A Probability Model of Credibility

Credibility plays a central role in the classical theory of strategic nuclear deterrence, as well as in many types of social and international relations. This article presents probability models of credibility for survival-retaliation, Wohlstetter-type, and generalized “chain” deterrent threats. Both scenario and systems analysis of these models indicate that (1) only moderate credibility occurs even when very high levels of performance are insured in actions necessary to implement the threat; (2) variations in performance levels induce a destabilizing, more than proportional, amplified variation on overall credibility; and (3) this hyperweakening effect is largest in complex threats. In sum, intuitive estimation of deterrence credibility is severely unreliable, since credibility is weaker than the weakest link in a deterring chain of events. The models are extended and generalized to calculate the credibility of complex systems of deterrent threats, such as the “strategic nuclear triads” deployed by the United States, USSR, United Kingdom, and France, as well as other general deterrents having “serial” and/or “parallel” systems of threats. Special “bottleneck effects” induced by the National Command Authority (NCA) on C 3 I are emphasized.