Akrasia is the phenomenon of acting against one's better judgment. This Demonstration contains an economic theory of akrasia control.
You choose how much effort to make on education of potential wrongdoers so that the amount by which they discount the future costs of wrongdoing is less variable. You choose how much effort to make to punish wrongdoers in the event that they are caught. You choose how much effort to spend on law enforcement to increase the probability that wrongdoers will be caught.
The Demonstration responds by showing the probability that a potential wrongdoer will succumb to akrasia and engage in wrongdoing; it also computes the total of wrongdoing cost, education cost, punishment cost, and law enforcement cost. You can also choose the public cost of wrongdoing, as well as the price of education, punishment, and enforcement. For a given cost of crime and given prices of education, punishment, and policing, see if you can find the choice parameters that minimize total cost. The left side of the Demonstration contains a tabbed view of the relationship between the three choice variables and total cost that should guide you in this effort.
The discount distribution function is a gamma distribution in which the user selects the mean directly through choosing the value of and selects the variance indirectly through choosing the amount of effort to spend on education. The use of a gamma distribution is not essential to this model; it makes some of the computations more tractable and has the proper domain.
In this model, education reduces the variability of the discount rate the potential wrongdoer employs and thus reduces the probability of akrasia. Effort on education, punishment and enforcement all exhibit diminishing marginal returns. A useful discussion of akrasia may be found in:
R. Cooter and T. Ulen, Law and Economics, 5th ed., Boston: Addison Wesley, 2007.