The model

Let an (n = {i, j, k, …}) denote the level of activity of country c and sd (d = {r, y, …}, for realpolitik, ideological, etc., spheres) denote the state of the system in dimension d. These are the endogenous variables – that is, the primary variables of interest in the model. The variable s contains multiple dimensions; one could be the balance of power, another could be the balance of ideology, and so forth, depending on the historical period in question. The actors exert effort (measured by the magnitude of a) to push and pull the status quo in this multidimensional space back and forth, until it reaches their constituencies' ideal points.

Let cnd represent a frequency distribution of constituency ideal points for state n on dimension d; in concrete terms this might correspond to the constituency's answers to a poll asking what their preferred distribution of power, ideology, etc., would look like. Let vn(·) represent state n's preference aggregation function (corresponding to the manner, in state n, that the answers to those poll questions are aggregated and transmitted to the leadership; are they simply averaged or weighted in some way?) and ωnd represents the salience of issue area d to the constituency of n (in other words, the answer to the question, “How much are changes in d” – whatever d is – “relevant to our national security?”). The variable πn represents the latent capabilities of state n or the resources it has available to convert actions into outcomes (scaled to 0 ≤ πn ≤ 1).