Nuclear Disarmament: Can Risk Analysis Inform the Debate?

This report is a preprint of a manuscript that has been submitted for possible journal publication. It should not be quoted or referenced without contacting the author to ensure it remains current. The author may be contacted at penelson@ne. The possibility of adapting risk analysis to events deemed to have infinite consequences is illustrated in the context of a simple dynamic two-event model. The results are employed in an effort to illuminate the divergent opinions regarding the desirability of nuclear disarmament. Risk functions (disutility functions to be minimized) considered include discounted expected risk (discount rate = γ), maximum risk rate encountered at any time, and long-term (asymptotic) risk rate. In the case of finite consequences (i.e., consequences of conventional war are considered commensurate with catastrophes occasioned by nuclear weapons), the conclusion that nuclear disarmament is preferable to the status quo rests partially on the conventional nondeterrence proposition. This proposition is expressed mathematically as () () 1 1 1 1 , a d C C λ λ ≥ where C 1 is the consequence of conventional war, and () () 1 1 , a d λ λ are respectively the rates of occurrence of conventional conflicts under the status quo and a regime of nuclear disarmament. This condition is a mathematical representation of the belief that nuclear arms do not deter conventional warfare sufficiently to offset the risk, as defined by the specified risk (disutility) function, posed by the nuclear arms per se. Under the same conditions a preference for nuclear disarmament is associated with some form of a benign disarmament proposition, which represents mathematically a belief that the two distinct risks associated with first achieving and second maintaining a global condition of nuclear disarmament are not sufficient, per the chosen risk function, to counter that associated with maintaining the nuclear-armed status quo. Under reasonable modification of the objective, a preference for nuclear disarmament under the assignment of infinite consequences to catastrophes associated with nuclear weapons depends only on some form of a benign disarmament principle. However, several mathematically different forms of benign disarmament appear. All can be written in the form () () 2 2 0 , a d w λ λ > + Λ where () () 2 2 , a d λ λ are respectively the rates of occurrence of nuclear-weapon catastrophes under the status quo and a regime of nuclear disarmament, Λ 0 is the probability of …