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Mathematical Models in the Study of Power: Comment on Mayhew and Levinger

Mayhew and Levinger (AJS 81 [March 1976]: 1017-49) have reported a model which attempts to explain the exclusion of individuals from effective participation in social organizations which appear to be growing larger in scale in modern societies. Beginning from apparently neutral assumptions about the decision-making process in face-to-face groups, the authors provide logical support for the theorems that (1) "the expected concentration of power is an increasing function of group size" (p. 1026), (2) "the expected relative size of the controlling component is a decreasing function of group size" (p. 1028), and (3) "the expected concentration of power within the controlling component is a decreasing function of group size" (p. 1031). The main purpose of the model is to provide a baseline for use in empirical research. The paradox of the present model, which provides its significance as a research tool, is that the mere assumption of random interaction (i.e., equal probabilities of participation by every group member in every decision) seems to lead to a baseline model which predicts increasing concentration of power as groups become larger. Thus it is concluded that " 'conspiracy' theories of elite formation are not required to account for the occurrence of oligarchy in conditions of focused, face-toface interaction. Oligarchic structures will develop, as we have seen, in the absence of concerted efforts by coalitions" (p. 1029), merely as an effect of group size. Students of power and organization will be interested in the propriety of such a baseline. Particularly since the publication of Blau's (1970) theoretical discussion of the effects of system size on structural differentiation, researchers have shown special interest in the importance of size in complex organizations. The effects of size on participation and power in societies (Dahl and Tufte 1973) and communities (Clark 1968) have also been the objects of recent attention. We evaluate here the MayhewLevinger model and explore some alternative formulations. We argue that an appropriate model depends heavily on what the researchers believe to be the correct underlying assumptions. We intend to demonstrate that significant substantive decisions are implicit in Mayhew and Levinger's model, in particular that they have selected assumptions which heavily bias their "baseline" in favor of "oligarchic" outcomes. We examine variations of their model to determine whether size and oligarchy are necessarily related given plausible alternative assumptions.