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WHAT IS IT?
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The model is the attempt to implement dynamically a paper of mine wrote for the conference of the European Association of Law and Economics. The paper is titled (at least the version of july 2006) "Why public prosecutors cannot appeal acquittals: a an explanation based on social stigma" This is the abstract:

Public prosecutors often face prohibition of appealing acquittals. This asymmetry twists the criminal procedure towards the interests of the defendant. This pro-defendant feature is usually justified on the reasonable assumption that it takes several erroneous acquittals to impose a social cost equal to that of one erroneous conviction for the same offence. The paper first inquires the impact of asymmetrical appeal powers on the number of convictions, acquittals and errors of type I and type II and offers evidence consistent with the traditional justifications of asymmetric appeal powers. In the second part, the paper offers an alternative positive signalling theory of asymmetric appeal powers: if criminal sanctions are signals that agents in society use to assess whether and how much stigma attribute to other agents, then an asymmetrical criminal procedure delivers a more reliable signal. We explore some implications of the model with an agent-based computational implemetation.

The paper is available here.

THE MODEL OF THE PAPER
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The model is mainly composed by two parts. In the first part of the model, a simple probability tree over a three-stages game is built. By choosing the kind of procedure (smmetric vs asymmetric) and setting the probabilities of convictions in each stage of the process (m,q,r,t) the aggregate probabilties of convictions (phi and sigma) are determined, as well as the the tradeoff between type I errors (the acquittal of the guilty) and type II errors (the conviction of the innocent).

In the second part of the paper I implement a mechanism by which agents assess their level of stigma to criminals based on how reliably a conviction is a signal of guiltyness.

Stigma is a cost to agents that decide whether to commit crime only if their ability to gain from crime (randomly allocated) are higher than the expected costs of crime (defined as (phi-sigma)x(stigma+fine) where phi, and sigma are defined according to the procedure. the fine is exogenous and stigma is instead defined endogenously.

In particular, stigma function of reliability, that in turn is defined by bayesian inferrence as the posterior probability of guiltyiness given the prior probability (the population of criminals) and the conditional probability (phi).

ALL VARIABLES EXPLAINED
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By pressing "allocate b" the gains from crime are distributed randomly accross the population ( the more white the agent is, the higher b is).

By pressing "Criminals" you calculate who is willing to commit crime (this in turns depend on whether the gains from crime are higher than the expecte costs of crime)

By pressing "Convicted?" you randomly condemn phi precentage of criminals and sigma percentage of innocents

By pressing "GO!" the process of updating the stigma, and thereofore the willingness to commit crime begins over an infinite time period

Py is the probability of being brought to trial for the guilt
q is the prob of being convicted in trial for the guilt
r is the prob. of being convicted in appeal once convicted in trial

Pn is the prob of being brought to trial if innocent
m is the probability of being convicted in trial for the innocent
s is the probability of being convicted in appeal for the innocent

Procedure offers the choice between "symmetric", "asymmetric" and "manual phi & sigma"

Initial Stigma sets the levl of stigma for the first round. Then the level is endogenized

Publicity determines how much stigma translates into a cost for the criminal

Fine determines the level of fine

phimanual and sigmanual determines the level of phi e sigma in case Procedure is set on manual

stigma-update, when set on off, introduces a mechanism of smooth update for the level of stigma instead of a more immediate one.

Ticks determines how many rounds the game is iterated ad maximum.

The last controls at the bottom, simply reproduce the settings used to obtain the respective graphs analysed in the paper.