The probability of war in then-crises problem: Modeling new alternatives to Wright's solution

In hisStudy of War, Q. Wright considered a model for the probability of warP “during a period ofn crises”, and proposed the equationP=1−(1−p)n, wherep is the probability of war escalating at each individual crisis. This probability measure was formally derived recently by Cioffi-Revilla (1987), using the general theory of political reliability and an interpretation of the “n-crises problem” as a branching process. Two new, alternate solutions are presented here, one using D. Bernoulli's St. Petersburg Paradox as an analogue, the other based on the logic of conditional probabilities. Analysis shows that, while Wright's solution is robust with regard to the general overall behavior ofp andn, some significant qualitative and quantitative differences emerge from the alternative solutions. In particular,P converges to 1 only in a special case (Wright's) and not generally.