A. The Noncomparative Basis of Comparative Judgments

Why should we think that the Problem is caused by vague covering values (Vagueness), rather than the options being “on a par” all the way down (Parity)? The explanation lies in the relationship between noncomparative and comparative judgments. Imagine that we have two sticks in two different locations, and we want to know which is longer. This will depend, ultimately, on an independent or noncomparative assessment of each stick's length. We examine Stick 1 and see that it is 24.22 inches long. Then we examine Stick 2 and see that it is 23.95 inches long. And thus we conclude that Stick 1 is longer (exhibiting more of the covering value of “length”). If the sticks were in the same location, we could place them side by side to see which was longer, perhaps, but the question would still depend on the degree to which each stick, considered on its own, exhibited “length.” Now consider Michelangelo versus Novice Composer with regard to their creativity. How creative is Michelangelo, exactly, just considered by himself? This is very hard. All we can say is something like, “He is unbelievably creative.” We cannot determine that he has, say, 78.4 units of creativity. Nonetheless, as indicated above, we can conclude with confidence that Michelangelo is more creative than Novice Composer, who is merely, let us say, “somewhat creative.” The point is that all we are doing with any comparison is examining the extent to which the options, independently of each other, exhibit a particular predicate. This is what we do when comparing Stick 1 and Stick 2 with regard to length, and there is no reason to believe that the comparison between Michelangelo and Novice Composer works differently, even though we cannot measure their independent levels of creativity with cardinal precision.

How does this relate to the question of whether Parity or Vagueness explains the Problem? In this way: if we can make noncomparative measurements with cardinal precision—as in the stick example—then we will never have a Problem case. We will be able to conclude that one option exhibits more of the covering value, or that they exhibit it equally. Problem cases can emerge only when we cannot measure the options independently of one another with cardinal precision. This is true even if—as in Michelangelo v. Novice Composer—not every comparison featuring coarse noncomparative judgments is a Problem case. The question then becomes: What causes our noncomparative judgements to be imprecise in Problem cases? Why are our measurements of Michelangelo and Mozart's creativity levels so coarse? Whatever explains this noncomparative coarseness, it seems, will also explain why we have a Problem case at the comparative level.

Thus, if Parity is meant to explain Problem cases—via the conclusion that the options are “on a par” all the way down—it would have to explain our noncomparative imprecision in those cases as well. Why is it that we cannot precisely measure someone's level of creativity? That is the most pertinent question for Mozart v. Michelangelo and I am doubtful that Parity, with its comparative focus, has much to say on the matter. To maintain that Problem cases were not caused by covering value vagueness, furthermore, it seems that Chang would have to deny that vagueness causes our noncomparative imprecision regarding such values. Such an argument seems very unlikely to succeed. It is far more plausible that creativity is a vague concept, the vagueness of which explains our inability to make refined measurements in the noncomparative cases, which in turn leads to an inability to resolve the comparative cases. Vague covering values entail uncertain noncomparative, cardinal judgments that, in turn, entail uncertain comparative, ordinal judgments. We conclude that Mozart and Michelangelo, considered independently of each other, are both something like “unbelievably creative,” but nonetheless are almost certainly not precisely equally creative, and then we are at an impasse with regard to our comparative judgement. We can thus conclude that Mozart and Michelangelo are “vaguely equally” creative.

Vagueness, importantly, does not imply that all Problem options are “vaguely equal” in this way. Chang, fully aware of Vagueness as a rival explanation of the Problem, mischaracterizes the argument on this point.Footnote ⁹ Sometimes the “vaguely equal” conclusion is appropriate, but in other instances, the covering value can be so vague that to imply the options are “almost” or “sort of” equal would be misleading, given our uncertainty about their relative worth. Rather than “vaguely equal,” they are simply “vaguely related.”Footnote ¹⁰ The covering value at the center of proportionality analysis—“injuriousness”—is one such example, as I discuss in Section II. Specific crimes (e.g., embezzling $250,000) are often only “vaguely related,” rather than “vaguely equal,” to specific punishments (e.g., 25 months in prison) in terms of their injuriousness.

Finally, if options being “on a par” were not a product of vague covering values—if it were indeed as basic a comparative relation as “better than,” “worse than,” and “equal to”—then we ought to see parity when comparing options with regard to nonvague covering values. But we never do. And the reason is that nonvague covering values, like length and mass, generate precise noncomparative judgments, which will always lead to precise comparative judgments of better than, worse than, or equal to. For the sake of completeness, epistemic uncertainty could generate a simulacrum of a Problem case with a nonvague covering value. Imagine that we do not have a ruler and cannot determine with the naked eye whether Stick 1 or 2 is longer. We would then conclude that, given the information we have, we cannot determine whether either stick is longer or if they are equally long. This is a simulacrum of a Problem case because we could make such a determination with complete epistemic information.Footnote ¹¹

B. Vagueness and Substantive Argument

This subsection considers Chang's central argument against Vagueness, against the idea that Problem cases are “borderline” applications of a vague predicate. Understanding how Chang's argument goes wrong, exactly, will provide us with important conceptual tools for assessing the degree to which reasons can determine the choice of a proportionately “injurious” punishment.

Chang's argument centers on a hypothetical. Pretend we have to choose whether a borderline case has passed the relevant threshold (e.g., whether Herbert, a borderline case of baldness, is “bald” or “not bald”), and then, in the context of a Problem case, pretend we have to choose whether one option exhibits more of the covering value, or whether they exhibit it equally.Footnote ¹² For instance, we would have to decide whether Mozart or Michelangelo is more creative, or whether they are equally creative or—to use a different example of Chang's—whether a particular act of promise keeping or a particular act of bringing about great happiness exhibits more “moral goodness,” or whether they exhibit it equally. Chang argues that we resolve the borderline and Problem cases differently.Footnote ¹³ While in borderline cases like bald-or-not-bald, she writes, “it is perfectly permissible to resolve the indeterminacy in favor of application or not by arbitrary stipulation,” in Problem cases only “substantive” argument could resolve the comparison permissibly.Footnote ¹⁴ If people disagreed on how to classify the Mozart or promise-keeping comparisons, there would be, Chang writes, “a genuine substantive disagreement between them, not a mere clash of arbitrary decisions.”Footnote ¹⁵ Chang then maintains that no conception of semantic vagueness explains how we could employ substantive debate, as opposed to arbitrary stipulation, to resolve vagueness.Footnote ¹⁶ Given that substantive debate will concern the meaning and interpretation of the relevant concepts, and given that vagueness entails that the meaning of such concepts will not determine the answer, what could there be to debate substantively? Thus, Chang concludes, we know that vagueness does not cause the Problem: only substantive argument could resolve such cases acceptably and substantive argument is incompatible with the resolution of vagueness.

As to Chang's first claim—that only substantive argument, as opposed to arbitrary stipulation, could acceptably resolve Problem cases—consider Herbert and Greg, two borderline cases of baldness. We want to know who is balder. While Herbert is balder in the front, Greg is balder in the back. We might imagine a small improvement problem, where making Herbert a touch balder fails to resolve the comparison.Footnote ¹⁷ Forced resolution of Herbert v. Greg would, I believe, be a matter of arbitrary stipulation, rather than substantive disagreement. If two people disagreed, they would have nothing to debate. If this holds, then we have determined, contra Chang, that resolution of Problem cases can be a matter of arbitrary stipulation.

As to Chang's more important second claim—that substantive argument is incompatible with the resolution of vagueness—I will attempt here to explain the possibility and, crucially, the limits, of providing reasons and substantive arguments to resolve vagueness as a practical matter. In the first instance, I am searching for an explanation that does not appeal to “external” considerations beyond the particular covering value, such as which choice meshes better with one's character or life plan.Footnote ¹⁸ I discuss this possibility further below. To be sure, Chang's claim was not meant to cover this possibility; her claim is that, looking only to the meaning of the covering value, we cannot use reason and substantive argument to resolve vagueness.

Chang explains that covering values have constitutive “contributory values.”Footnote ¹⁹ The contributory values of “baseball skill,” for instance, would be foot speed, ability to catch a baseball, ability to hit a curveball, etc. To compare two people's skill at baseball, we are said to examine the extent to which each person exhibits these contributory values. The degree to which we can employ reason to resolve a Problem case, I argue, depends on the nature of this covering value–contributory value relationship. When a vague covering value has one or two well-defined contributory values, as with the covering value of “baldness” and the contributory value of “hair coverage”—which we could possibly break down into “front of the head hair coverage” and “back of the head hair coverage”—there is nothing to substantively debate. We either think Herbert is bald, and balder than Greg, or we don't. We will report such beliefs as if they were scientific measurements.

However, when a vague covering value has numerous, interdependent covering values—as in the case of “creativity” and “moral goodness”—substantive debate involving the provision of reasons may sometimes be possible when forced to resolve the comparison. Let us call such covering values organic covering values. The term is taken from G.E. Moore's theory of “organic unities,” whereby intrinsic value often belongs to “organic” complexes, the value of which “bears no regular proportion to the sum of the values of its parts.”Footnote ²⁰ Organic covering values are vague for a number of reasons, in particular: we cannot precisely list the relevant contributory values; we cannot precisely state their relative importance; and we cannot precisely understand how they interdepend on one another. To demonstrate the interdependence of some contributory values, notice that improving one's eyesight would fail to improve his “baseball skill”—understood as the ability to increase the chances, on average, that a randomly selected baseball team will win a baseball game—if he lacked the ability to hold up a bat or to stand up. It would be an improvement to a particular baseball skill—an ability to perceive balls and strikes—but in a manner that does not impact the covering value of baseball skill simpliciter. Certain contributory values, in this way, are relevant only in the presence of other contributory values.Footnote ²¹

To see how we can sometimes provide reasons to resolve Problem cases centered on an organic covering value, consider a modified version of Raz's classic Problem case.Footnote ²² We have to choose one of two career options for Sarah: Financially Poor Clarinetist (FPC) or Miserably Bored Lawyer (MBL). The covering value at issue—“career goodness”—has numerous, often interdependent contributory values: skill in one's profession; career earnings; possibilities for advancement; work hours; types of people one will interact with, etc. That we are being forced to resolve such cases as a practical matter is important. Our real, theoretical conclusion as to whether FPC or MBL is the better career is clear: it's vague.Footnote ²³ On some “weightings” of the contributory values of “career goodness,” FPC is the better choice for Sarah, while on others MBL is better. But it seems possible to accept this conclusion and nonetheless debate FPC v. MBL substantively when forced to choose.

The explanation resides in the meaning of being forced to choose. It means, I believe, that one has to choose a “weighting” of the contributory values that will resolve the comparison. In the case of FPC v. MBL, maybe one chooses a weighting that prioritizes one's passion for her work, which leads to selecting FPC, or alternatively one that prioritizes financial security, which leads to MBL. The key is that it is possible to provide reasons for choosing one such weighting over another, and it is consistent with doing so that one accepts that each weighting on its own misses something fundamental about the meaning of “career goodness.” By accepting the possibility of multiple weightings, one is not committed to their absolute and context-independent equality at capturing the covering value's meaning. And when forced to choose, substantive debate concerns the following question. Among the weightings that could resolve this particular comparison in this particular context, which does the best job of capturing the meaning of the covering value, of, say, career goodness? In this way, we might describe the debate as being over which weighting is the least arbitrary. An important caveat is that some weightings would fail to resolve a comparison—like, for many people with regard to FPC v. MPL, a weighting that prioritized intellectual pursuit—and would thus be ineligible for debate when one was forced to choose.Footnote ²⁴

This method has rather severe limitations. Sometimes, when considering an organic covering value, its contributory values will be very difficult to conceptualize, or they will be entirely unknown, such that discovering any coherent “weighting” to argue for would be impossible or artificial. I suspect that this would be the case with regard to Mozart v. Michelangelo and “creativity.” While creativity is surely an organic covering value, with various considerations that interact in complex ways, the number and nature of these considerations is generally unclear. To create a list of contributory values that we ought to consider in judging someone's creativity would for the most part be forced and unhelpful—perhaps even dishonest. There are limits to the usefulness of Pro v. Con lists. At other times, one may be able to conceptualize the relevant contributory values, but there will be so many of them, and they will be so similarly weighted, and perhaps so vague and slippery themselves, that one simply cannot reach a considered judgment on the comparison. One's level of confidence in determining which weighting captures the greatest amount of the covering value's meaning will be low, perhaps vanishingly so. Rarely does life present vagueness as neatly as it does in some of Chang's Problem examples or in FPC v. MBL, where the considerations at issue are so limited and well-defined. In FPC v. MBL, for instance, we focused on only two contributory values, both of which have relatively clear meanings: financial security and passion for one's work.

The larger point, which I will return to when considering retributive proportionality, is that vagueness is on a spectrum, and some covering values and comparisons are vaguer than others. Substantive argument will not take us far when dealing with a certain level and type of vagueness, even if, contra Chang, it has some role to play elsewhere in the context of resolving vagueness. Even with those comparisons where substantive argument could have a role to play, like FPC v. MBL, its insights are rather coarse. For instance, if one had to choose the salary level of MBL that created an option equal to FPC in terms of career goodness, then substantive argument would not take us far; no weighting would seem to determine the matter. The comparison demanded by sentencing proportionality is structured in this manner (e.g., how many days in prison equals punching someone in the arm?).

C. External Reasons

Finally, where we have a practical dilemma centered on a vague covering value, and we cannot discern a “least arbitrary” weighting of the contributory values that will resolve the comparison, reason may have yet another arrow in its quiver when seeking the most justified choice. As suggested above, it may sometimes be possible to appeal to “external” reasons, which are relevant to the choice, but not to the options’ relative covering value exhibition. Even if we cannot declare a possible clarinet career better than, worse than, or equal to a possible law career, we might be able to use reason to choose between the two options by taking into account considerations that are not themselves relevant to “career goodness” as normally understood. Imagine that pursuing the clarinet career would require one to move cities, which would in turn very negatively impact the education of one's children. That the clarinet career is worse for one's children does not make it any worse at exhibiting “career goodness,” but it does provide one with a reason to choose the law career over the clarinet career. Of course, this reason may prove dispositive even if the clarinet career were definitively better than the law career, such that one had reason to pursue a worse career than she might have otherwise, with that reason being her children's well-being or her duties to her children. Another example of an “external” consideration is how the choice meshes with one's past commitments and conception of the good life as a whole, as Charles Taylor explains.Footnote ²⁵ Along these lines, when choosing between vaguely equal or related options, we may have reason to select the one that enables us to lead a life of integrity or narrative unity (e.g., we have thus far been committed to a life of music and, even though neither option is better as a career, to choose the law over the clarinet career would dishonor that past). These analyses will prove important in Section III, where I consider which “external” reasons a retributivist state might appeal to when selecting an option within the wide array of vaguely proportional sentences.

Section II has presented several arguments in favor of Vagueness, the idea that the “small improvement problem” is caused by vague covering values. I have attempted to unpack the structure of comparisons, to show how they rely ultimately upon noncomparative judgments; and that when we cannot resolve a comparison, it means that there is indeterminacy within our noncomparative judgments. Covering value vagueness, I have argued, generates such noncomparative indeterminacy, which means, in turn, that it generates our comparative uncertainty. I have also addressed Chang's argument that since the resolution of borderline cases must be a matter of arbitrary stipulation and the resolution of Problem cases is a matter of substantive argument, we know that vagueness does not cause the Problem. In reply, I have (1) presented an example of a Problem case, the resolution of which is a matter of arbitrary stipulation and (2) explained how reason can sometimes—to some degree—resolve a vague comparison, either by discerning a “least arbitrary” weighting of the contributory values that will resolve the comparison in a particular context, or by discerning dispositive “external” reasons.

A. Cardinal Proportionality

There are a few foundational issues to resolve before setting the comparison at the center of proportionality analysis. First is the distinction between ordinal and cardinal proportionality. “Ordinal” proportionality is the ideal that the scale of punishments ought to reflect the scale of offense severity, so that the “graver” the offense, the more severe the punishment. This is contrasted with “cardinal” proportionality, which is meant to “anchor” this scale by determining, for a minimum of one or possibly two offenses,Footnote ³² the absolutely deserved punishment, that is, the punishment deserved only by reference to the offense's moral gravity. The ordinal scale is set, in theory, by reference to these few points of cardinal judgment. Without such cardinal anchors, ordinal proportionality loses much meaning, as many commentators have noticed, since its principles would be realized even if the scale were set at an extremely high level, where minor regulatory offenses receive 100 lashes, and on up for the worst offenses, or at an extremely low level, where the worst offenses receive a $100 fine, and on down to a 10-cent fine.

Retributivists thus cannot escape the complexities of proportionality by appealing only to the less contentious ordinal conception. As Lacey and Pickard write, “[T]he very idea that a certain punishment is deserved—and with it, the whole basis for proportionality's purported capacity to set upper limits on, or to generate substantial criteria of fittingness of, punishment—rests on cardinal rather than ordinal proportionality.”Footnote ³³ Retributivists who accept this point, and set out to fix a point or two on an absolute scale, miss a larger criticism: if we can determine the cardinally proportional punishment for any offense, in order to set the ordinal scale, we should be able to do the same for every offense, and thus we should not require the ordinal conception at all. One might reply that the cardinal punishments for certain offenses—maybe murder—are easier to determine than others. Regardless, the takeaway point is that proportionality requires the establishment of at least some cardinal points, and so we will focus here on that possibility. Hereafter, by proportionality I refer to the cardinal conception.

B. Proportionate Injuries

How could one year in prison or a $1,000 fine be “proportionate with” or “equal to,” in any sense, punching someone? In determining the magnitude of punishment necessary to “negate” a crime, Hegel attempts to provide such an explanation. He argues that the “identity” of crime and retribution “is not an equality in the specific character of the infringement” but an equality of “value.”Footnote ³⁴ Hegel argues that the equivalence between punishments and crimes can be found at an abstract level, in terms of their “character as injuries.”Footnote ³⁵ This concept, which I refer to as “injuriousness,” and which is synonymous with “moral gravity,” is the relevant covering value, according to Hegel. He explains that the concept has “a determinate qualitative and quantitative magnitude.”Footnote ³⁶ By “qualitative magnitude,” Hegel refers to the offender's culpability level (e.g., intent, knowledge, recklessness, and negligence). The talionic, eye-for-an-eye methodology of retributive proportionality, by comparison, considers only the “quantitative magnitude” of the harm caused, at least as traditionally interpreted.Footnote ³⁷ It would not matter whether the offender intentionally poured or recklessly spilled acid into her victim's eye; in both cases we ought to intentionally pour acid into her own eye in response. For modern retributivists like Hegel, though, the gravity of an offense, and thus the severity of the punishment demanded by proportionality in response, increases not only with the amount of harm caused, but also with the degree of the offender's culpability.

Proportionality demands some ratio, some proportion, of crime injuriousness to punishment injuriousness. Classically, the ratio is 1:1—a proportion of equality. A proportional punishment will exhibit, on this view, no more (and, ideally, no less) injuriousness than the underlying offense. Though, accepting the concern with “qualitative magnitude,” we might conclude that a proportional punishment should be less harmful than the offense. The rationale is that the impact of culpability goes both ways, and we need to account for the fact that criminal punishments are thoroughly intended by the state. Thus, if an offender causes 10 units of harm due to her recklessness, then her proportional punishment would be less than 10 units of harm, given that these units would be delivered intentionally. We might imagine, following Camus, that even intentional crimes like murder cannot match the heavy purposiveness and deliberateness of the criminal process, such that even for intentional crimes, the amount of penal harm must be less than that inflicted on the offender's victim.Footnote ³⁸ To be clear, on the view considered here, where we limit the punishment's harm due to these culpability issues, the ratio of punishment to offense injuriousness remains 1:1. Even if the proper ratio is greater or lesser than 1:1, such that the injuriousness of the punishment should be greater or lesser than that of the offense, proportionality still requires a consistent ratio up and down the offense spectrum. That is, an extra “unit” of offense injuriousness should lead to the same amount of additional punishment injuriousness, regardless of the starting point along the spectrum.

We now have a better grasp of the relevant comparison. In setting a proportional punishment, a decision-maker—say, a judge employing her sentencing discretion or a lawmaker writing sentencing guidelines—is tasked first with assessing the injuriousness of the offense, understood as a combination of the harm caused and the offender's culpability. The next step is to take this “value” and then compare which of the available punishments exhibit the same degree of injuriousness, or whatever greater or lesser degree is required by a different ratio.

C. Analyzing the Comparison

The comparison of crimes and punishments with regard to the covering value of injuriousness will generate Problem cases, as indicated at the outset. Which is more injurious, the crime of embezzling $250,000 from a pension fund (Emb250) or the punishment of 25 months’ imprisonment (25Mo)? Or perhaps they are equally injurious, such that 25 months is the perfect retributivist punishment if the ratio is 1:1? This is a hard comparison. As stated above, if we imagine that the offender embezzled only $240,000, it would not help us to resolve the comparison, nor would it if she received only 24 months’ imprisonment.

Consistent with his analysis of other Problem cases, Raz would deem Emb250 and 25Mo incomparable, all the way down. They are injurious in such different ways, he might argue: one affects many people a little financially, while the other affects one person significantly in terms of her liberty over a period of time. Unless the crime matched up very closely with the form of punishment—e.g., the crime of false imprisonment and the punishment of imprisonment—it seems that Raz would have to deny the possibility of any proportionality judgments, and thus would reject the ideal of proportional punishments entirely. However, as suggested above, no two options will be incomparable in this deep way. For instance, if we take Emb250 as our “standard,” broadly following John Broome, and imagine a spectrum of sentences from one nanosecond at the bottom, to life without parole at the top, there will be a point in this spectrum above which the prison terms are clearly more injurious than Emb250, and a point below which they are clearly less injurious than Emb250.Footnote ³⁹ Emb250 is thus not irreducibly distinct from 25Mo, given that we can confidently compare Emb250 to options that exhibit the same variables as 25Mo (only in different degrees).

What then is going on with this comparison, where neither option is more injurious, nor are they equally injurious? We know from Mozart v. Michelangelo that the difficulty results from our uncertainty over how much injuriousness a crime and a punishment exhibit when considered independently of each other. How injurious, exactly, is embezzling $250,000 from a pension fund? And 25 months of imprisonment? Our final judgments will not involve any degree of cardinal precision such that we could conclude that one is injurious to, say, 58.6 degrees and the other to 42.7 degrees. This noncomparative imprecision results, in turn, from the vagueness of “injuriousness,” following the above discussion.

Let us unpack its vagueness. Injuriousness, consistent with Hegel's interpretation, has two core contributory values: harm and culpability. Andrew von Hirsch and Andrew Ashworth provide a convincing theory of harm as that which reduces someone's “standard of living”—the “means and capabilities that would ordinarily promote a good life.”Footnote ⁴⁰ It is only one conception of harm, of course, but it is a thoughtful and prominent conception, and there is no reason to believe that any other honest attempt could avoid the problems that beset their theory.Footnote ⁴¹

Von Hirsch and Ashworth argue that “standard of living” has four main components: (1) physical integrity, (2) material support and amenity, (3) privacy, and (4) freedom from humiliation.Footnote ⁴² “Standard of living,” so defined, is doubly organic, because while these contributory values are undoubtedly interdependent, they each in turn have their own set of interdependent contributory values. For example, many instances of material support and amenity (e.g., having a home) depend upon privacy for their impact upon one's living standard; meanwhile, material support and amenity is itself a complex, interdependent mixture of goods that depend on each other for their impact (e.g., food, shelter, clothes, liquid assets, communication devices, access to transportation, access to markets, etc.). Thus, while reduction of living standard seems to be the right metric for measuring harm, it is exceptionally vague. The room for reasonable disagreement over which offense is more significant than another in terms of its impact on one's living standard is expansive. Compare, for instance, the impact of a humiliating crime like being spat on by a stranger to that of a financial fraud that impacts one's material support, or to that of a burglary that impacts one's privacy in addition to one's material support. Finally, even if we were able to emerge from this harm analysis unscathed by vagueness—which we cannot—we would need then to combine it, somehow, with the culpability judgment. H.L.A. Hart expresses this final worry succinctly: “Is negligently causing the destruction of a city worse than the intentional wounding of a single policeman?”Footnote ⁴³ In this manner, we see how limited proportionality is as a device for determining criminal sentences. It requires precise measurements of “injuriousness,” which, due to the vagueness of that concept, cannot be determined.

We have here a vague comparison, moreover, that cannot be refined significantly by substantive argument when we are forced to decide, at least not when that argument is focused on the covering value itself, as opposed to “external” considerations. Of the contributory values that we can conceptualize, they are too numerous, too similarly weighted, and too vague and interrelated for us to be able to reach a considered judgment as to which weighting does the best job of capturing the meaning of injuriousness in a given case. We must add to this complexity a dose of humility regarding our ability to even conceptualize all the relevant considerations to be incorporated into our weighting. Any claim that a particular weighting is best—e.g., one that prioritized humiliating harms and ignored culpability—would be distinctly artificial. It is doubtful, furthermore, that any weighting could resolve the question of how many days in prison, or how large a fine, equals or is proportionate to the injuriousness of a particular offense. Substantive argument, accordingly, would not take us very far in the large majority of cases. What we are left with, if we appeal to proportionality alone, is an extraordinarily wide zone of discretion. And we should not be surprised, then, that Swedish and American penal systems have such dramatically different sentencing scales, even though they both look to the concept of retributive proportionality for authoritative sentencing guidance.Footnote ⁴⁴

This is not to say, however, that proportionality provides no sentencing guidance or limits at all. Just as we could determine that Michelangelo was conclusively more creative than Novice Composer, even though creativity is a vague, organic covering value, there are undoubtedly situations in which a form of punishment (say, twenty years in prison) is conclusively more injurious than a particular offense (say, theft of a bicycle).Footnote ⁴⁵ A twenty-year sentence would be deemed disproportionate to a bicycle theft in any system committed to retributive proportionality. Thus, while injuriousness is very vague, it nonetheless has some level of conceptual definition. Though, we should emphasize that such retributive upper limits would be largely irrelevant in the context of serious offenses, where severe or even degrading punishments would reside within the wide array of proportionally injurious sentences.Footnote ⁴⁶

D. Parity and Proportionality

Parity is less capable than Vagueness of delivering this critique of retributive proportionality. While Parity could inform us that the zone of sentencing discretion is wide, such that an offense is “on a par” with a wide range of punishments, it would mischaracterize the nature of the comparative relationships inside the zone of discretion. For parity, as conceived by Chang—and as understood colloquially—is connected closely to a judgment of equality; it is meant to explain, in particular, cases of seemingly “rough” or “imprecise” equality, as in the case of Mozart v. Michelangelo.Footnote ⁴⁷ Chang writes of parity emerging “between items that bear very different aspects of V and yet are nevertheless ‘in the same neighbourhood’ of V-ness.”Footnote ⁴⁸ But sometimes the covering value (the V) can be so vague, as indicated above, that deeming Problem options “on a par,” given this connection to equality, is inapposite.Footnote ⁴⁹ It fails to illuminate to deem embezzling $250,000 “roughly” or “imprecisely” equal to 25 months in prison with regard to injuriousness, given that it may also be “roughly” equal to 2 months or 10 years. The notion of rough or imprecise equality in this case—and thus of the options being “on a par”—has little purchase. The “neighbourhood” of V is so large that it does not help to determine that both options are residents.

Related, Parity is incapable of deeming options “really on a par” or “a little on a par.” Parity is either on or off, full stop, just like genuine equality; options cannot be really equal or a little equal. Thus, if Mozart is only “on a par” with a handful of sculptors in terms of creativity, while Emb250 is “on a par” with a wide array of punishments in terms of their injuriousness, Parity cannot distinguish between individual Problem cases based upon these comparisons. It cannot inform us that Mozart is much more closely related to Michelangelo in terms of his creativity than Emb250 is to 25Mo in terms of its injuriousness. The picture that Parity draws is of close comparisons—almost equality—up and down the zone of sentencing discretion, as if comparing Emb250 with all the sentences proportional to it is like comparing Michelangelo with many slightly different versions of Mozart. Vagueness, however, explains that, depending on the covering value's level of vagueness, a comparison can be a little vague or, as with regard to injuriousness, really vague. We have little sense of how a crime and a punishment relate with respect to injuriousness, except at the far extremes. Vagueness, unlike Parity, can account for such situations, where we know that the options are comparable, but our judgments of their relative worth are profoundly uncertain; and, unlike Parity, it can warn us that such comparisons, when engineered to deliver ethical or practical guidance, are of limited value.

Let us take stock. I have argued, contra Ruth Chang and Joseph Raz, that the small improvement problem is caused by vague covering values, not “parity” or “incomparability.” I have then applied this analysis to the retributivist ideal of the proportional penal sentence. I have attempted to unpack the comparison between a crime and a punishment upon which this ideal is based, arguing that the relevant covering value is “injuriousness,” and that the vagueness of this concept generates Problem cases. I have argued that “injuriousness” is not only vague, but exceptionally vague, featuring multiple layers of interdependent covering values, such that proportionality analysis is incapable of providing meaningful sentencing guidance or limits.

A. Retributivism and Inviolability

Pretend that retributive desert is our singular sentencing aim. We have no concern for deterrence, rehabilitation, or whatever it may be. Only retributive desert. We are then presented with an offender who, say, stood watch while his accomplice broke into someone's house and stole $5,000 worth of goods. How much punishment does he retributively deserve for wronging the homeowner in this way? Let's say that after considering the meaning of “injuriousness,” surveying contemporary and historic retributive sentencing scales worldwide, and engaging in reflective equilibrium, we decide that the range of “not undeserved” sentences for this offense is between 1 and 100 months of imprisonment.Footnote ⁵⁵ One could reasonably argue for a range even wider than this, I think, but the 1–100 scale provides some analytical clarity. How do we select a punishment within this range, given that our only positive sentencing aim is retribution? The answer is clear. We ought to sentence the offender to the least harmful “not undeserved” sentence: 1 month of imprisonment. To sentence him any more severely would just be cruel. That is, it would inflict wanton harm. It would harm him to a greater degree without in any way increasing the realization of our penal aim.

Let us now return to the real-world scenario where we have nonretributive sentencing aims, as well. Let us assume that sentencing offenders to the least harmful “not undeserved” sentence is not the optimal choice for realizing these other aims. Let us assume, more particularly, that sentencing offenders in this manner will lead to a dramatic increase in crime. Limiting retributivists would then dutifully argue that we ought to increase sentences to the optimal point for the purpose of generating deterrence, so long as we stay within the retributivist range—say, 50 months for offenses as serious as the one just mentioned. In this way, where the zone of discretion is exceedingly wide, the retributivism within limiting retributivism fails to provide much of any sentencing guidance, with all the work being done by the “external” nonretributivist considerations. The notion, then, that we are punishing an offender for the purpose of giving him his just deserts is almost completely diluted. Nonetheless, limiting retributivists would insist that the offender has no complaint if we increase his sentence, since we still do not punish him more than he deserves—and we might as well, because the rest of us will be much better off.

It strikes me that the offender could reasonably object that he is being sacrificed for the greater good in this instance. More particularly, he could reasonably object that he is being sacrificed to mitigate a social problem—future crime—for which he has no personal responsibility. When the state is concerned, and only concerned, to give him his just deserts he receives a one-month sentence. The only reason for inflicting a greater degree of penal harm is that it would help the rest of us to mitigate a social problem. But that is a good reason for harming someone more than we would otherwise be entitled to only if he is to some degree responsible for that problem. If he is not responsible, then by harming him further we fail to respect his inviolability. The principle of human inviolability just is the idea that it is wrong to harm people for the purpose of mitigating social harms or threats for which they lack responsibility (or at least the principle can be formulated as such).Footnote ⁵⁶ And if there are people in society who require the threat of nonmild punishments to desist from crime, the offender could rightly wonder why they are his problem.Footnote ⁵⁷ For without their presence, he would receive much less prison time, perhaps years less. The mere fact that he committed a wrong is not a sufficient explanation, given that, if we looked only to that wrong, he would receive a much more lenient sentence.

This argument has dramatic implications for retributivism. When determining how much penal harm to inflict upon an offender, the retributivist ought to ask herself what is the least harmful punishment that is “not undeserved” in terms of its degree of injuriousness. Given the remarkable vagueness of injuriousness, this principle will generate an extremely mild sentencing regime—mild by comparison to any contemporary system, let alone the harsh American and British systems.Footnote ⁵⁸ This is a prima facie attractive conclusion in this age of penal severity and mass incarceration.

B. Retributivism and Deterrence

But the question nonetheless remains. Will this be enough punishment for the sake of our nonretributive penal aims, most importantly for the sake of crime deterrence? Crime deterrence is, of course, not a luxury item. It is not simply about reducing the aggregate amount of harm; it is about maintaining the social trust that grounds a well-functioning and cooperative civil society, upon which, in turn, the possibility of human flourishing relies.Footnote ⁵⁹ While we cannot examine this issue in depth, there are at least three reasons to think that the least harmful “not undeserved” sentences would be enough punishment to reduce the objective threat of crime sufficiently. First, there is considerable evidence that the certainty of receiving some level of punishment is more important for the purpose of deterrence than the severity of the punishment received.Footnote ⁶⁰ Second, the money saved from lengthy sentences could be spent on nonpenal crime reduction policies, such as police presence (which increases the certainty of punishment)Footnote ⁶¹ and investments in the community like early childhood development programs.Footnote ⁶² Third, the threat of punishment is not the only reason that people desist from crime and cooperate; there are also, for instance, noncriminal legal institutions, like tort and contract law, as well as nonlegal social norms. Whether an extremely mild system of punishment would indeed be sufficient for the purpose of deterrence is a difficult empirical question.Footnote ⁶³ Importantly, the answer may vary from society to society, given all the variables that impact crime rates.Footnote ⁶⁴

Let us assume, though—not outrageously—that such a mild sentencing regime will be insufficient for the purpose of deterring crime.Footnote ⁶⁵ In that case, even if we accepted all of the retributivist claims about who deserves punishment and why, retributivism would fail as the foundation of state punishment; or at least it would fail as the sole foundation of state punishment. For it could justify the infliction of punishment, but not the infliction of enough punishment for the criminal law to realize its nonretributive function of maintaining a cooperative civil society.

What then for the retributivist? To inflict more penal harm than the least harmful “not undeserved” sentence, she would need to secure a nonretributivist theory of punishment, and one that did not itself violate human inviolability. It could not be an unadulterated utilitarianism, of course, given our refusal to merely sacrifice people to mitigate social problems for which they are not responsible. Utilitarians have a famously hard time explaining what is wrong with punishing innocent people, exactly, if doing so is an efficient means of decreasing crime, increasing happiness, and so forth. How, then, could we justify harming an offender for the purpose of deterrence if we can appeal to neither (a) the limiting retributivist argument that the punishment is not undeserved nor (b) the plain fact that doing so maximizes social utility?

In closing this section, I will sketch two examples of what such an argument would look like. The basic intellectual challenge is to explain how it is the offender's personal responsibility to decrease the threat of future crime, such that harming him for that purpose does not merely sacrifice him for the greater good. First is Victor Tadros's “duty” theory of punishment.Footnote ⁶⁶ Tadros argues that the offender has a duty to rectify the wrong he has committed against his individual victim. The offender fulfills this duty, Tadros continues, by protecting his individual victim from a future wrong. The offender can best achieve this, in turn, by allowing himself to be harmed by the state for the sake of general deterrence, thereby contributing to an umbrella of protection that will shield his individual victim from a future wrong. Second are the “corrective justice” and “social defense” theories of punishment that I have developed in recent work.Footnote ⁶⁷ I argue that the criminal law is a system of protections, upon which all citizens rely for their assured liberty, and that an offender weakens this system by contributing to “criminality,” not merely the perceived but the objective threat of crime in society. I conclude that the state is entitled to harm the offender for the sake of general deterrence as a means of rectifying his criminality contributions; over time, ideally, it would be as if he had never contributed to criminality at all, in terms of the average threat of crime faced by society. Assuming that extremely mild retributivist sentences were insufficient for the purpose of deterrence, then even the most ardent retributivist would have to bolt some such theory onto their system, with the result being that the offender both (a) deserves to suffer or to be censured, irrespective of its consequentialist impact and—potentially more importantly when it comes to justifying his punishment—(b) has a personal duty to contribute to crime deterrence.