Bargaining with asymmetric information: an empirical study of plea negotiations

By far, most US criminal cases are resolved before trial through plea bargain agreements between the defendant and the prosecutor. In return for a guilty plea, the prosecutor reduces or dismisses some of the charges against the defendant and/or recommends the court assign a relatively short sentence.

In 2001, for example, 94 percent of federal cases were resolved by plea bargain (Fischer, 2003). Similarly, in 2000, such deals accounted for 95 percent of felony convictions in state courts (Durose and Langan, 2003). By contrast, many jurisdictions worldwide limit or outright ban plea bargaining (Fair Trials, 2017).

Thus, the current debate in the United States over criminal justice reform can’t ignore the role of plea bargaining. Given the extent to which cases are settled before trial, the impact of sentencing reforms will depend largely on how they affect plea bargaining as opposed to the outcome of cases argued in court.

Further, reliance on plea bargaining raises questions over whether justice indeed is being served. In principle, the defendant and prosecutor will only agree to a deal that is mutually beneficial. But while a settlement will save all the parties involved the cost of a trial, a plea bargain deprives innocent defendants of the chance of acquittal. Such a miscarriage of justice not only penalizes the defendant, but can be viewed as a negative externality to society. For that reason, judges are required to assess the facts of a case before accepting guilty pleas (Schulhofer, 1992).

In this paper, I examine the potential impact of several hypothetical policy interventions on the outcome of criminal cases. My analysis begins by adapting and applying a theoretical model of litigation, originally proposed by Bebchuk (1984) to data on violent crime cases filed between 1996 and 2009 in North Carolina’s superior court system, the main general trial courts in the state. While this stylized model excludes several factors that influence plea bargaining in the real world, it provides a helpful tool for understanding the potential ramifications of sentencing reform.

For example, a simulated reduction in mandatory minimum sentences would result in a large reduction in the aggregate incarceration time assigned to defendants across the sample.

If plea bargains were banned, more than 20 percent of defendants who currently receive prison sentences would be acquitted. However, the aggregate time convicts would spend behind bars would increase substantially.

If plea bargains were banned, more than 20 percent of defendants who now receive prison sentences would be acquitted, the model predicts. However, those convicted would face much harsher sentences.

The model

In the model that I consider, a prosecutor and a defendant bargain over the outcome of a case. For the sake of simplicity, I assume that the prosecutor makes a take-it-or-leave-it offer to the defendant to settle for a sentence − that is, there is no give-and-take. If there is no agreement, the case proceeds to trial, which is costly to both parties.

Further, I assume that defendants – by knowing the extent of their culpability − are better informed than the prosecutor about the probability of their being found guilty at trial. This information, if revealed at the trial, would affect the odds of a conviction. To be sure, the prosecutor is aware of many factors that could influence the outcome at trial, such as the defendant’s previous criminal history, race, ethnicity and age. Still, the defendant has more precise information.

Both parties have similar expectations about the sentence that would result from a trial conviction. In equilibrium, the prosecution’s settlement offer depends on the anticipated trial sentence, trial costs and its perception of the odds of winning. Holding other factors constant, the plea offer would be more generous the less harsh the potential trial sentence. Once the offer is made, only the defendants who are sufficiently pessimistic about their chances in court would accept it.


My empirical analysis accounts for many observable characteristics of the cases in the sample. Race stands out as the most robust factor that appears to influence outcomes. Thus, in the paper, I divide the sample into two categories: group one consists of non-blacks, and group two of blacks. To make the two groups directly comparable, I hold constant other case characteristics. I consider only defendants who are male, have short criminal records and are represented by court-appointed attorneys.

As computed by the model, Figure 1 presents the settlement offer made by prosecutors, as a function of the anticipated trial sentence, for both groups. Note that the line on the graph for group two, the black defendants, is less convex than that for the other races. This suggests that in comparable cases prosecutors tend to offer longer sentences to black defendants than they offer those who aren’t black.

Figure 1. Settlement offer function estimates


Indeed, as estimated by the model, it is relatively rare to find black defendants at the lower end of the curve, where the chance of conviction is low. I estimate that half of black defendants are more likely to be convicted at trial, compared with one-third of other defendants. Following the logic of the model, prosecutors take this difference into account when making settlement bids: They offer longer sentences to blacks, banking on those defendants anticipating that they would fare worse at trial.

The model predicts that half of black defendants are more likely to be convicted at trial, compared with one-third of other defendants.

Counterfactual analysis

Using the estimated model, I simulate the impact of several policy interventions. Sentencing reform has been at the center of the public policy discussion, thanks to the growing consensus that the United States incarcerates too many people for too long. About 0.7 percent of Americans were in prison or jail at the end of 2010 (Glaze, 2011) − the highest incarceration rate in the world, according to some estimates (Walmsley, 2009). Two reform proposals that have gained traction are reducing mandatory minimum sentence lengths and making broader use of alternative punishments for less serious offenses. I consider each of these interventions separately.

The outcomes of interest in my counterfactual analysis are: (i) the incarceration time assigned to the average case, that is, regardless of the resolution method; and (ii) the probability that a case results in an incarceration conviction, be it by plea bargain or at trial.

Outcome (i) is the main variable of interest for those concerned about the total incarceration costs of current sentencing patterns. Those total costs would be based on aggregate incarceration time assigned across all defendants in any given period. That is determined by multiplying the number of defendants by the average of the length of sentences imposed in each case (for purposes of this calculation, I counted an acquittal as zero).

Admittedly, the counterfactual analysis that I conduct in the paper ignores important implications of sentencing reform, such as the effects on crime deterrence and recidivism. A more complete exercise would need to simultaneously account for these effects and plea bargaining.

What if the potential mandatory minimum sentence handed down for all court cases were reduced in length by 20 percent? My findings suggest that the aggregate incarceration time assigned would also fall by approximately 20 percent for both groups. Overall, the model predicts a linear relationship across the spectrum; in other words, a change in the length of potential trial sentences leads prosecutors to reduce the settlement offers proportionally. Since the vast majority of the cases settle, the reduction in the offers has a direct impact on the average sentence assigned across all cases.

With prosecutors offering more generous deals in response to lower mandatory minimum sentences, defendants would be more likely to settle, raising the total probability of conviction. For blacks, that probability would increase by .64 percent; for everyone else by 1.89 percent.

Thus, a reduction in the length of potential trial sentences is likely to increase the number of incarcerated individuals slightly in the short run, by leading to more convictions. But in the long run, the same intervention may lead to a major decrease in the inmate population, since the assigned sentences become much shorter.

I also analyze a scenario in which relatively short trial sentences are set to zero. Such a scenario simulates the effect of abolishing incarceration sentences for the mildest offenses. Specifically, I replace the 10 percent of cases with the lowest potential trial sentences with cases in which the potential trial sentence is zero. The intervention reduces the total probability of conviction by roughly ten percent for both groups. Nevertheless, its effect on the aggregate incarceration time assigned is relatively small − less than one percent for both covariate groups. The policy intervention considered here is rather extreme, and it is surprising that its effect on the expected sentence is so modest. An explanation for such a low magnitude is that the current expected sentences are largely influenced by the length of the most severe sentences. Even the complete elimination of the mildest cases has a small effect on the average outcome.

In a third policy experiment, I consider a scenario in which plea bargaining is not allowed, so that every case is decided at trial. Admittedly, given that roughly 90 percent of all criminal cases are currently settled, eliminating plea bargaining is not likely to happen. But considering this extreme scenario allows me to assess the loss of information that arises due to settlements. Specifically, I compute the proportion of defendants currently receiving incarceration sentences who would have been acquitted had their cases gone to trial.

If plea bargains were eliminated, the rate of cases resulting in an incarceration conviction would decrease between 6 percent and 21 percent for the black defendants. For everyone else, the rate would decline by 17 to 31 percent.

However, without the opportunity to bargain for a plea deal, defendants would face the prospect of much longer sentences. In fact, the increase on the assigned sentences would more than offset the lower probability of a conviction. The sentence expected ex-ante – that is, before knowing whether the case would result in a conviction or an acquittal at trial – would increase by between 28 percent and 54 percent for black defendants and by 76 percent to 110 percent for everyone else.

Therefore, although a large proportion of the defendants would be acquitted at trial after a ban on plea bargains, the aggregate incarceration time assigned would increase, and the average defendant would be considerably worse off.

This article summarises: ‘Bargaining with asymmetric information: an empirical study of plea negotiations‘ by Bernardo S. Silveira

Further reading

Bebchuk, Lucian Arye, “Litigation and Settlement under Imperfect Information,” RAND Journal of Economics, 1984, 15, 404-415.

Durose, Matthew R. and Patrick A. Langan, “Felony Sentences in State Courts 2000,” Bulletin NCJ 198821, US Department of Justice, Bureau of Justice Statis-tics, Washington, DC: US Department of Justice, June 2003.

Fair Trials, “The Disappearing Trial: Towards a rights-based approach to trial waiver systems,” Technical Report, Fair Trials, April 2017.

Fischer, George, Plea Bargain's Triumph: A History of Plea Bargaining in America, Palo Alto: Stanford University Press, 2003.

Glaze, Lauren E., “Correctional Population in the United States, 2010,” Bulletin NCJ 236319, US Department of Justice, Bureau of Justice Statistics, Washington, DC: US Department of Justice, December 2011.

Schulhofer, Stephen J., “Plea bargaining as disaster,” Yale Law Journal, 1992, 101 (8), 1979-2009.

Walmsley, Roy, “World Prison Population List − Eighth Edition,” Technical Report, International Centre for Prison Studies, January 2009.