Probabilism and the Number of Units Affected: Measuring Influence Concentration

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Abstract
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.

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