(DRAFT: SEPTEMBER 2015) PLEA BARGAINING AND CREDIBLE (LEGAL) THREATS

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1 (DRAFT: SEPTEMBER 2015) PLEA BARGAINING AND CREDIBLE (LEGAL) THREATS Ehud Guttel * Prosecutors seem simultaneously omnipotent and powerless. Although operating within strict budgets, prosecutors successfully induce many offenders to admit guilt. At the same time, however, prosecutors more than occasionally release or offer lenient plea deals to offenders who commit severe crimes. Addressing this puzzling contradiction, this Article sheds light on prosecutors ability to employ the threat of trial to make offenders sign plea deals. It shows that while conventional legal analysis has predicted that prosecutors can routinely mount effective threats, concerns of credibility often require them to select strategically between offenders. Against this background, this Article further highlights the significance of allocation of prosecutorial resources and offenders. It demonstrates that contrary to common wisdom, whether a case involving multiple offenders is handled by a single prosecutor who can conduct a few trials, or divided between several prosecutors who can each conduct a single trial, has far-reaching implications for prosecutors bargaining power. From a normative perspective, the suggested analysis offers insights into the interplay between equality, institutional design, and the maximization of offenders penalties. While this Article focuses on prosecutors and plea bargaining, its analysis can be extended to study a broad range of cases in which rightholders can execute a right against a single member, or a subset, of a large group. I. INTRODUCTION Consider the following dilemma commonly faced by prosecutors. Six offenders are arrested after committing a crime. The inculpating evidence against the offenders varies, rendering their expected penalties in the following descending order: If taken to court, offender A will be sentenced * Frieda & Solomon B. Rosenzwieg Chair in Law, Hebrew University Law Faculty. For helpful comments and discussions, I thank Robert John Aumann, Alon Harel, Eli Greenbaum, Yehonatan Givati, Ariel Porat, Shmuel Leshem, Motty Perry, Yuval Procaccia, Uzi Segal, Doron Teichman, and Eyal Winter, as well as participants of the 25 th American Law and Economics Association annual meeting (Columbia Law School, 2015). This Article was made possible by the generous support of the Barak Center for Interdisciplinary Legal Research.

2 2 PLEA BARGAINING AND CREDIBLE (LEGAL) THREATS to 10 years, offender B to 9 years, and so on, with the last offender sentenced to 5 years. Because of limited prosecutorial resources, however, trials can be conducted against only two offenders. The prosecutor in charge seeks to maximize the offenders years in prison. Consider next a slightly modified scenario. Facts are identical, but suppose that offenders and prosecutorial resources are now divided between two independent prosecutors. Each prosecutor s docket accordingly includes three offenders of whom she can take one to trial. The prosecutors, again, aim to impose the overall harshest penalty. Clearly, in both scenarios, the prosecutors can secure an overall sanction of 19 years. Filing charges and conducting trials against the two top offenders A and B will result in respective penalties of 10 and 9. But can the prosecutors do better, and obtain more than 19 years notwithstanding their ability to bring only two offenders to trial? And if so, will the two independent prosecutors perform as well as, worse, or better than the single prosecutor? Inspired by a seminal article by Frank Easterbrook, legal scholarship has long argued that plea bargains enable prosecutors to compensate for their restricted litigation power. 1 While prosecutors are able to take only a fraction of their cases to court, so the argument goes, they can induce offenders to admit guilt by repeatedly invoking the threat to try a case unless a plea bargain is reached. Although offenders are collectively better off if they reject all plea offers (forcing prosecutors to exhaust their budget on a few costly trials), each individual offender prefers a deal to a trial. Prosecutors thus need not actually carry out their threats. Each offender chooses to settle, which enables prosecutors to recycle the threat of trial against other offenders. Assuming no exceptional circumstances such as irrational offenders, mistakes, or collusion between offenders, prosecutors can therefore use limited resources to penalize offenders. As Professors Bar-Gill and Ben-Shahar have recently suggested, prosecutors ability to elicit many guilty admissions while possessing only limited litigation resources can be illustrated by the following analogy. A 1 Frank H. Easterbrook, Criminal Procedure as a Market System, 12 J. LEGAL STUD. 289, , (1983) (introducing offenders incentive scheme to settle when prosecutors resources are limited). See further, Frank H. Easterbrook, Plea Bargaining as Compromise, 101 YALE L.J (1992) (responding to critics). The cost-saving effect of plea bargains and the advantage they confer to budget-constrained prosecutors was first suggested (albeit only briefly) in William Landes, An Economic Analysis of the Courts, 14 J.L. & ECON. 61, 65 (1971).

3 3 PLEA BARGAINING AND CREDIBLE (LEGAL) THREATS budget-constrained prosecutor corresponds to an opponent with a single bullet who demands a battalion of unarmed soldiers to surrender. 2 The soldiers (i.e., offenders) can prevail if they jointly reject the demand, but each soldier prefers to duck and let the other soldiers mount the charge. The strategic opponent can make all soldiers capitulate by threatening to strike (bring to court) the first soldier who refuses to give in (accept a deal). Thus the opponent-prosecutor, although possessing only one threat (ability to litigate one case), is able to force the entire battalion of soldiers to surrender. 3 The one-threat-many-offenders argument has become a central theory in accounting for prosecutors stunning success in punishing offenders, despite scarce prosecutorial resources. 4 Yet reality seems to be more intricate. Although across a wealth of jurisdictions prosecutors induce many offenders to settle, the plea system as a whole falls short of achieving optimal punishment. Offenders facing severe charges and whose guilt can be readily proven in court are more than occasionally offered lenient pleas or full release. 5 The current state of affairs therefore presents a puzzling 2 Oren Bar-Gill, & Omri Ben-Shahar, The Prisoners (Plea Bargain) Dilemma, 1 J. LEGAL ANALYSIS 737 (2009). 3 Id., at RICHARD POSNER, ECONOMIC ANALYSIS OF LAW (9 th ed. 2014) (explaining that plea bargaining is worse for criminal defendants as a whole because they allow prosecutors to save resources and maintain their bargaining power); DAVID FRIEDMAN, LAW S ORDER: WHAT ECONOMICS HAS TO DO WITH LAW AND WHY IT MATTERS 91-2 (2001) (elaborating on offenders incentives to settle and showing the recycling effect that enables prosecutors to punish multiple offenders despite restricted resources); James S. Taylor, Plea Bargains, Constraining Options, and Respect for Autonomy, 18 PUB. AFFAIRS Q. 249, (2004) (same); Jacqueline E. Ross, The Entrenched Position of Plea Bargaining in United States Legal Practice 54 AM. J. COMP. L. 717, (2006) (discussing Easterbrook s contribution). See also Dirk Olin, Plea Bargain, N.Y. TIMES MAGAZINE, Sept. 29, 2002, at 29 (referring to David Friedman s book in discussing the prevalence of plea deals). 5 Empirical studies show that penalties in plea bargains are significantly lower than expected penalties from trial. This discrepancy suggests that the plea system does not fully penalize offenders. See Lindsey Devers, Plea and Charge Bargaining: Research Summary, Bureau of Justice Assistance-U.S. Department of Justice (2011) (reviewing the extensive empirical literature on offenders benefit from choosing plea agreements over trial). But compare David S. Abrams, Is Pleading Really a Bargain?, 8 J. EMPIRICAL LEGAL STUD. 200 (2011) (criticizing the methodology of several of these studies). Prosecutors willingness to offer some offenders particularly lenient plea deals can also be traced through court decisions. For recent examples in which plea agreements have been disapproved because of their leniency, see U.S. v. Jackson, 782 F.3d 1006 (D.

4 4 PLEA BARGAINING AND CREDIBLE (LEGAL) THREATS pattern. Prosecutors, despite their manifestly restricted resources, prevail upon many offenders to admit responsibility and be penalized (as in Bar Gill and Ben Shahar s insightful analogy), but at the same time let other offenders including offenders facing harsh expected sanctions escape liability. 6 Briefly put, prosecutors appear concurrently omnipotent and powerless. This Article looks to rationalize prosecutors behavior. It shows that prosecutors can use plea bargains to penalize offenders notwithstanding their deficient litigation power, as suggested by the one-threat-manyoffenders theory. However, to maintain the recycling effect that fuels this outcome, prosecutors must carefully choose between offenders. My claim is that conventional legal analysis has overlooked the implication of the process in which prosecutors negotiate with offenders. Prosecutors maximize offenders penalty through plea bargains under simultaneous negotiations. However, practical constraints as well as legal doctrine itself frequently preclude simultaneous negotiations, and prosecutors can extend plea offers to one offender (or only a few) at a time. Under such individual negotiations, threats made by prosecutors may lose their credibility, and consequently the dynamic that gives rise to offenders willingness to settle unravels. To address this concern, and restore credibility, prosecutors may have to forgo some of their cases and let guilty offenders escape liability. Thus, rather than implying ineffective law enforcement (as current scholarship maintains), release of guilty offenders and lenient plea deals may well show prosecutors strategic acumen. Mo. 2015) (rejecting plea deals of offenders convicted in drug-related offences); U.S. v. Garcia-Chihuahua, WL (Kan. 2015) (denying a plea agreement in an unlawful entry case); Dudley v. Ryan, 62 F. Supp. 3d 193 (D. Mass. 2014) (rejecting a plea bargain involving an offender guilty of unarmed robbery); U.S. v. Wright, 291 F.R.D. 85 (E. D. Pa. 2013) (disapproving a plea deal in a fraud case). Although courts possess certain review power over prosecutors decisions concerning plea bargains, plea deals are generally not subject to judicial approval and thus prosecutors are free to offer particularly lenient sanctions. See Rachel E. Barkow, Separation of Powers and the Criminal Law, 58 STAN. L. REV. 989, (2006) (describing prosecutors nearly unfettered control over the plea process). 6 See, e.g., Harry Hellerstein, When Being a Bigger Criminal Pays, WALL STREET JOURNAL, Dec. 26, 1990, at 16 (discussing cases where criminals who committed harsh offenses were offered more favorable bargains than criminals of lesser offenses); Fernanda Santos, Less Culpable, but with Longer Sentences, N.Y. TIMES, Apr. 6, 2013, at A9 (reporting and criticizing the existence of significant disparities in plea terms in favor of more culpable offenders).

5 5 PLEA BARGAINING AND CREDIBLE (LEGAL) THREATS Prosecutors challenge in mounting credible threats also brings to the fore the significance of allocation of prosecutorial resources and offenders for plea bargain negotiations. Existing legal scholarship has ascribed little weight to whether a case involving multiple offenders is handled by a single prosecutor who can conduct a few trials (as in the first scenario), or divided between a number of prosecutors who may each conduct a single trial (as in the second scenario). Following the conventional one-threat-manyoffenders theory, prosecutors in either circumstance have been assumed to be able to induce their offenders to admit guilt. As the following analysis shows, however, allocation of offenders and prosecutorial resources considerably affects prosecutors bargaining power. Rather counter-intuitively, prosecutors are worse off when offenders and prosecutorial resources are divided. Although division reduces the number of offenders with whom each prosecutor negotiates, it allows more offenders to reject their plea offers. The disadvantage of division stems from what makes prosecutors threats credible. A prosecutor can induce an offender to admit guilt that is, to mount a credible threat of trial only if the benefit of taking this offender to court outweighs the costs of the correspondingly shrunken prosecutorial budget (the loss from the need to give up on other offenders). Division undermines the credibility of prosecutors threats by increasing the costs of taking offenders to court. From a normative perspective, this Article offers two contributions. First, it shows that plea bargaining involves an inevitable tradeoff between efficiency and equality. While prosecutors strategic selection of offenders maximizes overall penalty, it subjects identical offenders to different individual penalties. Thus plea deals allow prosecutors to address the problem of scarce prosecutorial resources but create disparities between offenders sanctions. Furthermore, our analysis suggests that the Supreme Court s recent decisions aimed at fostering equality in plea negotiations by expanding the right to counsel may in fact facilitate the imposition of unequal penalties. Second, the significance of allocation for plea bargain negotiations sheds light on a fundamental choice regarding the institutional design of law enforcement. Two systems try offenders and impose penalties: federal and state. Critiques of Congress s ongoing expansion of federal criminal legislation often stress the advantage of letting states regulate crime. 7 An 7 For a review of the extensive literature that describes and critiques the federalization of criminal law, see, for example, Michael J. Zydney Mannheimer, Cruel and Unusual Federal Punishments, 98 IOWA L. REV. 69, 74-8 (2012).

6 6 PLEA BARGAINING AND CREDIBLE (LEGAL) THREATS essential trait of the state-based criminal system, however, is the dispersion of prosecutorial resources and offenders. States maintain independent lawenforcement budgets and seek to punish crime within their own jurisdiction. States, therefore, are analogous to independent prosecutors who divide resources and offenders. The federal criminal system, by contrast, corresponds to a single prosecutor ; as a centralized system, it pools together resources and offenders. Our analysis thus shows that the federal system enjoys an important advantage in deterring socially undesirable activities. By avoiding division, it allows law enforcement agencies to maximize the credibility of their threats. The remainder of the Article proceeds as follows: Part I elaborates on the conventional one-threat-many-offenders argument and shows that given the individual nature of plea negotiations, prosecutors ability to mount credible threats is in fact constrained. Against this background, Part II rationalizes prosecutors decisions to let guilty offenders escape punishment. It further shows that to maximize offenders total penalty, budget-constrained prosecutors may need to give up on offenders with high rather than low expected sanctions. Part III examines the effect of allocation of offenders and resources on the credibility of prosecutors threats. It demonstrates that division never improves and often harms prosecutors credibility. Part IV shows the interplay between equality, institutional design and the maximization of offenders total penalty. A short Conclusion follows. PART I: THREATS AND OFFENDERS A. One Threat, Many Offenders Prosecutors interest in signing plea agreements is straightforward. Given their limited budget, trying each and every offender would require prosecutors to release many guilty offenders. Plea agreements, as the Supreme Court has long acknowledged, enable prosecutors to punish offenders while avoiding prohibitive litigation costs. 8 Offenders incentives to admit guilt seem far less clear. In determining whether to enter a plea agreement, offenders will compare prosecutors 8 Santobello v. New York 404 U.S. 257, 260 (1971) (noting the cost-saving effect of plea agreements).

7 7 PLEA BARGAINING AND CREDIBLE (LEGAL) THREATS offers with their expected sanction from trial. Because prosecutors can take only a fraction of their cases to court, expected sanctions are low. Rational offenders, cognizant of the small risk of litigation, should thus prefer to take their chance and refuse deals in which they are subject to considerable penalties. As Professor Easterbrook has pointed out, however, offenders do not coordinate their responses. In view of prosecutors scarce litigation resources, offenders indeed are collectively better off if they jointly reject their offers. But offenders decisions are made individually, and an offender will choose a plea if he anticipates that other offenders prefer a deal to a trial. 9 Building on Easterbrook s insight, subsequent literature has shown the implications of offenders lack of coordination. Offenders facing high expected sanctions settle their case, which induces other offenders (facing less severe expected sanctions) to settle as well. An example can illustrate the logic of the one-threat-many-offenders prediction. Suppose that the expected punishments from trial (in prison years) of three offenders A, B and C are 10, 9 and 8, respectively. As offenders know, due to budget constraints the prosecutor can bring to court only one of them. The prosecutor extends to each offender a take-it-orleave-it plea offer that is equal to each offender s expected punishment, minus one day. 10 Specifically, the prosecutor makes an offer of ten years minus a day to offender A, nine years minus a day to offender B, and eight years minus a day to offender C. Each offender knows of the offers made to the other two offenders. Consider initially offender A s response. Looking to minimize his punishment, offender A will examine the consequences of rejecting his offer, given the other offenders likely responses. Because there exist two additional offenders B and C there are three potential scenarios that offender A ought to consider: 9 [D]efendants will compete to settle, lest the prosecutor obtain attractive settlements for other defendants that increase the productivity of his office (and thus raise the minimum settlement demand). Easterbrook, Criminal Procedure as a Market System, supra note 1, at The assumption that prosecutors extend take-it-or-leave-it offers simplifies the exposition, but is not essential. Empirically, prosecutors often make one-time offers. See G. NICHOLAS HERMAN, PLEA BARGAINING 6:20 (2 nd Ed., 2004) ( Because the prosecutor almost always possesses superior bargaining power over the defendant, defense counsel is often faced with a take-it-or-leave-it plea offer ).

8 8 PLEA BARGAINING AND CREDIBLE (LEGAL) THREATS (1) B and C both accept their offers (2) B and C both reject their offers (3) One accepts, while the other rejects In the first scenario (both accept), should A decline his plea offer, he will be tried. Because he is the only offender left, taking him to trial is within the prosecutor s budget. In this case, therefore, offender A will be imprisoned for ten years. Next, in the second scenario (both reject), should A reject his offer, he will again face trial (and be imprisoned for ten years). This is so, because if the prosecutor must choose one offender among the three (given that all of them rejected their offers), taking A to court maximizes overall penalty (10 > 9 > 8). 11 Finally, in the third scenario (either B or C accepts, while the other rejects), should A decline his offer, he (again) will be tried. Between him and the other offender who rejected the plea offer (whether B or C), offender A faces a higher expected punishment (10 > 9; 10 > 8) and thus will be selected by the prosecutor. This analysis reveals that offender A has a dominant strategy to accept his plea offer. Irrespective of the other offenders responses, it is always in offender A s best interest to enter into an agreement that allows him to avoid an otherwise certain trial. The analysis also suggests that the penalty discount, offered by the prosecutor to induce offender A to sign a plea, can be minimal (e.g., one day). We can turn next to offender B, and similarly analyze his best response against all possible combinations of the other offenders responses. Note that pursuant to our discussion of offender A s strategy, we must strike out the possibility that offender A will ever reject his offer. Consequently, from B s perspective, in gauging the implication of rejecting his offer, there are only two scenarios to be considered: 11 As empirical findings suggest, not only social-welfare concerns of optimal crime deterrence but also prosecutor s own private interests drive prosecutors to maximize overall prison sentences. Professor Richard Boylan examined the effects of U.S. Attorneys job performances on their subsequent career outcomes. Using a sample of 570 U.S. Attorneys, Boylan showed that prosecutors who successfully maximized overall prison sentences (rather than conviction rates or number of indictments) were more likely to become a federal judge or a partner in a large law firm upon completing their term. Richard T. Boylan, What Do Prosecutors Maximize? Evidence from the Careers of U.S. Attorneys, 7 AM. L. ECON. REV. 379 (2005).

9 9 PLEA BARGAINING AND CREDIBLE (LEGAL) THREATS (1) C accepts (and so does A) (2) C rejects (whereas A accepts) If offender C chooses to accept his plea offer (first scenario), a decision by B to reject a plea offer will result in his trial. Because in this case B is the only offender left (given that both A and C accepted their offers), taking him to court is within the prosecutor s budget. If offender C chooses to decline (second scenario), B s rejection will again result in trial. This is so, because if the prosecutor must choose between C and B, taking B to court provides the highest punishment (9 > 8). Thus, in either scenario, should offender B reject his offer he will be sentenced to nine years. It is in offender B s interest, therefore, to accept a plea. As in the case of offender A, the penalty discount can be small, setting the sanction just a little below nine years. It is straightforward to see that offender C as well will accept his offer. Because C understands that both offenders A and B will enter plea agreements, he realizes that a decision to reject his offer will result in trial. Anticipating this result, C will accept an offer that is equal to (or just slightly less than) his expected punishment. Although our example involves three offenders with specific expected penalties, it can be generalized. First, results would be similar for any number of offenders. Because it is the dominant strategy of the top offender to accept his plea offer, it becomes also the best response of all other offenders. 12 Each offender (in descending order) reasons that should he decline to settle he will be tried and accordingly opts to sign a deal. Second, it is not only that all offenders are punished but also that their benefit from admitting guilt is minimal. Irrespective of the number of offenders and their characteristics (the offense they committed and their respective expected penalties), prosecutors need only offer a penalty that is slightly less than each offender s expected sanction from trial. As scholars have stressed, the one-threat-many-offenders prediction is predicated on two rather simple and straightforward assumptions. First, offenders decide non-cooperatively whether or not to settle. 13 As noted, if offenders could cooperate they would all collectively reject their plea deals, forcing prosecutors to exhaust their budget on costly litigation. Such cooperation requires, however, that offenders enter complex agreements in 12 Formally, the result is obtained by applying the reasoning of iterative elimination of strictly dominated strategies. For further discussion of this concept see, for example, JOEL WATSON, STRATEGY: AN INTRODUCTION TO GAME THEORY (3 rd Ed., 2013). 13 Bar-Gill & Ben-Shahar, supra note 2 at 758.

10 10 PLEA BARGAINING AND CREDIBLE (LEGAL) THREATS which some (low expected sanction) offenders promise to compensate other (high expected sanction) offenders for refusing to enter plea agreements. 14 In addition, agreements in which offenders are promised compensation for rejecting plea deals are probably not legally enforceable. 15 Offenders cannot be sure payments will ever be made if they refuse a prosecutor s offer in order to benefit others. Thus, cooperation among offenders is unlikely (and indeed rarely occurs). 16 A second assumption is that offenders can surmise the relative significance of their case to prosecutors. Knowing that offender A ranks at the top, followed by offender B and so on, each offender (or his defense counsel) independently concludes that a refusal to plead guilty will result in trial. Pertinent legislative material (e.g., sentencing guidelines) and courts precedents often provide information for offenders to predict their relative expected sanctions quite accurately. 17 Although some murkiness may exist, because prosecutors usually possess resources to conduct several trials, a strict ranking order is not necessary. Every few offenders, in descending order, will settle even if offenders within each group only approximately know their specific rank. 14 In our example, collaboration among offenders will make A worse off (as he will be tried and subject to a full 10-year penalty) and both B and C better off (as they escape liability). B and C will thus be required to offer a side payment to A. But this payment can be anywhere between the value of a single day (A s loss from rejecting his plea offer) and the value of 17 years (the joint gain of B and C). Also, as B and C must determine how to divide their payment to A, they may attempt to free ride on one another. See Robert Cooter, The Cost of Coase, 11 J. LEGAL STUD. 1, (1982) (explaining how strategic behavior over dividing gains often inhibits efficient bargaining). 15 Bar-Gill & Ben-Shahar, supra note 2 at 759 (discussing the legal unenforceability of such agreements). 16 Offenders lack of coordination has long been acknowledged as an essential prerequisite for high plea rates: If all the defendants should combine to refuse to plead guilty, and should dare to hold out, they could break down the administration of criminal justice in any state in the Union. But they dare not.... JUSTICE HENRY T. LUMMUS, THE TRIAL JUDGE 46-7 (1937). 17 See, e.g., Ronald F. Wright, Trial Distortion and the End of Innocence in Federal Criminal Justice, 154 U. PA. L. REV. 79, 129 (2005) (noting the rise in plea deal rates in the 1990s following the promulgation of the sentencing guidelines, and attributing this result to the greater certainty the guidelines provided with respect to sanctions); see also Bar-Gill & Ben-Shahar, supra note 2 at (arguing that defense counsels experience can assist offenders in determining the relative importance of their case).

11 11 PLEA BARGAINING AND CREDIBLE (LEGAL) THREATS The one-threat-many-offenders theory sets forth a compelling account for the prevalence of plea deals. 18 It shows that even with severely constrained prosecutorial budgets, prosecutors can induce offenders to admit guilt. But while the one-threat-many-offenders theory explains offenders willingness to sign plea agreements, it only underscores the puzzle of prosecutors decisions to let guilty offenders escape punishment. B. Prosecutors Credibility and Individual Plea Negotiations There is a third assumption, although rarely acknowledged, that underlies the conventional analysis of plea bargaining negotiations. The one-threatmany-offenders prediction postulates that prosecutors can negotiate with offenders simultaneously. Practical constraints and legal doctrine, however, usually prevent such simultaneous negotiations. Rather than approaching all offenders at once, prosecutors are restricted to negotiating with offenders individually, extending plea offers to one offender (or a few) at a time. One obvious reason that precludes simultaneous plea negotiations is prosecutors constrained budgets (the reason they engage in plea bargaining to begin with). With limited resources, bargaining concurrently with a large number of offenders is beyond the reach of most prosecutors. 19 Perhaps less obvious, evidence law rules strongly discourage simultaneous negotiations. Inculpating testimonies by accomplices or by witnesses who may themselves have committed crimes are a central resource in 18 The notion that a principal can use a single threat to obtain concessions from multiple agents has been subject to limited analysis in other contexts. Game theorists, for example, have shown that regulations that grant homeowners of rent-controlled buildings a right to evict one tenant may harm all tenants. By recycling the threat to evict, a homeowner arguably can make each tenant concede to a rent increase. See, e.g., HERBERT GINTIS, GAME THEORY EVOLVING: A PROBLEM-CENTERED INTRODUCTION TO MODELING STRATEGIC INTERACTION 62-3 (2 nd ed. 2009) (discussing the rent control example); AVINASH K. DIXIT & BARRY J. NALEBUFF, THINKING STRATEGICALLY 18 (1991) (same). Yet this literature has not considered the effect of the form of negotiations (simultaneous or individual) on rightholders credibility. In the same vein, this literature has not addressed how allocation of threats and agents the focus of the next Part influences rightholders credibility. 19 See, e.g., Adam M. Gershowitz & Laura R. Killinger, The State (Never) Rests: How Excessive Prosecutorial Caseloads Harm Criminal Defendants, 105 NW. U. L. REV. 261, (2011) (presenting data showing that prosecutors handle more than one thousand felony cases per year although guidelines set a recommended annual limit of 150 cases).

12 12 PLEA BARGAINING AND CREDIBLE (LEGAL) THREATS prosecutors evidentiary arsenal. 20 However, making one offender testify against another might not be legally feasible if the first offender has not yet completed his own trial. Consider the case of accomplices. Because an accomplice who takes the stand may implicate himself, he can invoke his Fifth-Amendment privilege and refuse to testify. 21 This evidentiary hurdle is removed, however, if the prosecutor approaches offenders one after the other. By signing a plea with the first offender or dropping all charges against him (thereby completing his prosecution), and only then approaching the subsequent offender, the prosecutor can require the first offender to testify (as the risk of self-incrimination no longer exists). 22 Furthermore, even in cases in which offenders are willing to waive their Fifth-Amendment privilege and testify against other offenders before their own trial is over, the credibility of their testimonies is undermined. Because accomplices are accused of committing a joint offense, so long as their case is pending one accomplice may well falsely incriminate the other in the hope of reducing his own relative share of the blame. 23 More generally, any accused who awaits trial has a special interest in lying in favor of the prosecution, believing that such collaboration may garner a more favorable treatment in his case. In light of these concerns, jury instructions explicitly alert jurors that testimonies of witnesses who themselves still await the outcome of their trial must be treated suspiciously. 24 Approaching offenders one by one thus does not only increase the probability they will testify, but also raises the probative weight of their testimonies. 20 John G. Douglass, Confronting the Reluctant Accomplice, 101 COLUM. L. REV. 1797, (2001) (noting prosecutors extensive reliance on accomplices testimony); The Kings of the Courtroom, THE ECONOMIST, Oct. 4, 2014 (reviewing recent data and noting that now [m]ost federal cases are resolved using the actual or anticipated testimony of co-operating defendants ). 21 Douglass, supra note 20, at (discussing accomplices broad use of their Fifth- Amendment privilege). 22 Mitchell v. United States, 526 U.S. 314, 326 (1999) (holding that the right against self-incrimination is extinguished once prosecution has been completed or disposed of). 23 See, e.g., Christine J. Saverda, Note, Accomplices in Federal Court: A Case for Increased Evidentiary Standards, 100 YALE L.J. 785, n.40 (1990) (discussing accomplices incentives to lie). 24 See, e.g, CONNECTICUT CRIMINAL JURY INSTRUCTION ( In weighing the testimony of an accomplice who has not yet been sentenced or whose case has not yet been disposed of, you should keep in mind that (he/she) may in (his/her) own mind be looking for some favorable treatment in the sentence or disposition of (his/her) own case or hoping not to be arrested.... Therefore, you must look with particular care at the testimony of an accomplice and scrutinize it very carefully ).

13 13 PLEA BARGAINING AND CREDIBLE (LEGAL) THREATS Consider accordingly our three-offender example against the background of individual negotiations where the prosecutor approaches one offender at a time. Each offender, in his turn, is offered to sign a plea agreement. If the offender accepts, he is subject to the proposed sanction and the prosecutor preserves her budget. If the offender declines, the prosecutor then decides whether to take this offender to court (and exhaust her budget), or release him and continue to the next offender. Suppose that the prosecutor first approaches offender A. Backwardinduction reasoning shows that A s best response is now to reject the prosecutor s offer. The key point is that under sequential bargaining, the prosecutor s threat to take offender A to court, should he decline to settle, is no longer credible. From the prosecutor s perspective, if offender A refuses to admit guilt it is better to release him than to exhaust her budget on litigating his case. By giving up on A and preserving her budget, the prosecutor is able to maintain the credibility of her later threats when subsequently approaching offenders B and C. The ensuing benefit from credibly threatening these offenders exceeds the loss from releasing offender A. Anticipating that the prosecutor will prefer a release to a trial, A can thus reject his offer at no cost. To see further into this argument, consider the next table which contrasts the overall penalty the prosecutor can obtain under either course of action (trying or releasing) given that offender A rejects his offer. Response to A s Rejection Offenders Overall Penalty Trying A Offender A: 10 (Trial) Offender B: 0 (Release) Offender C: 0 (Release) Total: 10 Releasing A Offender A: 0 (Release) Offender B: 9 (Plea) Offender C: 8 (Plea) Total: 17 Trying offender A provides the prosecutor a benefit (in prison years) of 10, as A is subject to the full sanction. The prosecutor then remains, however,

14 14 PLEA BARGAINING AND CREDIBLE (LEGAL) THREATS with no leverage when negotiating with subsequent offenders. Knowing that the prosecutor has no additional resources to file charges and litigate their cases, B and C will clearly refuse any plea offer. The prosecutor s total benefit from trying offender A, therefore, equals 10. If the prosecutor releases offender A, by contrast, she can credibly threaten offender B to accept a plea offer of (nearly) 9 years. Because there are now only two offenders (B and C), if B rejects his offer the prosecutor will take him to court with certainty. This is so because between B and C, the prosecutor will prefer to go after B and release C (9 > 8). Offender B will therefore accept any plea offer that is just slightly less than 9 years to avoid an otherwise sure trial. Most important, given that B settles his case, the prosecutor maintains her budget and can also credibly threaten offender C in the next negotiation. Thus the prosecutor s total benefit equals 17 (9 + 8), which exceeds the benefit obtained from taking offender A to court (17 > 10). The consequence of this difference in the prosecutor s benefit is that she cannot credibly threaten offender A. In a three-offender case, this will be the result whenever offender A s sanction is less than the aggregate sanction of B and C (that is, if A < B + C). Because the prosecutor gains more from dropping the case against offender A than from litigating it, offender A can reject an offer and escape punishment. Upon A s refusal to enter a plea agreement, the prosecutor will prefer to sacrifice A s case so as to maintain the credibility of her threats when negotiating with B and later with C. 25 Our analysis therefore shows that the prosecutor is incapable of inducing all three offenders to accept a deal. Note that this result does not hinge on the order in which the prosecutor approaches the offenders. In fact, changing the negotiation order makes things even worse for the prosecutor. For example, a reverse sequence in which the prosecutor approaches offender A last only further weakens the credibility of the prosecutor s threats. Under this reverse order, both C s and B s best response is to reject their respective offers in turn, leaving the prosecutor with a benefit of only Prosecutors guidelines seem to support such strategic selection of cases: a plea disposition in one case may facilitate the prompt disposition of other cases, including cases in which prosecution might otherwise be declined. This may occur simply because prosecutorial resources will become available for use in other cases... UNITED STATES ATTORNEYS MANUAL, , at 26 By taking either B or C to court the prosecutor obtains less than 10 (A s sanction). Under a sequence in which A is approached last, offender B and C know that the prosecutor will not follow through on her threats to take the lower-value offenders to trial.

15 15 PLEA BARGAINING AND CREDIBLE (LEGAL) THREATS Likewise, our result remains even if prosecutors are willing to offer particularly generous penalty discounts for offenders who are willing to plead guilty. Because the prosecutor is better off dropping the case against A than bringing him to court, she will not follow through on her threat of trial. Knowing this, offender A will refuse any plea offer as lenient as it may be to settle his case. 27 PART II: OPTIMAL SELECTION OF OFFENDERS Although prosecutors might not be able to induce all offenders to settle, they can increase the overall penalty by selecting among offenders. In our example, releasing offender A enabled the prosecutor to impose an overall penalty of 17. But the prosecutor can increase offenders total sanction further. Suppose the prosecutor gives up on offender C and then negotiates with the remaining offenders, starting with offender A and then moving on to offender B. Given that A s expected punishment is greater than B s (and because C has been released), offender A knows that a rejection of the prosecutor s offer will cost him a sure trial and will thus choose to settle for a penalty just below 10. Because the prosecutor maintains her budget she can induce offender B, in the next negotiation stage, to enter a plea agreement as well. 28 Therefore, by releasing C, then approaching offender A and subsequently offender B, the prosecutor imposes a total sanction of 19 (10 + 9). Analyzing all alternative options shows that 19 is the maximum total sanction the prosecutor can obtain. 29 Intuition seems to suggest that in the face of an insufficient prosecutorial budget, prosecutors best strategy is to always set free offenders with low 27 It is possible that offenders may nevertheless choose to sign plea deals (involving mild penalties) even when they face no credible threat of trial, as a way to ensure the disposition of the charges. Upon entering a plea agreement (and offenders compliance with its terms), prosecutors are legally barred under double jeopardy doctrines from filing future charges. See Ricketts v. Adamson 483 U.S. 1, 8 (1987). This explains the fact that some cases may result in lenient plea deals instead of a full release. 28 More generally, as our analysis shows, a prosecutor armed with a single threat can credibly induce any two offenders to sign a deal. The top offender, who realizes his refusal to settle will cost him trial, admits guilt, which allows the prosecutor subsequently to induce the remaining offender to admit guilt as well. 29 Because the prosecutor cannot induce all three offenders to settle, giving up on C (the offender with the lowest expected sanction) maximizes the overall penalty.

16 16 PLEA BARGAINING AND CREDIBLE (LEGAL) THREATS expected penalties. The next table considers four groups of offenders, and indicates in each group the offender whose release will maximize the overall penalty (assuming the prosecutor s resources permit only a single trial). As this table demonstrates, prosecutors maximizing strategy may in fact require the release of offenders other than those with the lowest expected sanctions. Offender A Offender B Offender C Offender D Example 1: Example 2: Example 3: Example 4: It might be worthwhile to begin with example 1, where the prosecutor, despite her limited budget, can induce all four offenders (10, 6, 2, 1) to sign a plea. Note that in this example, starting with offender A and onward, each offender s individual sanction exceeds the aggregate sanction of all offenders who follow: A > C + B + D 10 > 9 ( ) B > C + D 6 > 3 (2 + 1) C > D 2 > 1 This sanction profile enables the prosecutor to credibly threaten each offender in his turn. Consider offender A. If A rejects his offer, the prosecutor is better off taking him to court even at the cost of giving up on B, C and D (10 > 9). Offender A will therefore enter a plea bargain to avoid trial. With the same logic, the prosecutor s offer to offender B in the next negotiation stage is also backed up by a credible threat; if B refuses to settle (for just less than 6 years), the prosecutor is better off litigating his case even at the cost of releasing offenders C and D (6 > 3). Offender B will thus

17 17 PLEA BARGAINING AND CREDIBLE (LEGAL) THREATS also enter an agreement, which induces offender C (3 > 2) and later offender D also to accept their respective offers in turn. Against the backdrop of example 1, one can see that in the remaining examples the prosecutor cannot induce all offenders to enter plea agreements. In example 2, whereas from offender B and onward each offender s individual sanction exceeds the aggregate sanction of the offenders that follow (thus allowing the prosecutor to credibly threaten each of them), offender A s sanction is lower than the aggregate sanction of the subsequent offenders: A < B + C + D 10 < 11 ( ) B > C + D 6 > 5 (3 + 2) C > D 3 > 2 The implication is that offender A can safely refuse to settle because the prosecutor gains more from going after B, C, and D than from litigating A s case (10 < 11). But setting free offender A is not the prosecutor s best strategy. Better yet, she can retain offender A and release offender D. In this case, each of the offenders individual sanctions outweighs the aggregate sanction of the offenders that follow (A > B + C and B > C) and can thus be credibly threatened to accept a plea. Here, as in our three-offender example, the release of the offender with the lowest expected sanction (offender D) indeed allows the prosecutor to impose the overall harshest sanction (19 years). Example 3 seems to present a similar sanction pattern to that of example 2: the interplay between the sanctions of the last three offenders is such that they can each be induced to accept a plea, while the prosecutor cannot credibly threaten offender A: A < B + C + D 10 < 13 ( ) B > C + D 7 > 6 (5 + 1) C > D 5 > 1 In contrast to example 2, however, the release of offender D is now insufficient to make offender A accept a plea. Note that subsequent to D s release, the overall sanction of the remaining offenders B and C is still greater than A s sanction, that is, A < B + C (10 < 7 + 5). If A declines to settle (after D s release), the prosecutor still gains more from dropping his case and going after B and C; the prosecutor s threat to take offender A to court is accordingly empty. Only the release of offender C renders the

18 18 PLEA BARGAINING AND CREDIBLE (LEGAL) THREATS prosecutor s sequential threats credible, because A > B + D (10 > 7 +1) and B > D (7 > 1). In example 4, even the release of offender C is insufficient because A < B + D (10 < 7 + 4). The prosecutor, despite C s release, still gains more from dropping the case against A (and going after B and D) than from litigating it. Offender A thus has no incentive to settle, and the prosecutor will have to release him as well. Giving up on both offenders C and A means a loss of 15 (10 + 5). The prosecutor can instead release offender B (a loss of only 7). Each offender s individual sanction is then greater than the aggregate sanction of the offenders that follow (A > C + D, C > D), and thus all remaining offenders will settle their case. No other alternative (releasing other offenders) provides a better result. 30 As these examples illustrate, plea bargains mitigate but do not eliminate the problem of scarce prosecutorial resources. Using the threat of trial to punish offenders through plea deals may require prosecutors to choose between cases. Strategically giving up on some offenders enhances the credibility of prosecutors threats, since such concessions decrease the cost of taking the remaining offenders to court. Furthermore, to maximize overall penalty, prosecutors may have to let heavy-weight offenders escape punishment (while going after offenders expecting lower sanctions). Thus the seemingly incompatible characteristics of the plea system high rates of plea deals together with occasional lenient treatment of offenders who are guilty of committing serious crimes can be two sides of the same coin. It is the lenient treatment of those culpable offenders that allows prosecutors to credibly threaten the other offenders. PART III. ALLOCATION AND CREDIBILITY Existing legal scholarship, following the one-threat-many-offenders prediction, has paid little attention to the allocation of resources and 30 If the prosecutor releases D, she will also have to give up on A, for a total loss of 14. Another alternative is releasing C and D. Left with A and B, the prosecutor can then approach A and later B and credibly threaten them. But giving up on C and D means a loss of 9 (5 + 4), which exceeds the loss from releasing B (7).

19 19 PLEA BARGAINING AND CREDIBLE (LEGAL) THREATS offenders among prosecutors. 31 Whether offenders are assigned to a single prosecutor whose resources permit many trials, or rather divided between multiple prosecutors who can take only a single offender to court, has been regarded as inconsequential to offenders willingness to settle. The conventional wisdom that prosecutors can routinely mount credible threats suggests that rational offenders under either allocation will plead guilty. As our preceding discussion has demonstrated, however, prosecutors may not be able to credibly threaten all offenders. One may intuitively infer from the analysis in Part II that greater division of prosecutorial resources and offenders (distributing them among more prosecutors) increases prosecutors bargaining power. As we have seen, prosecutors with scarce resources can maximize overall penalties by strategically reducing the number of offenders with whom they negotiate. Division seems to allow a similar result. As offenders are divided among more prosecutors, each prosecutor negotiates with fewer offenders. Obviously, from prosecutors perspective, if division of prosecutorial resources and offenders can increase their bargaining leverage, it has a clear advantage as it may diminish the need for strategic release of guilty offenders. Yet in fact division undermines the credibility of prosecutors threats. The disadvantage of division can be shown by establishing the following two outcomes: First, concentrating prosecutorial resources and offenders (distributing them among fewer prosecutors) never harms prosecutors. Thus, for example, a single prosecutor negotiating with several offenders will never fare worse than two (or more) independent prosecutors sharing an identical budget and negotiating with the same offenders. Second, and perhaps more surprisingly, greater dissemination of offenders and prosecutorial resources can turn prosecutors credible threats into noncredible ones. Thus two (or more) prosecutors might fail to reach the penalty that a single prosecutor can obtain Existing scholarship has mostly been empirical, focusing on how resources are allocated among competing authorities. See, e.g., Rachel E. Barkow, Federalism and Criminal Law: What the Feds Can Learn From the States, 109 MICH. L. REV. 519 (2011) (examining allocations of power and resources between local authorities within states). 32 The extensive scholarship on threats (based on the seminal work of Thomas Schelling) has mostly focused on strategies for bolstering the credibility of a single threat. See Avinash Dixit & Barry J. Nalebuff, Making Strategies Credible, in STRATEGIC REFLECTIONS ON HUMAN BEHAVIOR 161, (Richard Zeckhauser ed., 1991). Our analysis, which examines the case of principals who possess multiple threats (but face an