A Dynamic Theory of Deterrence and Compliance

Classical thinkers like Bentham saw deterrence as a dynamic process in which the punishment of violators today helped deter potential violators in the future by increasing their subjective probability of apprehension. Modern deterrence theory took a different path, analyzing deterrence as a static equilibrium framework in which the subjective and objective probabilities of apprehension are equal. We follow Bentham’s lead, assuming that the subjective probability is determined by the recent history of violations and apprehensions. Further, we assume that the objective probability is increasing in the quantity of enforcement resources and decreasing in the number of violations. Together these assumptions imply that deterrence is a dynamic stochastic process with the potential for disruptive positive feedback. We use simulation techniques to explore deterrence policy in a parameterized version of the more general process. We find that managing the dynamics of positive feedback is the core problem in developing and implementing effective deterrence policy. Our dynamic theoretical framework helps clarify and unify aspects of the research on optimal deterrence capacity, crime waves, and the efficacy of crackdowns and hot spot policing strategies