The threat of the death penalty makes defendants more willing to accept a given plea bargain offer.  But a tough-on-crime DA takes up the slack by making tougher offers.  What is the net effect?  A simple model delivers a clear prediction:  the threat of the death penalty results in fewer plea bargains and more cases going to trial.

The DA is like a textbook monopolist but instead of setting a price, he offers a reduced sentence.  The defendant can accept the offer and plead guilty or reject and go to trial taking his chances with the jury. Just like the monopolist, the DA’s optimal plea offer trades off marginal benefit and marginal cost.  When he offers a stiffer sentence, the marginal benefit is that defendants who accept it serve more time.  The marginal cost is that it is more likely that the defendant rejects the tougher offer, and more cases goes to trial.  The marginal defendant is the one whose trial prospects make him just indifferent between accepting and rejecting the plea bargain.

Introducing the death penalty changes the payoff to a defendant who rejects a plea deal (his reservation value.)  The key observation is that this change affects defendants differently according to their likelihood of conviction at trial. Defendants facing a difficult case are more likely to be convicted and suffer the increased penalty.  (Formally, the reservation value is now steeper as a function of the probability of conviction.)

One thing the DA could do is increase the sentence in his plea bargain offer just enough that the pre-death-penalty marginal defendant is once again indifferent between accepting and rejecting.  The rate of plea bargains would then be the same as before the death penalty.

But he can do better by offering an even tougher sentence. The reason: his marginal benefit of such a move is the same as it was pre-death penalty (the same infra-marginal defendants serve more time) but the marginal cost is now lower for two reasons.  First, compared to the no-death penalty scenario, fewer defendants reject the tougher offer.  Because we are moving along a steeper reservation value curve.  Second, those who do reject now get a stiffer penalty (death) conditional on conviction.

The DA’s tougher stance in plea bargaining means that fewer defendants accept and more cases go to trial.  Evidence?  Here is one paper that shows that re-instatement of the death penalty in New York lead to no increase in the rate of plea bargains accepted (and a clear decrease in the size of plea bargain offers.)

About these ads