The study of social dynamics often entails the analysis of systems of equations. When we move from univariate to multivariate models, we usually work with a single equation that describes how one variable, say Xt, affects the behavior of another variable, call it Yt. As we learned in the preceding chapter, these models are appealing because they are relatively easy to use. But implicit in such a single equation model is the assumption that there is no feedback between the variables (see the Appendix for details on this point). That is, we assume that the variables on the right-hand side of our equation are not affected by changes in the variables on the left-hand side. Substantively, this assumption often is problematic. Our theories and policy debates emphasize the existence and implications of feedback between variables.
Consider the conflict in the Middle East, referred to Figure 4.1. Clearly the behavior of the Israelis directed toward the Palestinians depends on recent and past behaviors of the Palestinian directed towards the Israelis and vice versa. And the behavior of the United States toward the belligerents depends on the Israelis and Palestinians directed behaviors it has observed in the Middle East. But this conflict is even more complicated. For example, Palestinian behavior toward the Israelis also depends on American behavior directed toward both parties. Students of intrastate and international rivalry conceive of this case as a conflict system in which one belligerent's directed behaviors are both responses to and a provocation toward other belligerents.