¹ Theft Act 1978, s 3.

² The proposed example is a variation on the familiar rodeo stadium example. See Cohen, LJ The Probable and the Provable (Oxford: Oxford University Press, 1977) pp 74–75CrossRefGoogle Scholar.

³ For a relatively old example see the famous American case of Smith v Rapid Transit, Inc 58 N E2d 754 (Mass 1945) that decided to the same effect in a civil case.

⁴ Criminal Appeal 2921/18 The State of Israel v Aviv Betzalel (27 October 2019).

⁵ Above n 4, para 24.

⁶ The Criminal Justice Act 2003 regulates the introduction of ‘bad character evidence’. Section s 103(1)(a) in combination with s 101(1)(d) make admissible any prosecution evidence going to ‘the question whether the defendant has a propensity to commit offences of the kind with which he is charged’. F Picinali has noted that this covers controversial generalisations: see Picinali, F ‘Generalisations, causal relationships and moral responsibility’ (2016) 20 International Journal of Evidence & Proof 121CrossRefGoogle Scholar at 129.

⁷ For the alleged identity of such generalisations see Tillers, P ‘If wishes were horses: discursive comments on attempts to prevent individuals from being unfairly burdened by their reference classes’ (2005) 4 Law, Probability and Risk 33CrossRefGoogle Scholar.

⁸ Inferences from direct and circumstantial legal evidence are almost always inductive, and inductive reasoning involves generalisations (often in the form of ‘defendants against whom such evidence exists are guilty’).

⁹ For these proposed grounds see Wasserman, DT ‘The morality of statistical proof and the risk of mistaken liability’ (1991) 13 Cardozo Law Review 935Google Scholar; Pundik, A ‘Statistical evidence and individual litigants: a reconsideration of Wasserman's argument from autonomy’ (2008) 12 International Journal of Evidence and Proof 303CrossRefGoogle Scholar; Pundik, A ‘Freedom and generalisaion’ (2016) 37 Oxford Journal of Legal Studies 189Google Scholar; A Pundik ‘Against racial profiling’ (2017) 67 University of Toronto Law Journal 175; CR Nesson ‘The evidence or the event? On judicial proof and the acceptability of verdicts’ (1985) 98 Harvard Law Review 1357 at 1378; RW Wright ‘Causation, responsibility, risk, probability, naked statistics, and proof: pruning the bramble bush by clarifying the concepts’ (1998) 73 Iowa Law Review 1001 at 1054. These proposed explanations have been convincingly rebutted. See especially Picinali, above n 6. Another attempt to explain the difference between controversial and uncontroversial generalisation has referred to an alleged normative superiority of ‘inference to the best explanation’. See especially RJ Allen and A Stein ‘Evidence, probability, and burden of proof’ (2013) 55 Arizona Law Review 557. The authors mention that inference to the best explanation provides for better-reasoned decisions (at 597); yet they fail to properly explain why reasons to prefer one narrative over another are better than reasons to think one narrative true. After all, given that there are endless possible narratives, the two proposed narratives might be false. The authors refer to the existence of reasons to rule out alternative explanations (ibid) but this comes to little more than a description of ‘inference to the best explanation’.

¹⁰ See for example M Smith ‘When does evidence suffice for conviction’ Mind (published online 17 October 2017); D Enoch and T Fisher ‘Sense and “sensitivity”: epistemic and instrumental approaches to statistical evidence’ (2015) 67 Stanford Law Review 557, and D Enoch et al ‘Statistical evidence, sensitivity, and the legal value of knowledge’ (2012) 40 Philosophy and Public Affairs 197; MS Pardo ‘Safety vs sensitivity: possible worlds and the law of evidence’ (2018) 24 Legal Theory (forthcoming; U of Alabama Legal Studies Research Paper No 3100246. Available at SSRN: https://ssrn.com/abstract=3100246); and MS Pardo ‘The field of evidence and the field of knowledge’ (2005) 24 Law and Philosophy 321. See also MS Pardo and RJ Allen ‘Juridical proof and the best explanation’ (2008) Law and Philosophy 223.

¹¹ The value of knowledge for any practical decision remains uncertain. For a recent attempt to resolve this question see S Goldberg To the Best of Our Knowledge: Social Expectations and Epistemic Normativity (Oxford: Oxford University Press, 2018); SC Goldberg ‘Should have known’ (2017) 194 Synthese 2863; SC Goldberg Assertion: On the Philosophical Significance of Assertoric Speech (Oxford: Oxford University Press, 2015) section 1.1; and see his discussion of ethics in section 7. See also J Hawthorne and J Stanley ‘Knowledge and action’ (2008) 105 The Journal of Philosophy 571; and J Stanley Knowledge and Practical Interest (Oxford: Oxford University Press, 2015). But compare with J Hawthorne and O Magidor ‘Reflections on the ideology of reasons’ in D Star (ed) The Oxford Handbook of Reasons and Normativity (Oxford: Oxford University Press, 2018).

¹² These include mainly Enoch et al, above n 10, and Smith, above n 10.

¹³ D Papineau ‘The disvalue of knowledge’ Synthese (published online 4 October 2019).

¹⁴ See L Levanon 'Statistical evidence, assertions and responsibility' (2019) 82(2) MLR 269.

¹⁵ This assumption is controversial. See further discussion below, n 17.

¹⁶ Cohen, above n 2.

¹⁷ These are controversial assumptions. First, as a descriptive matter, some criminal law doctrines are not founded on moral grounds (constructive liability and strict liability are, arguably, examples). Second, some have suggested that criminal law can and should be understood only in institutional terms and without reference to morality. See for example V Chiao ‘What is the criminal law for?’ (2016) 35 Law and Philosophy 137 at 139. Still, the prevailing view seems to be that regardless of its institutional nature, criminal law does or at least should contain moral judgement; see for example RA Duff The Realm of Criminal Law (Oxford: Oxford University Press, 2018) ch 2. Last, the question whether moral judgement has a cognitive or noncognitive basis remains open.

¹⁸ The broader category of moral decision-making includes all decisions that are based on moral principles, with or without a critical stance. Examples are discussed below.

¹⁹ The critical stance means that moral judgement is not just a matter of moral belief; it involves the adoption of an attitude.

²⁰ This is a syllogism based on deductive reasoning.

²¹ It is tempting to think that this has to do only with the deductive nature of the inference, but as we shall see below, this is not the case. Some inductive inferences work in the same way.

²² Here, we have moved to the realm of inductive reasoning, but again this is insignificant; what matters is the defensibility of the inferred propositions.

²³ The indefensibility of the affirming proposition can be further elucidated as follows: affirming propositions ‘D rather than A’ negate the possibility that the inference is true for instances of type A rather than for instances of type D. But where the generalisation entails errors as logical certainty, such negation is impossible. This is because the two types of instances (A and D) are within the scope of the generalisation.

²⁴ Inferences based on such a generalisation are inductive; but we can again set this aside.

²⁵ For example, it is possible that the testimony has been misunderstood, and in fact it does not incriminate D.

²⁶ The same is true for generalisations based on DNA evidence. Here, the generalisation means that there is high probability that there is no other person whose DNA matches the evidence sample as closely as that of the defendant; hence the evidence would not lead to errors as a matter of logical certainty; and accordingly the evidence supports the main proposition (that D is guilty) and the affirming proposition (that it is D rather than any other potential defendant who is guilty). Had it been known that there is even one more person whose DNA matches the evidence sample as closely as the defendant's, the evidence would not have supported the affirming ‘D rather than A’ proposition, and conviction solely based on it would have been unattainable and indeed improbable. It can be further shown that the same is true also for statistical evidence that is commonly used by civil courts to establish causation in mass torts litigation. See Steel, S ‘Justifying exceptions to proof of causation in tort law’ (2015) 78 Modern Law Review 729CrossRefGoogle Scholar; S Steel Proof of Causation in Tort Law (Cambridge: Cambridge University Press, 2015).

²⁷ Philosophical literature has also considered the alleged independent value of the truth in the context of belief. See for example J Raz From Normativity to Responsibility (Oxford: Oxford University Press, 2011) ch 3; J Dancy Practical Shape: A Theory of Practical Reasoning (Oxford: Oxford University Press, 2018). Our question, however, is about the justificatory power of the truth in the context of moral judgement, rather than in the context of belief.

²⁸ Moral luck has been the subject of heated debates in the literature, and its rejection is not uncontroversial. See B Williams Moral Luck (Cambridge: Cambridge University Press, 1981); T Nagel Mortal Questions (Cambridge: Cambridge University Press, 1979), especially pp 37–38. For some recent rejections of moral luck see JJ Thomson ‘Morality and bad luck’ in D Statman (ed) Moral Luck (Albany, NY: State University of New York Press, 1993) p 195; B Rosebury ‘Moral responsibility and moral luck’ (1994) 104 Philosophical Review 499; N Richards ‘Luck and desert’ (1986) 65 Mind 198; S Wolf ‘The moral of moral luck’ (2001) 31 Philosophic Exchange 4.

²⁹ Allegedly, this objection could be avoided if all those for which the generalisation applies are convicted, including both D and A. Such a solution does not seem viable in the context of criminal convictions; and in any case, it does not avoid the objection: even if all members of the group are judged guilty, it is still presumed that some are judged wrongly and are in fact innocent, and the judgement of each member of the group includes the proposition that it is someone else rather than this member who is innocent.

³⁰ Rawls uses ‘moral arbitrariness’ as referring to the attribution of moral significance to factors that are randomly distributed among the population. See J Rawls A Theory of Justice (Harvard University Press; reissue edition, 2005). In its core, this is the idea that chance cannot provide the basis for moral judgement. Significantly, Rawls uses the concept of moral arbitrariness only in the context of distributive justice and not in the context of retributive justice. Yet this can be explained on the background of Rawls’ radical interpretation of chance events; and furthermore, Rawls’ distinction between retribution and distribution has been heavily criticised. See M Sandel Liberalism and the Limits of Justice (Cambridge: Cambridge University Press, 2nd edn, 2010) p 90; S Scheffler ‘Responsibility, reactive attitudes, and liberalism in philosophy and politics’ (1992) 21 Philosophy & Public Affairs 299 at 306.

³¹ See Nagel, above n 28, at [28]; MJ Zimmerman Living with Uncertainty: The Moral Significance of Ignorance (Cambridge: Cambridge University Press, 2008) at [376].

³² Possibly, this metaphysical position is implied in several of Herbert Morris’ comments on guilt, for example in ‘Guilt and suffering’ (1971) 21 Philosophy East and West, reprinted in H Morris On Guilt and Innocence (Berkley, CA: University of California Press, 1976) pp 89–90, where he says: ‘Reflection on being guilty … may lead to the view that there is a logic of guilt, that there are rules that, among other things, guide us in determinations of guilt and innocence…’. The logic of guilt here is the logic of the determination of guilt.

³³ For a statement of this argument in the context of ‘bad character evidence’ see (Legal Studies article).

³⁴ For the elements of the Aristotelian tragedy see The Poetics of Aristotle (3^rd edn, edited with critical notes and a translation by SH Butcher, 1902) Part VI and Part IX; D Frede ‘Necessity, chance, and “what happens for the most part”’ in A Rorty (ed) Essays on Aristotle's Poetics (Princeton, NJ: Princeton University Press, 1992) pp 197, 205 and 212. The defendant's tragic error here is her omission to exclude herself from the relevant reference class through lifestyle choices, difficult as these may be to pursue. For example, a defendant who belongs in a socio-economic class in which crime is prevalent could have excluded herself from this statistical reference class by, say, juggling between two full-time jobs. Statistically, she would then belong in the narrower class of the heavily employed members of that socio-economic class, in which the prevalence of crime is at least unknown (and presumably lower).

³⁵ See A Stein Foundations of Evidence Law (Oxford: Oxford University Press, 2005) ch 3.

³⁶ In law, arbitrariness implies the unavailability of appropriate reasons or the inability to predict and scrutinise the reasons underlying a decision. See M Krygier ‘The rule of law: pasts, presents, and two possible futures’ (2016) 12 Annual Review of Law and Social Science 199, especially at 203–205. See also CN Cimini ‘Principles of non-arbitrariness: lawlessness in the administration of welfare’ (2005) 57 Rutgers Law Review 451. For the requirement to provide reasons in English law and its connection to fairness and due process see Flannery v Halifax Estate Agencies Ltd [2000] 1 All ER 373.

³⁷ For initial analysis see Levanon, above n 14.

³⁸ For some conceptions of responsibility see TM Scanlon What We Owe to Each Other (Cambridge, MA: The Belknap Press of Harvard University Press, 1998), especially ch 6; PF Strawson ‘Freedom and resentment’ (1962) 48 Proceedings of the British Academy (G Watson (ed)) 1; G Watson Agency and Answerability: Selected Essay (Oxford: Oxford University Press, 2004); M McKeena Conversation and Responsibility (Oxford: Oxford University Press, 2012); D Shoemaker Responsibility from the Margins (Oxford: Oxford University Press, 2015).

³⁹ This argument requires further exploration; yet since we have already seen that the judgement is unjustifiable for a range of other reasons, and considering limitations on space, this exploration will not be conducted here.

⁴⁰ Levanon, above n 14.

⁴¹ For a helpful discussion of conceptions of legitimacy see A Bottoms and J Tankebe ‘Police legitimacy and the authority of the state’ in A du Bois-Pedain et al (eds) Criminal Law and the Authority of the State (Oxford: Hart Publishing, 2017) p 47. The authors discuss the conceptions proposed in W Hinsch ‘Justice, legitimacy, and constitutional rights’ (2010) 13 Critical Review of International Social and Political Philosophy 39.

⁴² This is the case at least according to anti-luck epistemologists. See D Pritchard ‘Anti-luck epistemology’ (2007) 158 Synthese 277; D Pritchard ‘In defence of modest anti-luck epistemology’ in K Becker and T Black (eds) The Sensitivity Principle in Epistemology (Cambridge: Cambridge University Press, 2012) p 173; D Pritchard ‘Sensitivity, safety and anti-luck epistemology’ in J Greco (ed) The Oxford Handbook of Skepticism (Oxford: Oxford University Press, 2011) p 437; A Hiller and R Neta ‘Safety and epistemic luck’ (2007) 158 Synthese 303. But compare with N Ballantyne ‘Anti-luck epistemology, pragmatic encroachment, and true belief’ (2013) 41 Canadian Journal of Philosophy 485; and Ballantyne, N ‘Does luck have a place in epistemology?’ (2014) 191 Synthese 1391CrossRefGoogle Scholar.

⁴³ See Levanon, above n 14. Scanlon's account of substantive responsibility refers, roughly, to attributability of a burden to the person who carries it; it is associated with diminished grounds to complain against others for having to carry a burden (see Scanlon, above n 38, ch 6). Accordingly, in the current context it is responsibility for the burden that the judging agent herself carries when erring.

⁴⁴ For elaboration of these considerations see Levanon, above n 14.

⁴⁵ The question merits further discussion elsewhere, but it is generally agreed that some level of control that precludes total subjection to chance events is necessary for responsibility (as a precondition for moral appraisal). See for example Zimmerman's discussion, above n 31; and Scanlon, above n 38, at [22]. Questions have been raised about the essence of control and the amount and nature of luck that can still be operative without undermining moral responsibility, especially following compatibilist challenges posed originally in Frankfurt, HG ‘Alternative possibilities and moral responsibility’ (1969) 66 Journal of Philosophy 829CrossRefGoogle Scholar, and further developed in JM Fischer and M Ravizza Responsibility and Control: A Theory of Moral Responsibility (Cambridge: Cambridge University Press, 1998).

⁴⁶ Thus, it would be impossible to acquit a defendant based on an alleged reasonable doubt raised by statistics indicating, say, that his class members do not tend to commit crimes of the same description or category as the crime at issue. At least to the extent that an acquittal involves a moral judgement of innocence, such a judgement would include arbitrary propositions if based on statistical generalisations.

⁴⁷ Above n 2.

⁴⁸ Abduction and ‘inference to the best explanation’ are not considered here, as they rise to serious questions of interpretation, and there are different views on their relation to one another and to induction. See Harman, GH ‘The inference to the best explanation’ (1965) 74 Philosophical Review 88CrossRefGoogle Scholar; Schum, DA The Evidential Foundations of Probabilistic Reasoning (Evanston, Ill: Northwestern University Press, 1994) pp 468–469Google Scholar.

⁴⁹ Cohen, above n 2, at [130]–[131].

⁵⁰ Cohen, above n 2, at [130].

⁵¹ Cohen offers a qualification regarding the differences between inductive reasoning and inductive probability above n 2, at [41]–[42].

⁵² For the implications of the availability of merely partial reasons for such decisions see Zimmerman, above n 31.

⁵³ Predicting effects on general deterrence is hardly straightforward; it can nevertheless be assumed for the purposes of this discussion that this is indeed the case.

⁵⁴ See D Enoch and L Spectre ‘Statistical resentment’ (draft with the author).