Kolber’s Teaser

In sports gambling, a “teaser” is a multi-proposition bet where the bettor combines two or more different wagers and receives more favorable odds on each (or all) of them. For example, suppose the New England Patriots are favored to win by four points over the Buffalo Bills in one game while the Green Bay Packers are favored to win by seven points over the Atlanta Falcons in another game. You think it is very likely that the Patriots and the Packers will both win by comfortable margins. If you place a two-team teaser bet on both games, then you can adjust the point spreads by around six total points across the games in any way that you choose—for example, by reducing the Patriots’ point spread to one and the Packers’ point spread to four. To win the teaser bet, both the Patriots and the Packers must win by more than their point spreads.

Should a gambler make teaser bets? At first, the deal looks fantastic. If you thought it was very likely that the Patriots would win by four, then you should think it even more likely that they will win by one. The same goes for the Packers. On a closer look, however, the probabilities are not so favorable. The odds of any particular favorite winning are generally pretty close to 50%. Suppose that a three-point adjustment in the point spread improves a favorite’s odds of winning to around 65%. Even so, the requirement that both favorites win in order to for you to win the bet reduces the expected payoff from around 50% to around 42%. Teasers are difficult bets, in other words, because of the math of conditional probabilities. Yet, teasers are appealing to some gamblers precisely, because they fail to understand this math.

Professor Adam Kolber’s thesis in Punishment and Moral Risk1 is subject to both a modest and more audacious interpretation. For Kolber, retributivism is, roughly, the idea that an offender’s deserving punishment provides a sufficient basis for punishing him or her.2 The modest version of Kolber’s thesis is that retributivism has many theoretical presuppositions and commitments. Those unwilling to defend these presuppositions and commitments should not embrace retributivism. On this point, Kolber is convincing. Someone who is a hard incompatibilist about free will and moral responsibility should not embrace retributivism (which presupposes that people can, at least sometimes, be morally responsible for their actions). The same reasoning applies for a hard-core anarchist about political legitimacy who denies that state coercion could ever have an adequate moral basis. Such an anarchist should not adopt the idea that punishment involves the state giving a defendant what he or she deserves, since anarchism requires denying that a state could ever be in an appropriate position to mete out this kind of harsh treatment. Although the modest version of Kolber’s thesis is convincing, it is unlikely to convince many punishment theorists. The ranks of retributivists who embrace hard incompatibilism about moral responsibility or hard-core anarchism are thin.

A more ambitious reading of Kolber’s thesis aims to convince the died-in-the-wool retributivist that his or her positions are untenable in light of normative uncertainty. To achieve this ambition, Kolber offers what is, in essence, a teaser gambit against retributivism.

The first step of this gambit is to decompose retributivism into a series of inquiries regarding the criminal justice system as a whole3 and that system’s operation in a specific case.4 Some of these propositions are purely philosophical, others concern the character of criminal justice institutions, and others are purely empirical. The second step is to gauge the retributivist’s confidence in the truth of these propositions. If the retributivist were to give an honest assessment, he or she might answer each of these propositions in the affirmative, but his or her confidence in each proposition would not be absolute—he or she would concede at least some possibility that each proposition should not be answered affirmatively. For Kolber, vindicating retributivism requires more than gauging the retributivist’s confidence in each proposition. Rather, he or she must be confident in the conjunction of all of these and other propositions. Because the retributivist must resolve many separate propositions and his or her confidence in any of them is likely to be relatively low, he or she should have low confidence in the overall conclusion. On Kolber’s teaser, then, moral uncertainty should render a retributivist unable to justify virtually any token of criminal punishment. Unless the retributivist is also an abolitionist about the practice of punishment, this conclusion should be disturbing.

I agree with several aspects of Kolber’s ambitious thesis. First, retributivism has direct implications for criminal procedure. Advocates of retributivism should not take important procedural questions for granted, although many of them do. Second, retributivist theories of punishment cannot be isolated from broader questions about political philosophy, such as the state’s legitimate enforcement of the criminal law and the state’s role in creating the conditions under which defendants criminally offend.5 Third, many retributivists exhibit a complacency about the truth of the background-level and case-level propositions that comprise retributivism. This complacency is unwarranted, and it is perhaps also theory-driven. Fourth, the justification for criminal punishment is a complex issue. This complexity should invite greater skepticism (rather than certainty) about whether tokens of punishment are justified and whether our punishment practices are justified as a whole.

In my opinion, however, Kolber’s teaser gambit does not provide a compelling internal critique of retributivism. I first note a methodological problem with Kolber’s analysis then highlight a more substantive response from retributivists that, if true, would undermine the teaser gambit.

The Non-Independence of Kolber’s Propositions

The propositions that Kolber tasks the retributivist with resolving are not independent of each other. Therefore, Kolber’s strategy for calculating the moral uncertainty facing retributivist accounts of punishment is inappropriate.6

Two propositions are independent of each other when the truth or falsity of one does not affect, constrain, or provide useful information about the truth or falsity of the other. The multiplication rule that Kolber utilizes for determining the moral uncertainty of retributivism is only appropriate if all of the propositions are independent of each other. If the propositions are interrelated, then different methods should be deployed to calculate probability.

Another sports wagering example might illustrate this point. Suppose that there are two propositions, each of which has a roughly 50% chance of being true. P1 is that the New England Patriots win the Super Bowl, and P2 is that Patriots quarterback Tom Brady is named Super Bowl Most Valuable Player (“MVP”). To determine the joint probability of P1 and P2, one should not simply multiply the probability of P1 by the probability of P2. Why not? The truth or falsity of P1 influences the odds that P2 will be true or false, and vice versa. Historically, the Super Bowl MVP is almost always awarded to a player from the winning team. Therefore, an affirmative answer to P1 is very likely to affect the truth of P2. Likewise, because Brady is a focal point of the Patriots’ offense, it is difficult to imagine the team winning the Super Bowl without Brady playing well. As a historical matter, the chances that quarterback who plays well is named MVP are also very high. P1 and P2 are not independent, in other words, because the considerations that influence the truth or falsity of P1 also influence the truth or falsity of P2 and vice versa. Of course, it is not impossible that the Patriots could win the Super Bowl and Brady would not win MVP. These odds are far lower than 25%, however, which is what the multiplication rule would predict. Because P1 and P2 are not independent propositions, the multiplication rule should not be used to calculate their joint probability.

Many of the propositions that Kolber identifies are (or at least could be) linked in the way that “Patriots win the Super Bowl” and “Brady is named Super Bowl MVP” would be linked. Here are two particularly clear examples, although each of the propositions that Kolber identifies seems to be linked to other propositions. First, Proposition (1) is “Human beings ordinarily have the kind of free will (and all other properties) required for moral responsibility”;7 while Proposition (2) is “Taking the prior numbered proposition as given, those who commit serious wrongs deserve to be punished (or to suffer) in response.”8 The truth of Proposition (1) clearly influences the truth of Proposition (2). If Proposition (1) is false and there is no such thing as free will, then it almost certainly does not make sense to say that those who commit serious wrongs deserve punishment (or anything else, for that matter) in the sense that most retributivists use the term “deserve.” Moreover, the truth of Proposition (2) also provides relevant information regarding the truth of Proposition (1). On most versions of retributivism, the considerations in light of which someone can deserve punishment influence the type of free will that a theory posits as sufficient to ground moral responsibility.

Likewise, Proposition (4) states that “state coercion generally can be just and, more particularly, the state is morally permitted to impose on the citizenry to create institutions that punish (or make suffer) those who deserve it”;9 while Proposition (7) is that “police conduct and judicial proceedings were of sufficient quality that just punishment has not been precluded.”10 These two propositions are not independent. The truth of each proposition can affect the likelihood that the other is true. Proposition (7) can inform Proposition (4): Lawless conduct by the police or the judiciary in a particular case can influence whether a state has political legitimacy overall. Likewise, Proposition (4) can inform Proposition (7): Whether a state has the general authority to create institutions that punish those who deserve to be punished is relevant to assessing the lawfulness of police or judicial conduct in any particular case.

Kolber is correct that the retributivist must answer a variety of difficult questions to justify any specific token of punishment. Since the propositions that Kolber identifies are not independent from each other, however, the burden of normative uncertainty facing the retributivist is not as daunting as Kolber’s gambit suggests.

The Normative Division of Labor

In addition to this methodological disagreement, a retributivist might also differ with Kolber on substantive grounds. One such disagreement concerns Kolber’s contention that retributivists (unlike judges, officials, or even consequentialists) must solve both background- and case-related propositions as part of meeting their “justificatory standard of proof.”11 This move is crucial to Kolber’s contention that calculating retributivist’s justificatory requires combining uncertainty across different categories of propositions.

The retributivist could respond to Kolber’s teaser gambit by arguing from a normative division of labor. Such an argument might invoke John Rawls’s distinction between “justifying a practice” and “justifying a particular action falling within” a practice.12 The former task implicates different normative principles and identifies different types of considerations as relevant than the latter does.13

Assume that a retributivist accepts the normative division of labor argument with regard to the justification for punishment.14 One implication of this argument is that uncertainty related to the justification of a practice is analytically distinct from uncertainty related to the justification of actions within a practice. For example, consider Kolber’s Proposition (5): that the defendant engaged in the “conduct alleged.”15 A retributivist faced with such case-based uncertainty might have his or her doubts assuaged, for example, by strong evidence that the defendant has engaged in culpable behavior for which he or she is not charged and has not been punished. If (as many retributivists assert) punishment of the deserving is appropriate and/or intrinsically valuable, then it is tempting to justify the punishment of a “trivially innocent” defendant—that is, a defendant who did not commit the offense with which he is charged, but “committed another offense (or offenses) of at least equal seriousness.”16 The retributivist might mollify his or her doubts about whether Proposition (5) is realized by relaxing the “offense restriction,” or the notion that “a defendant’s desert bases only bear on his or her liability to punishment if they are related to” a charged offense.17 The retributivist (although, one hopes, not the judge in situ) might instead invoke a fallback proposition familiar to many in the criminal justice system who have similar doubts in specific cases—that “[i]f the defendant didn’t commit this particular crime, he did something somewhere, sometime.”18 Moreover, the retributivist’s comfort with punishing the trivially innocent might be justified by his or her confidence in the background-level propositions that, on Kolber’s gambit, are to be taken for granted when assessing confidence in case-level propositions. On the other hand, uncertainty regarding background-level propositions would not likely be assuaged by an appeal to a fallback proposition. For example, a retributivist’s uncertainty about Proposition (1), which concerns whether anyone has free will,19 would likely not be assuaged by strong evidence related to Proposition (5).

The normative division of labor argument in response to Kolber’s gambit, then, takes two steps. First, different normative principles apply to background- and case-level propositions, and categorically different normative and empirical considerations are relevant to establishing the truth-value of these propositions. Yet, Kolber’s gambit only works if the same (or commensurable) principles and considerations apply to the evaluation of background- and case-level propositions. Second, in light of discrepancies between background- and case-level propositions, uncertainty about one category of proposition seems incommensurable (or, at least, not easily comparable) with uncertainty about the other. Yet, Kolber’s gambit assumes that uncertainty about one type of proposition is comparable with uncertainty about the other. Therefore, according to this argument, Kolber’s gambit is mistaken.

Kolber would almost certainly deny both aspects of the normative division of labor argument on the merits.20 Is the normative division of labor argument ultimately correct? I am not sure, although it at least seems plausible to me. The correctness of this argument, however, is beside the point. Many retributivist accounts of punishment could (and, likely, would) appeal to something like the normative division of labor argument in response to Kolber’s teaser gambit.21 Kolber’s gambit assumes that the normative division of labor argument is false. As such, Kolber’s gambit is external to retributivism (or, at least, to those versions of retributivism that would embrace the division of labor argument). Yet, much of the power of Kolber’s gambit is that it purports to offer an internal critique of retributivism.22 As with the argument from non-independence, then, the normative division of labor argument suggests that things are not as dire for the retributivist as Kolber’s critique portends.


Professor Kolber is one of the most astute critics of retributivism and one of the most innovative contemporary punishment theorists. Has he succeeded in confounding retributivism, of knocking it from its spot as the preeminent contemporary theory of punishment? Perhaps not this time. But I would not bet against him.

*  Associate Professor of Law at the University of Tulsa College of Law. Thanks to Emad Atiq, Mihailis Diamantis, and Chad Flanders for feedback.

1. Adam J. Kolber, Punishment and Moral Risk, 2018 U. Ill. L. Rev. 487, 487 (2018).

2. Kolber defines retributivism as a view that “those who commit a serious moral wrong deserve proportional suffering or punishment from the state.” Id. at 489 (emphasis added). This definition is not neutral to retributivists. Rather, it increases the sting of Kolber’s critique. In particular, it construes proportionality to be part of the definition of retributivism, rather than a desideratum that retributivist theories might aim to capture. Yet, at least two of the controversial propositions that comprise Kolber’s critique (namely, Proposition (3) and Proposition (9)) concern the difficulty of determining when a punishment is proportionate to an offender’s culpability. Id. at 501, 511. A retributivist might reduce the force of Kolber’s critique by simply refuting his definition of retributivism—that is, contending that proportionality is a goal for retributivist punishment to strive for but not (as Kolber puts it) a more integral aspect of the retributivist justification for punishment.

3. Id. at 492–520.

4. Id. at 525–31.

5. In positing this connection, Kolber is in good company. See, e.g., Chad Flanders, Political Philosophy and Punishment, in Palgrave Handbook on Applied Criminal Justice (forthcoming); Vincent Chiao, What is the Criminal Law For?, 35 Law & Phil. 137, 138 (2016); Alice Ristroph, Respect and Resistance in Punishment Theory, 97 Cal. L. Rev. 601, 602–03 (2009); cf. Stephen J. Schulhofer, The Mathematician, the Monk, and the Militant: Reflections on the Role of Criminal Law Theory, 88 Cal. L. Rev. 705, 707 (2000) (“[P]olitical philosophy—the theory of the state—is for the most part unimportant for purposes of doing work in criminal law theory. . . . [T]here is rarely mileage to be gained, in terms of criminal law theory, from sorting out which is the appropriate theory of the state.”).

6. Lawrence Solum made a similar critique of an earlier version of Kolber’s article. Kolber, supra note 1, at 504 n.62. As far as I can tell, Kolber highlights but does not address Solum’s critique, aside from noting that “there is surely considerable independence among” the propositions he identifies. Id. “Considerable” independence is not the complete independence that the multiplication rule requires. To state that the propositions are even somewhat interdependent is to concede that the product rule should not be used to determine probability.

7. Id. at 497.

8. Id. at 499.

9. Id. at 502.

10. Id. at 508.

11. Id. at 512–17.

12. John Rawls, Two Concepts of Rules, 64 Phil. Rev. 3, 3 (1955). A retributivist might appeal to such a normative division of labor argument without also embracing what Rawls calls the “practice” conception” of rules. Id. at 24–29. A retributivist also does not necessarily invoke the normative division of labor argument, or what Arthur Applbaum calls the argument from “constituted description,” according to which “if . . . . institutional facts [] describe actions, we can use only institutional criteria to evaluate those actions.” Arthur Isak Applbaum, Are Lawyers Liars?: The Argument of Redescription, 4 Legal Theory 63, 74 (1998). The argument from constituted description is a particularly stringent version of a normative division of labor argument, not a general entailment of it.

13. In this respect, the normative division of labor argument resembles what is sometimes called the “moral division of labor” argument regarding whether principles of justice apply only to the organization of social institutions, or to both social institutions and the actions of individual within a society. See Samuel Scheffler, Egalitarian Liberalism as Moral Pluralism, 79 Proc. Aristotelian Socy 229, 248 (2005) (arguing that under moral division of labor argument, “on the one hand, the primary subject of justice remains the basic structure of society and, on the other hand, there are many other values and norms that should appropriately regulate individual conduct within the basic structure”).

14. This move would have the retributivist embrace something like the position that Kolber calls the “separate questions approach” to “punishment hybridity,” according to which different principles operate at the background and case levels of the criminal justice system. Kolber, supra note 1, at 524–26. On H.L.A. Hart’s version of that approach (which Kolber contemplates), consequentialist principles provide the general justifying aim of the practice of punishment, while retributivist principles assume preeminence in the distribution of punishment. Id. at 525. Kolber rejects Hart’s version of the “separate question approach” for its lack of clarity about how to “bridge the gap between retributivism and consequentialism.” Id. Kolber’s condemnation applies to Hart’s version of the approach, but it does not indict the approach as such. In any event, many versions of retributivism embrace some version of the separate-questions approach. See, e.g., Mitchell N. Berman, Modest Retributivism, in Legal, Moral, and Metaphysical Truths: The Philosophy of Michael Moore (Stephen J. Morse & Kimberly Kessler Ferzan eds., 2015).

15. Kolber, supra note 1, at 504.

16. Stephen R. Galoob, Retributivism and Criminal Procedure, 20 New Crim. L. Rev. 465, 476 (2017).

17. Id.

18. Patricia J. Williams, Reasons for Doubt, Nation (December 12, 2002), https://www.thenation.com/article/reasons-doubt/. Kolber doubts that retributivists would embrace this fallback position. See Kolber, supra note 1, at 504 n.63. I am unsure what a survey of retributivists would reveal about their thoughts on the problem (if any) presented by trivial innocence. Yet, however unjust it is to permit punishment of the trivially innocent, many versions of retributivism are logically committed to it as an entailment of their other commitments. See Galoob, supra note 17, at 468-76.

19. Kolber does not specify which form of free will argument (compatibilist or incompatibilist) would be sufficient to answer this proposition affirmatively. Of course, some incompatibilists might contend that compatibilist picture of free will is just such a fallback position.

20. Kolber rules out the first move of the normative division of labor argument in his denial of the “separate question” approach to punishment hybridity, discussed supra note 14. More broadly, Kolber would presumably deny that there is any important difference between justifying a practice and justifying an action within that practice. The logic of Kolber’s argument would also rule out the second premise of the normative division of labor argument—Kolber’s critique rules out the first premise, and the second premise follows logically from the first premise. Moreover, Kolber’s use of the multiplication rule to calculate normative uncertainty for retributivists implicitly denies what the second premise of the normative division of labor argument asserts—namely, that the kinds of uncertainty raised by background-level propositions are commensurable with the uncertainty raised by case-level propositions.

21. See, e.g., Mitchell N. Berman, Punishment and Justification, 118 Ethics 258 (2008); Douglas Husak, Holistic Retributivism, 88 Cal. L. Rev. 991 (2000)

22. Kolber, supra note 1, at 519 n.116.

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