"Graphing" an Optimal Grand Strategy

Graph theory provides a useful framework for generating insights into problems of sufficiency and optimality across a wide variety of physical relationships. Applied to the realm of grand strategy, this approach assists in developing a methodology for estimating the minimum level of forces required and determining the optimal deployments for the successful pursuit of national security goals. In theory, the adoption of a defense-in-depth maneuver strategy provides the most efficient use of scarce resources. However, deterrence stability attenuates due to the absence of robust local balances of forces. Comparative case analyses of the Roman and British empires confirm the efficiency of depth defense, as well as the weakening of deterrence. Implications for U.S. policy are that, despite sizeable reductions, two regional wars can be fought and won, nearly simultaneously, even below base force levels. However, the deployments required to effect this grand strategy may make challenges to conventional deterrence more likely. Finally, it is demonstrated that small increases in forces above minimum requirements create a valuable "margin of safety" and may significantly improve crisis and deterrence stability. The specter of decline confronts all great powers eventually. A substantial body of literature, associated generally with theories of either power transition or cycles of relative power, addresses the onset of and efforts to cope with this unavoidable problem (Doran 1971; Organski and Kugler 1980; Gilpin 1981; Kennedy 1987; Modelski 1987; Goldstein 1988). Fundamentally, decline poses a strategic dilemma: that of either trying to maintain the status quo with scarce resources, even by means of preventive war (Gilpin 1981,191); or by retrenching, unilaterally reducing spheres of influence. Both approaches can entail great risks. Imperial Spain, for example, faced with declining resources, attempted to hold all of the vast gains it made in the 16th century, and found itself consistently "overstretched," unable to deter predatory attacks, or to defend successfully against them (Elliott 1991). The Soviet Union, on the other hand, recognized its material deficiencies, and chose, a few years ago, to retrench preemptively, resulting not only in the swift breakup of its imperium, but also in the substantial dissolution of its own polity. Of the two strategic approaches, "holding the line" appears less risky at the margin, perhaps because the effects of decline may be mitigated by spreading them over a longer period of time. The Spanish empire took nearly 300 years to collapse, from the loss of Holland in 1609 to the war with the United States in 1898. The Ottoman empire followed a similar temporal pattern of senescence. The former Soviet Union, which instead chose retreat, is absorbing the substantial, wrenching consequences of imperial loss over an extremely short period. Even Britain, which withdrew skillfully from empire in the wake of the Second World War, suffered some of the immediate economic and politico-military consequences of strategic retreat, though they were cushioned by the willingness of the United States to fill the British void. Because of the seemingly high risks of retreat, even of partial withdrawal, this study concentrates its analysis on the stodgier option, maintaining the status quo, and upon the implications, for deterrence and defense, of adopting a grand strategy of "holding the line." It introduces first a mathematical graphing methodology by means of which optimal choices for using scarce resources may be identified. Previous efforts along these lines have employed insights from geometry to develop a framework for successful defense at the tactical and operational levels (Gupta 1993). This study focuses upon the grand strategic level of analysis, and considers the prevention of war as well as defense against aggression. With regard to successful deterrence, special attention is given to the perceived need to achieve favorable immediate or short-term local balances of forces (Huth and Russett 1984,1988; Huth 1988). This new methodological approach to optimizing security strategies is then applied retrospectively to the two most notable historical cases of great empires, one primarily continental, the other maritime, as they confronted potential decline: Rome in the 4th century and Britain before World War I. Insights drawn from these studies will then be applied to help analyze the current situation of the United States in the post-Cold War world, with special emphasis given to the propriety of the current "Graphing" an Optimal Grand Strategy