Minimization of Attack Risk with Bayesian Detection Criteria

Abstract

Strategic deterrence operates in and on a vast interstate network of rational actors seeking to minimize risk. Risk can be minimized by employing a likelihood ratio test (LRT) derived from Bayes’ Theorem. The LRT is comprised of prior, detection, and false-alarm probabilities. The power-law, known for its applicability to complex systems, has been used to model the distribution of combat fatalities. However, it cannot be used as a Bayesian prior for war when its area is unbounded. Analytics applied to Correlates of War data reveals that combat fatalities follow a log-gamma or log-normal probability distribution depending on a state’s escalation strategy. Results are used to show that nuclear war level fatalities pose increasing risk despite decreasing probability, that LRT-based decisions can minimize attack risk if an upper limit of impending fatalities is indicated by the detection system and commensurate with nominal false-alarm maximum, and that only successful defensive strategies are stable.