Point and Line Vulnerability as Bases for Predicting the Distribution of Power in Exchange Networks: Reply to Willer

David Willer's comment on our 1983 AJS article provides us with a useful opportunity to describe the progress that we have made in refining the measure of vulnerability introduced in that article. To place Willer's commentary in perspective, the primary purpose of our article was to present the results of an experiment and of computer simulations on network centrality and its relation to power in exchange networks. Willer's comment does not deal with these findings. At the very end of the article, we proposed-as a preliminary notion-the idea that vulnerability might be a useful theoretical concept (see p. 299), and we suggested point vulnerability as one potential technique or measurement ool for determining points of minimum dependence in networks. Such points would thus be the most powerful network locations according to powerdependence theory. Willer's main criticism is that our measure of vulnerability, Reduction in Maximum Flow (RMF), is not generalizable across all types of networks. On this point he is quite correct. In fact, we clearly noted this limitation (see p. 301, n. 21). We introduced the RMF measure merely as an illustration of the theoretical potential of the notion of vulnerability, not as a refined procedure for use in empirical research. We thought hat we had made this clear. For example, on page 299 we stated, "Ourfirst step toward a theoretical solution . .. was prompted by the. .. concept of 'vulnerability' " (emphasis added). Although Willer takes us to task for not developing a better measure, he does not propose an alternative. Subsequent to publication of our experimental results, we continued to work on this measurement problem and to explore the limitations of our preliminary measure. In this work we explored the use of both point and line vulnerability as the basis for a more general measure. The task that we set for ourselves was to develop a more comprehensive measure. We will briefly describe our proposed solution (more details are available from us in a technical report). The simplest network in which our original RMF measure of vulnerability fails to predict the distribution of power is the four-person etwork shown in figure 1. In this network, all points are predicted by the RMF measure to be of equal power. However, simulation results how that A is