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A micro approach to mathematical arms race analysis Aboughoushe, Adam


Even with the end of the Cold War, the question, Were the United States and the Soviet Union engaged in an action-reaction arms race? remains important and controversial. The bulk of empirical mathematical arms race research suggests that the US and USSR were not so engaged. Indeed, most such research into the matter suggests that US arms acquisitions were driven overwhelmingly by internal or domestic forces, as were Soviet arms acquisitions. Given the longstanding political, economic and military rivalry, between the US and USSR, the finding that they were not engaged in an arms race is perplexing. This is particularly so with respect to nuclear weapons acquisitions. Orthodox nuclear deterrence theory clearly posits that the attempt by each side to maintain a balance of nuclear forces with the other and hence deter the other from launching a first-strike should result in an action-reaction nuclear arms race. Why, then, does the overwhelming mass of quantitative research suggest that the opposite was true, in practice, in the US-Soviet case? The problem, in part, has been that researchers have been using underspecified mathematical models of action-reaction arms race interaction. The most famous of these models is Richardson’s 1960 action-reaction model. Researchers have long been aware that Richardson’s model is underspecified and as such that it may not be capable of revealing the true nature of US-Soviet military interaction. Since the late 1960s, arms race researchers have attempted to move beyond Richardson’s simple arms race specification. Several new approaches to arms race analysis have subsequently emerged: the game theoretic approach, the economic (stock adjustment) approach, and the expectations (adaptive, extrapolative, and rational) approach. Taken individually, neither of these approaches has, however, yielded much fruit. In this dissertation, the game, stock adjustment, and rational expectations approaches were combined for the first time into a single, more comprehensive, analytical approach and a new action-reaction arms race model was derived, which we have named the GSR Model. In addition, it was argued that a new approach was needed for testing arms race models. Arms races are generally seen as competitions of total armed versus total armed might. Arms race models have, accordingly, been tested against data on states’ annual military expenditures. We argued instead that an arms race is made of several subraces, the object of each subrace being a specific weapons system and a specific counter weapons system, deployed by an opponent and designed to thwart the former’s political and military effect. Models should, then, be tested for each subrace in a given arms race, that is, against data on weapons system-counter weapons system deployment levels. Time frames for the analysis of a given weapons system-counter weapons system competition should be set to accord with the period in which those systems were dominant in the military calculations of the competing states. In effect, we have specified an alternative approach to mathematical arms race analysis, the micro approach to mathematical arms race analysis. The GSR Model was tested against data on annual US and Soviet strategic nuclear warhead deployment levels, — specifically, those onboard ICBMs (1960-71) and submarines (1972-87). The GSR model was also tested against annual US-Soviet aggregate strategic nuclear warhead deployment data (ICBM, SLBM and bomber based totals), 1967-84. Estimates of the GSR model suggest that the US and USSR were in fact engaged in an action-reaction arms race over submarine launched nuclear warheads. Regression analysis also indicates that the US and USSR strongly interacted, asymmetrically, over ICBM based nuclear warheads. There appears to have been no interaction over aggregate warhead deployments. Finally, the implications of these findings for the maintenance of a stable nuclear deterrent were discussed.

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