Socially Optimal Criminal Justice System Waiting Times: A More General Theoretical Analysis

Criminal justice system delay, which is defined as the time elapsing between the defendant being charged and the case being listed at court, has up to some point, socially valuable flexibility value. This insight borrowed from the options literature in finance, makes it potentially possible to formally model and estimate socially optimal criminal justice system waiting times. This exercise is attempted in this paper by randomising the defendant’s probability of conviction, which is a critical argument in the defendant’s expected cost of going to trial and the monetary value of a conviction to society .The probability of conviction is assumed to conform to a uniform probability distribution with increasing variability until the trial date. What drives this variability is a continuous stream of information impacting on the defendant’s probability of conviction, which is continuously evaluated by the defendant and prosecutor as they formulate their different strategies given their respective conflicting objectives. Endogenising the probability of conviction in this way enables the respective payoffs of the defendant and prosecutor to be expressed as dynamic net present values per unit of time. The economic value of this flexibility to wait is measured as the rate of change in the sum of these dynamic NPVs per unit of time. Socially optimal delay is defined as the trial wait, which maximises the dollar value of the sum of the economic value of flexibility to the prosecutor (society) and the defendant simultaneously, and is the optimal time to list the case at the court. The corresponding dollar value is the total marginal social value of delay. Corresponding to the socially optimal wait and the total marginal social value of delay will be the optimal sentence discount for the prosecutor (society) to offer the defendant and the defendant’s optimal plea. Society makes a trade off between two conflicting objectives, the need to ensure justice to the defendant as legally and morally defined with the need to resolve the issue as quickly as possible.