,” Social Forces, 31 (05, 1953), 360–362.CrossRefGoogle Scholar Brams' incorporation of hierarchical levels of control into his PC index is of course another way of dealing with this problem, but it requires several distinct indices (one for each two levels) for each system, thus complicating the comparison of two different systems.

7 See, inter alia, Dahl, Robert A., “The Concept of Power,” Behavioral Science, 2 (07 1957), 201–215 CrossRefGoogle Scholar; Harsanyi, John C., “Measurement of Social Power, Opportunity Costs, and the Theory of Two-Person Bargaining Games,” Behavioral Science, 7 (01 1962), 67–80 CrossRefGoogle ScholarPubMed; Peter Bachrach and Morton Baratz, “Two Faces of Power,” this Review, 56 (December 1962), 947–952; and William Riker, “Some Ambiguities in the Notion of Power,” this Review, 58 (June 1964), 341–349.

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