Reinganum Plea Bargaining Flashcards
What are the timing of events in the Reinganum plea bargaining model?
- The defendant type (t=g,i) and the strength of the prosecutors case (π) are set. The defendant observes his type and the prosecutor observes the case strength. Information is private to both the defendant and the prosecutor.
- The prosecutor offers the defendant a plea sentence S (in utility terms).
- The defendant observes the plea sentence S and chooses to accept or reject on the basis of his private information (his type) and inference about the strength of the case based on S.
- If the defendant rejects S, the case goes to trial and both agents incur some additional trial cost (k for the defendant and c for the prosecutor). The known sentence if guilty at trial is denoted x.
What are the key assumptions of the model?
- f(π) is the probability of a guilty verdict at trial given the strength of the case π. We assume f’(π)>0 such that this probability is increasing in the strength of the case.
- The model assumes that the arrest process is random and contains no information about a defendants guilt. As such, q denotes the proportion of guilty among those arrested such that q=pr(t=g).
- The defendants type and strength of the prosecutors case are correlated.
- The defendants expectation of the strength of the case is higher if they are guilty than if they are innocent. Thus, a guilty defendant faces a stronger case (in expectation) than an innocent defendant.
- The prosecutors preferences align with those of society.
What is the prosecutors strategy?
Prosecutor observes S and sets π, their strategy is denoted S(π). For low values of π it might be that S(π)=0 (they dismiss the case). When S(π)>0 we can get either a separating or pooling case.
What is the defendants strategy?
Defendant observes S and knows t, they then decide to accept or reject S. They reject S with probability p_t(S).
Describe the separating equilibrium result.
If the plea bargain offer (S) reveals the strength of the case (π) then the guilty and the innocent will have identical expectations about π given the offer S (as π is known). In this case we can assume the guilty and the innocent have the same strategy p(S). Intuitively, because defendants know the strength of the case against them, the fact that they are innocent or guilty does not impact their willingness to accept or reject S.
We can notice that the prosecutors utility is decreasing in the cost of going to trial. Thus, the more likely the defendant is to accept the plea offer S, the lower the prosecutors utility.
In equilibrium, the prosecutor will offer s=0 if π<π(0) because when the case is sufficiently weak. The prosecutor will offer s=πx+k if π>π(0).
In the separating case, what does a(π) denote?
Denotes the expected net social utility of an additional unit of disutility imposed upon a defendant against whom there is a case of strength π. Notice that a(π) is increasing in f(π) so as the probability of guilt at trial increases the probability that you get utility from prosecuting someone guilty rises. γ represents is the rate at which society values disutility to the guilty, and λ represents is the rate at which society values disutility to the innocent. We can also define π(0) such that a[π(0)]=0.
What is meant by a model with a regime of restricted discretion?
This is when the prosecutor is required to offer the same sentence (plea bargain) to every defendant who is charged with the same crime, independent of the prosecutions case strength. This is the pooling case.
What governs the defendants decision to reject or accept the plea bargain in the pooled case?
It is the defendants expectation of the strength of the case given their type. In other words the defendants expectation of the likelihood of conviction given their guilt. This expectation is higher for guilty than it is for innocent. This expectation governs the defendants decision.
What is the result of the pooling case?
There is a plea offer s that will be rejected by the innocent and accepted by the guilty.
