1. Ruth Chang refers to it as the “small improvements argument.” Chang, Ruth, The Possibility of Parity, 112 Ethics 659, 667 (2002)CrossRefGoogle Scholar. For earlier explications of the phenomenon, see Sousa, Ronald de, The Good and the True, 83 Mind 534, 544–545 (1974)CrossRefGoogle Scholar; L.J. Savage, The Foundations of Statistics (1954), at 17.

2. Norval Morris, Madness and the Criminal Law (1982), at 179.

3. See id.; Norval Morris & Michael Tonry, Between Prison and Probation: Intermediate Punishments in a Rational Sentencing System (1990); Frase, Richard S., Punishment Purposes, 58 Stan. L. Rev. 67 (2005)Google Scholar; Richard Frase; Just Sentencing: Principles and Procedures for a Workable System (2012).

4. Ruth Chang, Introduction, in Incommensurability, Incomparability, and Practical Reason 1, 4–5 (R. Chang ed., 1997).

5. Chang, supra note 1, at 659.

6. Joseph Raz, The Morality of Freedom (1986), at 321–366.

7. Id. at 334; see also Elizabeth Anderson, Practical Reason and Incommensurable Goods, in Incommensurability, Incomparability, and Practical Reason 90 (Ruth Chang ed., 1997) (arguing that intrinsic and instrumental goods are fundamentally incomparable).

8. See Chang, supra note 4, at 14–17; see also Tribe, Laurence, Policy Science: Analysis or Ideology?, 2 Phil. & Pub. Aff. 66 (1972)Google Scholar; Griffin, James, Are There Incommensurable Values?, 7 Phil. & Pub. Aff. 39 (1977)Google Scholar.

9. Chang, supra note 1, at 664–665, 679–688. See also James Griffin, Well-Being: Its Meaning and Measurement (1986), at 80–81, 96–98, 104 (discussing “rough equality”); Thomas Hurka, Perfectionism (1993), at 87; John Laird, An Enquiry into Moral Notions (1935), at 245–264.

10. See Derek Parfit, Reasons and Persons (1987), at 430–431 (referring to “rough comparability”).

11. There are theorists who argue that epistemic uncertainty, rather than semantic indeterminism, is responsible for vagueness itself, such that there are precise, cardinal answers in terms of Mozart and Michelangelo's creativity levels, but we simply lack the epistemic resources to discern them. See, e.g., Timothy Williamson, Vagueness (1994). I will continue in this paper on the assumption that vagueness is caused by semantic indeterminism, that the difficulty of Mozart v. Michelangelo is grounded in the imprecision of “creativity” all the way down. Nonetheless, in terms of the degree to which we can use reason to resolve vague practical dilemmas—which is our ultimate aim in this section—very little hangs on whether vagueness is semantic or epistemic. See infra note 24. On vagueness as semantic indeterminism, see, e.g., Fine, Kit, Vagueness, Truth and Logic, 30 Synthese 265 (1975)CrossRefGoogle Scholar.

12. Chang, supra note 1, at 679–686. This methodology, of pretending we are “forced” to choose, is rather probative. For in our everyday lives, we are “forced” to choose between Problem options all the time—Should I play basketball or read a novel? Should I support Candidate A or Candidate B?—with the pragmatic principle that some choice will be better than none doing the “forcing.”

13. Id. at 682.

14. Id. at 682–683.

15. Id. at 685.

16. Id. at 686.

17. Johan Gustaffson introduces a baldness Problem case. Gustaffson, Johan E., Indeterminacy and the Small-Improvement Argument, 25 Utilitas 433, 436 n. 10 (2013)CrossRefGoogle Scholar.

18. For analysis of the various methods of resolving hard comparisons beyond considerations inherent to the particular covering value, see Urbina, Francisco J., Incommensurability and Balancing, 35 Oxford J. L. Stud. 575, 596–603 (2015)CrossRefGoogle Scholar.

19. Chang, supra note 4, at 5.

20. G.E. Moore, Principia Ethica (1903), at 27–28.

21. Below I explain how “injuriousness,” the covering value at the center of proportionality analysis, is doubly organic, insofar as its interdependent contributory values each have their own set of interdependent contributory values. See infra Section II.C.

22. Raz, supra note 6, at 328.

23. As Chang writes, “[o]f course in one way, there is already a ‘resolution’ in a borderline case: it is borderline.” Chang, supra note 1, at 682.

24. As indicated above, I am focusing here on methods of resolving semantic vagueness, but this could be a method of resolving epistemic vagueness as well (if vagueness was in fact epistemic). On the epistemic view, there is a precise answer, in reality, as to whether FPC or MBL exhibits more “career goodness.” The method, then, would not be about finding the weighting of contributory values that captures the greatest amount of the covering value's meaning. It would rather be about reaching some sufficient level of confidence that could serve as an evidentiary tie breaker, as was incisively suggested by an anonymous reviewer. So, the epistemicist would admit that she does not know the answer to FPC v. MBL, but given that there must in fact be an answer, a good argument in favor of a particular weighting would mean that there is now sufficient reason to choose either FPC or MBL, rather than to merely flip a coin.

25. See Charles Taylor, Leading a Life, in Incommensurability, Incomparability, and Practical Reason 170 (Ruth Chang ed., 1997). See also Michael Stocker, Abstract and Concrete Value: Plurality, Conflict, and Maximization, in Incommensurability, Incomparability, and Practical Reason 196 (Ruth Chang ed., 1997) (arguing that alternatives are rarely considered in the abstract, but rather are usually considered in more concrete ways, such as whether they contribute to one's own good life).

26. See generally Timothy Endicott, Vagueness in Law (2000).

27. I will not consider here how the above sections relate to constitutional proportionality analyses, which involve “balancing” various constitutional considerations in determining the legality of state action. On this issue see generally Barak, Aharon, Proportionality and Principled Balancing, 4 Law & Ethics Hum. Rts. 1 (2010)CrossRefGoogle Scholar; Timothy Endicott, Proportionality and Incommensurability, in Proportionality and the Rule of Law: Rights, Justification, and Reasoning 311 (Grant Huscroft, Bradley W. Miller & Gregoire Webber eds., 2014); Craig, Paul, The Nature of Reasonableness Review, 66 Current Legal Probs. 131 (2013)CrossRefGoogle Scholar; Alexy, Robert, The Construction of Constitutional Rights, 4 Law & Ethics Hum. Rts. 20 (2010)Google Scholar; Webber, Gregoire, Proportionality, Balancing, and the Cult of Constitutional Rights Scholarship, 23 Can. J. L. & Juris. 179 (2010)CrossRefGoogle Scholar.

28. “Censuring” retributivists, like Antony Duff, as well as “traditional” or “strict” retributivists, like Michael Moore, are committed to proportionality. As Duff writes:

R.A. Duff, Punishment, Communication, and Community (2001), at 132 (internal citations omitted).

29. Since the mid-1970s this ideal has grown increasingly influential within American, British, and Nordic sentencing policy, to a significant degree displacing concerns with rehabilitation, deterrence, and incapacitation. See David Garland, The Culture of Control (2001); David Garland, Punishment and Welfare (1985); F. A. Allen, The Decline of the Rehabilitative Ideal (1981).

30. See Nicola Lacey & Pickard, Hanna, The Chimera of Proportionality: Institutionalising Limits on Punishment in Contemporary Social and Political Systems, 78 Mod. L. Rev. 216, 227–228, 231 (2015)Google Scholar.

31. Id. at 216.

32. See Roebuck, Greg & Wood, David, A Retributivist Argument Against Punishment, 5 Crim. L. & Phil. 73 (2011)Google Scholar.

33. See Lacey & Pickard, supra note 30, at 227.

34. G. W. F. Hegel, Elements of the Philosophy of Right (Allen W. Wood ed. & H. B. Nisbet trans., 1991), at 127 (§101).

35. Id. at 128 (§101).

36. Id. at 127 (§101).

37. See Black's Law Dictionary (6th ed. 1990), at 913 (Lex talionis “requires the infliction upon a wrongdoer of the same injury which he has caused to another” and is “expressed in the Mosaic law by the formula, ‘an eye for an eye; a tooth for a tooth,’ etc.”). The Bible is in fact ambivalent with regard to the talionic ideal, calling for non-talionic punishments in a number of instances. See Exodus 21-22, in The Holy Bible: King James Version (2010) (“And he who curses his father or his mother shall surely be put to death,” id. at 21:17).

38. Albert Camus, Resistance, Rebellions, and Death (J. O'Brien trans., 1974), at 199.

39. John Broome, Is Incommensurability Vagueness?, in Incommensurability, Incomparability, and Practical Reason 67 (Ruth Chang ed., 1997).

40. ANDREW VON HIRSH & ANDREW ASHWORTH, PROPORTIONATE SENTENCING: EXPLORING THE PRINCIPLES (2005), at 145.

41. Thanks to an anonymous reviewer for raising this point. See, e.g., Joel Feinberg, The Moral Limits of the Criminal Law, Volume 1: Harm to Others (1987), at 31 (defining a “harm” as a “setback to interest”).

42. Von Hirsh & Ashworth, supra note 40, at 145.

43. H.L.A. Hart, Punishment and Responsibility (1968), at 162.

44. See Lacey & Pickard, supra note 30, at 217, 227–228, 231.

45. See Duff, supra note 28, at 132 (“Such intuitions as we have about proportionality do seem to include intuitions about absolute, as well as relative, proportionality. Five years’ imprisonment would be a grossly disproportionate sentence for a parking offense, and a fine of 10 dollars a grossly disproportionate sentence for a brutal murder.”).

46. What about “fair play” retributivism? Perhaps that theory could provide more definite sentences? Fair play retributivists reject the traditional retributivist idea that an offender, by committing a moral wrong, deserves to suffer or to be censured “because, and only because” it is morally deserved. Michael S. Moore, The Moral Worth of Retribution, in Responsibility, Character, and the Emotions: New Essays in Moral Psychology 179, 179 (Ferdinand Shoeman ed., 1987). Rather, they understand penal desert to derive from a commitment to fairness. If we assume that an offender has benefitted from everyone else's restraint in following the law—not always a safe assumption, Jeffrie Murphy argues—then he has gained an unfair advantage by breaking the law and failing to restrain himself in turn; and the harm or suffering of punishment is thus deserved as a means of stripping away the offender's unfair gain. See Murphy, Jeffrie G., Marxism and Retribution, 2 Phil. & Pub. Aff. 217 (1973)Google Scholar; Morris, Herbert, Persons and Punishment, 52 Monist 475 (1968)CrossRefGoogle Scholar; Dagger, Richard, Playing Fair with Punishment, 103 Ethics 473 (1993)CrossRefGoogle Scholar. See also George Sher, Desert (1987), at 69–90. There are number of well-documented, I think fatal problems with this view, and so I will not examine in detail the nature of fair play proportionality. Most importantly, fair play retributivism requires the position that mala in se offenders have indeed profited from their offenses, “that the unpunished rapist is really better off than men and women who resist the temptation or feel no temptation to rape,” as M. Margaret Falls writes. Falls, M. Margaret, Retribution, Reciprocity, and Respect for Persons, 6 Law & Phil. 25, 31–32 (1987)CrossRefGoogle Scholar. There is the further problem that we seem less tempted by mala in se offenses than by mala prohibita offenses, as Antony Duff argues. Would fair play theory entail that the former deserve less punishment than the latter? See R.A. Duff, Trials and Punishments (1986), at 213. Duff writes: “[T]alk of the criminal's unfair advantage implies that obedience to the law is a burden for us all: but is this true of such mala in se? Surely many of us do not find it a burden to obey the laws against murder and rape, or need to restrain ourselves from such crimes: how then does the murderer or rapist gain an unfair advantage over the rest of us, by evading a burden of self-restraint which we accept?” Id. Regardless, we should not think that fair play sentencing could proceed with precision. How many days in jail is injurious enough to erase the advantage that someone gained by punching someone? Thus, instead of comparing the injury of the offense with the injury of the punishment, fair play proportionality would demand that we compare an injury (the punishment) with a benefit (the offense) in terms of their impact (positive or negative) on one's well-being or living standard. If anything, this comparison is more difficult than the one demanded by traditional retributivism, which at least has the advantage of comparing two forms of injury. I am grateful to an anonymous reviewer for pressing me to consider this issue.

47. See Chang, Ruth, Parity, Imprecise Comparability and the Repugnant Conclusion, 82 Theoria 182 (2016)CrossRefGoogle Scholar.

48. Id. at 193.

49. For relevant discussion see Gert, Joshua, Value and Parity, 114 Ethics 492, 506–508 (2004)CrossRefGoogle Scholar.

50. Morris, supra note 2, at 179 (emphasis added).

51. Frase, supra note 3, at 3–4.

52. Model Penal Code: Sentencing §1.02(2) (2017) (“(2) The general purposes of the provisions on sentencing, applicable to all official actors in the sentencing system, are: (a) in decisions affecting the sentencing of individual offenders: (i) to render sentences in all cases within a range of severity proportionate to the gravity of offenses, the harms done to crime victims, and the blameworthiness of offenders; (ii) when reasonably feasible, to achieve offender rehabilitation, general deterrence, incapacitation of dangerous offenders, restitution to crime victims, preservation of families, and reintegration of offenders into the law-abiding community, provided these goals are pursued within the boundaries of proportionality in subsection (a)(i)…”); American Bar Association, ABA Standards for Criminal Justice: Sentencing (3d ed., 1994); American Bar Association Justice Kennedy Commission, Reports with Recommendations to the ABA House of Delegates (2004).

53. Frase, supra note 3, at 4.

54. Id.

55. Consider the contrast between the U.S. and Swedish sentencing guidelines on burglary. Depending on factors such as criminal history, the value of the property taken, damaged, or destroyed, the degree of planning, and whether the burglar possessed a dangerous weapon, the U.S. Sentencing Guidelines’ recommended range for “residential burglary” is 24 to 210 months (17.5 years). U.S. Sentencing Guidelines Manual §2B2.1 (U.S. Sentencing Comm'n 2016), at 118–120. In Sweden, by comparison, “theft” has a maximum sentence of two years. Brottsbalken [BrB] (Penal Code) 8:1 (Swed.), translation available at https://www.government.se/contentassets/5315d27076c942019828d6c36521696e/swedish-penal-code.pdf. The range is different, however, for “gross theft.” “In assessing whether the crime is gross, special consideration shall be given to whether the unlawful appropriation took place after intrusion into a dwelling, whether it concerned the appropriation of property borne by a person, whether the accused was equipped with a weapon, explosive or similar aid, or whether the act was otherwise of an especially dangerous or ruthless nature, concerned property of considerable value or entailed a keenly felt loss.” Id. at 8:4. If the offense is deemed “gross theft,” the sentencing range is six months to six years. Id.

56. See Robert Nozick, Anarchy, State, and Utopia (1974), at 28–33.

57. On the question of whether harming an offender as a means of deterring would-be future offenders merely sacrifices him for the greater good, see Bronsther, Jacob, Two Theories of Deterrent Punishment, 53 Tulsa L. Rev. 461, 462 (2018)Google Scholar (“[D]eterrent punishment seems to violate the non-sacrifice principle rather straightforwardly, as the state inflicts suffering upon an offender as a prudential warning to would-be future offenders, for whom the offender has no responsibility. I call this the ‘Means Problem.’ Why, if at all, is the state entitled to use offenders as a means of bringing about general deterrence?”); Victor Tadros, The Ends of Harm: The Moral Foundations of Criminal Law (2011), at 113–114, 181–182, 266–267.

58. See Nick Cowen & Nigel Williams, Comparisons of Crime in OECD Countries, CITIVAS: Institute for the Study of Civil Society (April 2012), http://www.civitas.org.uk/content/files/crime_stats_oecdjan2012.pdf (comparing crime and punishment rates within OECD states).

59. On the notion that the function of the criminal law is the maintenance of a cooperative civil society, see Lindsay Farmer, Making the Modern Criminal Law: Criminalization and Civil Order (2016), at 37–60; Nicola Lacey, State Punishment: Political Principles and Community Values (1988), at 160–201; Thomas Hobbes, Leviathan (Richard Tuck ed., Cambridge 1996) (1651), at 86–90; Alice Ristroph, Hobbes on “Diffidence” and the Criminal Law, in Foundational Texts in Modern Criminal Law 23 (Markus D. Dubber ed., 2014); John Finnis, Natural Law and Natural Rights (2d ed. 2011), at 261–262; Neil MacCormick, Institutions of Law: An Essay in Legal Theory (2007), at 293; Hyman Gross, A Theory of Criminal Justice (1979), at 10.

60. See Daniel S. Nagin, Deterrence in the Twenty-First Century: A Review of the Evidence, in Crime and Justice in America: 1975–2025 199 (Michael Tonry ed., 2013); Andrew von Hirsch et al., Criminal Deterrence and Sentence Severity: An Analysis of Recent Research (1999), at 27, 36, 45; Nagin, Steven N. Dulauf & Daniel S., Imprisonment and Crime: Can Both be Reduced?, 10 Criminology & Pub. Pol'y 13 (2011)Google Scholar.

61. Dulauf & Nagin, supra note 60.

62. There is significant evidence that early childhood development programs are effective in reducing crime. See Heckman, James, Pinto, Rodrigo & Savelyev, Peter, Understanding the Mechanisms Through Which an Influential Early Childhood Program Boosted Adult Outcomes, 103 Am. Econ. Rev. 2052 (2013)CrossRefGoogle ScholarPubMed; Piquero, Alex R. et al. , Effects of Early Family/Parent Training Programs on Antisocial Behavior and Delinquency, 5 J. Experimental Criminology 83 (2009)CrossRefGoogle Scholar.

63. In this way, there is uncertainty with regard to deterrence proportionality (i.e., how much ought to we punish if we want X degrees of deterrence?), just as there is with regard to retributive proportionality. There are two important differences, though. First, our uncertainty with regard to deterrence proportionality is epistemic, while our uncertainty with regard to retributive proportionality is conceptual. There is an empirical answer to the deterrence question—like there was when we compared Sticks 1 and 2—and it seems that we are indeed making (slow) progress on it. But there are deep and permanent conceptual barriers to making progress on retributive proportionality. Second, given what criminologists now know about deterrence, the uncertainty of deterrence proportionality seems less extreme than that of retributive proportionality. If we polled criminologists as to what the sentencing guidelines should be if we were only concerned with deterrence—and assuming that we wanted to do this in a parsimonious way that accounted for the harm inflicted on offenders—the average range of sentences proposed for a given offense would, I think, be considerably narrower than the retributivist range for that offense. I am grateful to an anonymous reviewer for pressing me to consider this point.

64. See generally Lacey, Nicola, Soskice, David & Hope, David, Understanding the Determinants of Penal Policy: Crime, Culture, and Comparative Political Economy, 1 Ann. Rev. Criminology 195 (2018)CrossRefGoogle Scholar (analyzing four paradigmatic determinants of penal policy—crime rates, cultural dynamics, economic structures and interests, and institutional differences—and considering the impact of race as an independent determinant of U.S. penal policies); Nicola Lacey, The Prisoners’ Dilemma: Political Economy and Punishment in Contemporary Democracies (2008) (examining political economic, institutional, and cultural determinants of penal severity); Pratt, John, Scandinavian Exceptionalism in an Era of Penal Excess, Part I: The Nature and Roots of Scandinavian Exceptionalism, 48 Brit. J. Criminology 119 (2008)CrossRefGoogle Scholar (arguing that high levels of social trust and solidarity have grounded Scandinavian criminal justice systems and considering demographic and economic factors conducive to those high levels); Pratt, John, Scandinavian Exceptionalism in an Era of Penal Excess, Part II: Does Scandinavian Exceptionalism Have a Future?, 48 Brit. J. Criminology 275 (2008)CrossRefGoogle Scholar (same); James Q. Whitman, Harsh Justice: Criminal Punishment and the Widening Divide Between America and Europe (2003) (arguing that cultural and ideological differences explain the difference between the American penal regime, on the one hand, and French and German regimes, on the other); Nicola Lacey & Soskice, David, Crime, Punishment and Segregation in the United States: The Paradox of Local Democracy, 4 Punishment & Soc'y 454 (2015)Google Scholar (arguing that local government autonomy in the United States, and the resulting fact that criminal justice policies are filtered through local electoral politics, presents unique challenges for garnering political support for integrative criminal justice policies).

65. See Sverdlik, Steven, Desert as a Limiting Condition, 12 Crim. L. & Phil 209, 219–220 (2018)Google Scholar (arguing that, if the probability of punishment is low, maximally harmful retributive punishments may be insufficient for the purpose of deterrence).

66. Tadros, supra note 57.

67. Bronsther, supra note 57.