Statistical resentment, or: what’s wrong with acting, blaming, and believing on the basis of statistics alone


Statistical evidence—say, that 95% of your co-workers badmouth each other—can never render resenting your colleague appropriate, in the way that other evidence (say, the testimony of a reliable friend) can. The problem of statistical resentment is to explain why. We put the problem of statistical resentment in several wider contexts: The context of the problem of statistical evidence in legal theory; the epistemological context—with problems like the lottery paradox for knowledge, epistemic impurism and doxastic wrongdoing; and the context of a wider set of examples of responses and attitudes that seem not to be appropriately groundable in statistical evidence. Regrettably, we do not come up with a fully general, fully adequate, fully unified account of all the phenomena discussed. But we give reasons to believe that no such account is forthcoming, and we sketch a somewhat messier account that may be the best that can be had here.

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  1. 1.

    Here and below we use small caps for names of cases.

  2. 2.

    It is not entirely neglected. See, for instance, Enoch et al. (2012, pp. 222–223), Buchak (2014), Enoch (2018) and Pundik (2020).

  3. 3.

    We focus on resentment rather than on blame in order to avoid the practical implications that are sometimes associated with blaming. With resentment, we can postpone all practical questions and focus just on the appropriateness of resentment itself.

    Buchak (2014) seems to mean by blaming only or almost only the reactive attitudes. In this respect, then, her discussion is directly relevant to ours. In others, though, not so much: Buchak is less concerned with explaining what is problematic with statistical resentment or blaming, and more in taking as data the fact that we don’t assign blame proportionally to credence in blameworthiness as evidence for the indispensability of beliefs in a framework that already utilizes credences.

  4. 4.

    Originally from Cohen (1977).

  5. 5.

    For this and related cases, see Enoch et al. (2012), and the references there.

  6. 6.

    In previous work (Enoch et al. (2012); Enoch and Fisher (2015)) we argue that the epistemic condition known as Sensitivity nicely explains the intuitions in all of these cases. We also insist, however, that it cannot justify the legal suspicions against statistical evidence, because, in a slogan, the law shouldn’t care about epistemology. Instead, we offer a Sensitivity-related incentive story. It’s not clear, however that that incentive story—or any other one—can be applied to The Central Resentment Case. More work needs to be done, then, in search of a more unified account. Hence this paper.

    For critical discussions of these theories of ours, see Blome-Tillmann (2015), Pardo (2018), Smith (2017), Gardiner (2018a) and Littlejohn (2017). We hope to discuss these criticisms elsewhere. For pushback against Pardo (2018), and an overview of our account, see Enoch and Spectre (2019).

  7. 7.

    This is a common example. See, for instance, Pundik (2008, p. 303), Buchak (2014, p. 305).

  8. 8.

    This is so, we believe, even if in order to achieve medical knowledge, or the best kind of medical knowledge, there’s a need for more than just statistical evidence, like perhaps some access to the underlying causal mechanism. For an overview and some references, see Reiss and Ankeny (2016, section 5). The role of causal explanations in medical knowledge and practice is a delicate and contested matter. Compelling causal explanations are arguably responsible for the persistence of medical practices long after statistical evidence debunks their efficacy or shows them to be harmful or dangerous. See Parsad and Adam (2015). We cannot, of course, engage these complexities here.

  9. 9.

    We think that this suffices to reject Basu’s (2019a) use of Sherlock Holmes as an example of someone who mistreats people merely by studying them scientifically. It’s possible, of course, that she does not go for the most general version of this claim, in which case the point in the text is one she can accept.

  10. 10.

    For an emphasis on the need to accommodate the directionality of the relevant wronging—that it’s wronging the relevant person—and for the (plausible) claim that the theory we put forward in Enoch et al. (2012) fails to satisfy this desideratum, see di Bello and O’Neill (2019).

  11. 11.

    We’re not sure what to say of generic admiration, as when we may admire nurses and fire-fighters for their often courageous and compassionate work. The example in the text is not about admiring the class, but specific members within it, based on purely statistical evidence. (There will be more of generics below).

  12. 12.

    Which means—pace Pundik (2008)—it can’t be about autonomy and certainly not about freedom of will.

  13. 13.

    There may be differences between them of the kind we discuss in Sect. 4, below. For an emphasis on such stories, see Gardiner (2018b, pp. 184–186).

  14. 14.

    This doesn’t mean that you should believe, of a specific Asian car, that it is fuel-efficient based solely on the statistical evidence.

    As a reviewer rightly noted, in some cases there may be further, not statistical evidence about Asian cars (say, that they have some relevant technological feature). Our point in the text is that preferring the Asian car makes sense even in the absence of such further evidence.

  15. 15.

    These are paraphrases on the pre-punishment literature. See, for instance, Smilansky (1994).

  16. 16.

    Notice that cases like Pre-resentment work better with causal accounts (see Thomson (1986)) according to which a necessary condition for E being evidence for H is that H plays a role in causing E. But such causal accounts have other problems facing them.

  17. 17.

    Notice that some of these attitudes may be held vis-à-vis non-person things. So the problem doesn’t seem to be person-specific either.

  18. 18.

    Joel Kim Booster—a stand-up comedian of Asian descent who was adopted at a young age by a white American family—tells the story of how his adopting parents were disappointed to discover that he was not good at math ( Regardless of how accurate the story is, the inappropriateness of his parents’ expectation and disappointment strengthens the point in the text.

  19. 19.

    Or on the basis of the statistics. Perhaps the very same statistics amounts to statistical evidence for the proposition that the ticket is a losing one, and a different kind of evidence for the proposition that the ticket is highly unlikely to win. (We thank Dan Baras for this point.) This difference doesn’t make a difference for our point in the text, though.

  20. 20.

    The example is loosely based on related rumors among those whose income depends on such things. For a similar example in the American context, see Basu (2019b), though she never explicitly distinguishes between the problem with the generalization and the problem with the belief about a specific person.

    In the background are also partly linguistic issues that we can’t address here: How are generics (“Dogs bark.”; “Sharks are dangerous.”; “Ashkenazis are worse tippers.”) best understood? What evidence is appropriate for accepting them, or for rejecting them? But matters here are more complicated than merely the understanding of generics. Presumably, there’s nothing suspicious about the generalization that non-drinkers are worse tippers. Different generics behave differently here.

  21. 21.

    Things may get messy here, because, as a reviewer pointed out, it’s natural to be suspicious of the statistical evidence about tipping in a way that it’s not natural to be suspicious of the statistical evidence in Lottery. This is true, but it doesn’t do away with the intuitive difference between these two cases (once such distorting factors are stipulated away), or if need be other cases. Consider, for instance, Moss’s (2018b) at least somewhat problematic example of believing of someone that they are probably straight.

    The reviewer also pointed out—rightly—that the relevant intuitions may be context-sensitive in all sorts of ways. But all we need for our purposes here is that there are some—perhaps perfectly natural—contexts in which such differences as between Ashkenazi Tippers and Lottery are manifested. Suppose that a waiter tells a colleague: “Can we switch tables? I probably won’t win the lottery and so I need more than minimal tips.” There need be nothing wrong with the premise or the conclusion. But if it’s clear that what explains the utterance is that sitting at the relevant table are Jews of Ashkenazi descent (and not, say, just the different sizes of the tables), then the inference starts to look problematic in a statistical-resentment reminding way.

  22. 22.

    The combined story we suggested in Enoch et al. (2012) and Enoch and Fisher (2015)—in terms of a Sensitivity requirement and the relevant incentive structure—actually does a remarkably good job with DNA cases.

  23. 23.

    Other names in the literature for impurist views include Subject Sensitive Invariantism, pragmatic encroachment, and Interest-Relative Invariantism. “Invraintism” implies a rejection of contextualism and relativism. For our purposes “Impurism” carries no such rejection. All of the claims we’ll be making can hold across and within contexts (or assessment points).

  24. 24.

    See, for instance, DeRose’s (1992) discussion of what have come to be called bank cases. See also Lewis (1996), whose Belief Rule is stakes-dependent.

  25. 25.

    See, for instance, Fritz (2017).

  26. 26.

    The example is from Ross and Schroeder (2014).

  27. 27.

    E. g. Hawthorne (2003), Stanley (2005) and Moss (2018b).

  28. 28.

    Moss (2018b).

  29. 29.

    The relation between doxastic wrongdoing and impurism takes central stage for Basu (2019a, b). See also Schroeder (2018a, b) and Basu and Schroeder (2019). For the record, we reject doxastic wrongdoing, though we don’t rely on this rejection here. See our “There Is No Such Thing as Doxastic Wrongdoing” (ms.).

  30. 30.

    See Pace (2011), Enoch (2016, 2017), Moss (2018a, b). See also Gardiner (2018b), and the references there (mostly in the first three sections).

  31. 31.

    In the pragmatic encroachment literature, usually the issue is the strength of the evidence, not its kind (Moss (2018a) is a prominent exception). But perhaps this is just an oversight. For a similar suggestion (in the political context), see Enoch (2017, p. 152).

  32. 32.

    For one distinction between radical and moderate impurism, see Fritz (2020).

  33. 33.

    For a critical discussion of moral encroachment, which we are largely sympathetic with, see Gardiner (2018b, Sect. 5). See also the references there. For some examples of critical evaluation of pragmatic encroachment, see Reed (2010), Brown (2013), Anderson and Hawthorne (2018a, b), and Jackson (2019).

  34. 34.

    We briefly revisit Moss’s theory in the next section.

  35. 35.

    For a comprehensive impurist (Subject Sensitive Invariantist) account regarding lack of knowledge and lotteries, see Hawthorne (2003). For a critique of the notion of stakes (or stakes dependence) see Anderson and Hawthorne (2018a, b).

  36. 36.

    It is, of course, controversial what these relations precisely are. But it’s not as controversial that knowledge entails justified belief.

  37. 37.

    The closest we know of in the literature is Gao (2019). But even Gao, for the most part, endorses only what she calls “creedal pragmatism” as a descriptive thesis (about how people’s credences in fact change in the face of a change in the stakes). For reasons we cannot get into here, we find her initial normative discussion (Sect. 3) unpromising.

  38. 38.

    For explicit rejections, see Buchak (2014, pp. 303–304) and Ross and Schroeder (2014, p. 260). For an implicit one, see Brown (2013). For some discussion, see Gau (2019), Fritz (2020), Fritz and Jackson (forthcoming).

    Moss’s (2018b) view is special, in that she thinks that credences too are encroached on—but only in the sense that pragmatic considerations affect whether or not a given credence amounts to knowledge (as she insists some credences do). Moss too, however, stops short of accepting credence-impurism.

  39. 39.

    Jackson (2019) relies on belief-credence dualism in order to reject impurism, but she does things in a very different way from ours.

  40. 40.

    Despite Marušić’s (2015) resisting talk of stakes, we think that the objection in the text, suitably modified, applies to his view as well.

  41. 41.

    Bolinger (2020) discusses the credence case, and mentions many real-life considerations—of the kind we proceed to discuss in Sect. 4 (especially Sect. 4.2)—that complicate matters. But she seems to agree that when no such complicating considerations apply, credences should just follow probabilities.

    We can also rely on Lewis’s Principal Principle that the conditional credence of event A given the objective chance that A is x, is x: cr(A|ch(A) = x) = x (assuming (ch(A) = x) > 0 and that the background evidence is all about events before A takes place).

  42. 42.

    At least if you have any credence at all. The argument in the text is not affected by the possibility of permissible credence-suspension.

  43. 43.

    Williamson (forthcoming-a) rejects any systematic relation between belief and credence: On his view, one may have a fully justified credence 1 that p, while it would nevertheless be irrational for one to believe that p. Even Williamson, though, doesn't deny that in such a case a probabilistically hedged belief—that it's highly likely that p—would be rational. The discussion of credences and of probabilistically hedged beliefs below shows why this suffices for our purposes.

  44. 44.

    For a related discussion—also re Basu and Schroeder—see Gardiner (2018b, p. 179, fn 28).

  45. 45.

    Buchak (2014) takes it for granted that statistical evidence can unproblematically support credence and probabilistically hedged beliefs; she takes the unacceptability of basing blame on statistical evidence as evidence that beliefs are not best understood in terms of credences. Buchak is thus a kindred spirit—but note that, as we show throughout this paper, we don’t think that putting things in terms of beliefs solves the puzzle of statistical resentment.

  46. 46.

    For some discussions along these lines, see Blome-Tillman (2017), LittleJohn (2017) and Gardiner (forthcoming).

  47. 47.

    Williamson (2000, p. 256) seems committed to the idea that belief in the loss of a lottery ticket is less than perfectly rational and is at least sympathetic to a knowledge norm of belief (see Hawthorne et al. (2016) for discussion). He clearly endorses and defends a knowledge norm of belief in more recent work: Williamson (2011, 2013, 2017, forthcoming-b, forthcoming-a). This is not to suggest that Williamson is the only one to endorse a knowledge norm of belief. Several theorists—e.g. Moss (2018a, b)—have accepted his (or similar) norms, some have advanced knowledge norms of belief independently. See, for instance, Bird (2007).

  48. 48.

    Applied to the cases that interest us here we have sentences such as “John is confident that Mary is badmouthing him, but it’s not that he believes that she is.” This is, we think, Moore paradoxical. Also, “confident that” doesn’t neg-raise: From “I’m not confident that p” it doesn’t follow that “I’m confident that not-p”. A central claim in Hawthorne et al. (2016) is that “believe that” does neg-raise, and that neg-raising is an indication of relatively weak epistemic standards. If so, “confident that” is more evidentially demanding than “believe that”. And notice that there’s reason to believe that “think that” (as in the text) and “believes that” behave alike for current purposes.

  49. 49.

    We are relying here on Hawthorne et al. (2016). See also Williamson’s (forthcoming-a) response to the former. In Williamson (2017, n. 11, pp. 160–170) he takes a more neutral attitude toward the idea that belief is weak and suggests that perhaps the necessary and sufficient condition for knowledge is rational sureness.

  50. 50.

    Hawthorne et al. (2016) argue that the burden of proof has been on the knowledge side all along. If indeed believing that your ticket won’t win the lottery is unjustified, it’s hard to explain the epistemological attention Kyburg’s (1961) lottery paradox has been—and still is—getting.

  51. 51.

    And not only them. Martin Smith’s (2016) interesting discussion of normic support also invokes a sharp divide between beliefs and credences, and so he too is vulnerable to the point in the text.

  52. 52.

    Moss (2018b) as noted earlier, stops short of endorsing a knowledge norm of credence levels. With regard to belief, though, she clearly wants to defend a knowledge norm. For an exchange on this point see Moss (2019), Williamson (forthcoming-a), and Rothschild (2019). Other views have been proposed along the Hawthorne et al. (2016) line: Dorst (2019), Holguín (ms).

  53. 53.

    Again see the discussion of “neg-raising” in Hawthorne et al. (2016). Note that this example is problematic on Smith’s (2016) normic support view.

  54. 54.

    This may come as good news for a Sensitivity-based account. If knowledge is needed for appropriate resentment, then, and if insensitive belief is (even just almost) never knowledge, then given that beliefs based on statistical evidence are insensitive, it follows that statistical resentment is never appropriate. And a Sensitivity-based account has the resources not just to assert that the relevant beliefs don’t amount to knowledge, but also to offer a plausible explanation why this is so.

  55. 55.

    See Enoch et al. (2012).

  56. 56.

    So in particular, this reinforces the objection from the previous section against Moss’s (2018b) impurist, relevant-alternatives version of a knowledge-based account. Note also that while in some contexts, relevant alternatives views are associated with contextualist views, this is not so in our context, where all of the relevant factors (the statistical and the non-statistical evidence, in the different cases) are those believers are sensitive to, not knowledge attributors. So the relevant kind of sensitivity is subject-sensitivity, not context-sensitivity.

  57. 57.

    Throughout—including in the context of discussing knowledge—we’ve been putting things in terms of beliefs. Bolinger (2020) discusses, in a similar context, acceptance, an attitude that combines epistemic and pragmatic features. In the text we assume that resentment, and perhaps related phenomena as well, go with belief rather than with acceptance (to the extent that the two are distinct). One reason Bolinger’s acceptance won’t do here is that resentment cases need not have any further practical implications. Moreover, going for acceptance does not immune one from Moorean results. The following sentence, we submit, is Mooreanly incoherent: “He believes she’ll win but it’s not that he accepts it”.

  58. 58.

    Much of the discussion in this section is in the general spirit of Gardiner’s (2018b, mostly in section 6) discussion. But at the end of the day, Gardiner seems less tentative about the success of this project than we are.

  59. 59.

    This observation coheres nicely also with the suggestion that the fact that these attitudes are usually de re makes a difference here.

  60. 60.

    Gardiner (2018b, pp. 185–186) emphasizes a similar point.

  61. 61.

    Or perhaps, if we’re working with some subjective or epistemic notion of probability, what’s needed is that you know or reasonably believe that he is typical.

  62. 62.

    See Karlander and Spectre (2010), especially the appendix.

  63. 63.

    See here Posner’s (1999, p. 1509) similar suggestion about the legal treatment of statistical evidence.

  64. 64.

    Or, if Moss (2018b) is right, in believing about someone about whose sexuality you know nothing in particular, that he is probably straight.

  65. 65.

    What if the statistics are very strong? Wouldn’t that make it rational not to further investigate the issue? Actually, in many cases strong statistical evidence is unstable, in the sense that it’s fairly easy to come by evidence that will outweigh it, and then, stopping inquiry may not be justified. For instance, the very strong statistical evidence you have that your lottery ticket won’t win is easily outweighed by the phone call from the lottery company saying that you did win. (The denominator of the Bayes factor is very small because a mistaken call to you is extremely unlikely forcing the posterior probability way up.) Certainly, you shouldn’t stop inquiry and refuse to take their call. See here Buchak’s talk of resilience (2014, p. 294). And for discussions of stability and revisability in our context, see Schroeder (2018b), Gardiner (2018b, p. 189), and Bolinger (forthcoming). Resilience (or Stability) is developed as an overall account of rational belief in Leitgeb (2014). For a good and less detailed discussion of resilience see Joyce (2005) and the references there. Leitgeb doesn’t argue that lottery beliefs are irrational in all contexts; in fact, his view is designed to vindicate their rationality at least sometimes.

  66. 66.

    Or the explanatory order may proceed in the opposite direction. We’re genuinely not sure.

  67. 67.

    A reviewer pointed out that the symmetry we’re assuming in the text between the evidence-related practices leading up to the belief and those that follow (say, a decision to stop one’s inquiry) cannot be taken for granted. This may be so, but we believe that the point in the text, with sufficiently creatively stipulated hypothetical cases, holds even if this symmetry assumption is relaxed.

  68. 68.

    One of us is more convinced about this than the other.

  69. 69.

    For a closely related point (in the context of criticizing Stroud’s discussion of epistemic partiality) see Enoch (2016, pp. 31–33).

  70. 70.

    Here’s an updated table of the new lessons—since the previous table—learned from cases, both new ones and ones that were already introduced in Sect. 1:

    Name Additional lessons
    Gatecrashers Counts against a knowledge-based account (because of knowledge-fetishism)
    Blue Bus Company Counts against a knowledge-based account (because of knowledge-fetishism)
    Physician Action based on statistical evidence clearly justified—so either such evidence suffices for knowledge, or knowledge is not needed. Either way, a problem for a knowledge-based account
    Truth to Power Low stakes; so encroachment is not the solution
    Math and Car Hard to distinguish on purist knowledge-based accounts
    Pre-resentment Counter-example to knowledge-based accounts
    Surprise Knowledge-based accounts can’t distinguish between Surprise Lottery and Surprise Resentment
    Dna A challenge to knowledge-based accounts
    Urn A counterexample to credence-impurism
    Ashkenazy Tipper: Credence The moral objection applies just as powerfully to the credence case; given the implausibility of credence impurism, this shows impurism will not solve our problem
    Probably Ashkenazy Tipper Still objectionable. Again, against impurism
    Credit Card Pin Some beliefs based on purely statistical evidence seem justified and may amount to knowledge. A problem for the knowledge-based account
    Joint Appointment Resentment is problematic (in some cases) even when based on statistical evidence together with other evidence
    Stranger Statistical resentment is problematic even in the absence of rich information, so the problem is not just that of screening off
  71. 71.

    Notice that once the full generality and uniformity ambition is deserted, the story we initially told about the legal case of statistical resentment may be vindicated after all. And indeed, perhaps then incentive stories can do work elsewhere as well, not as a general explanation, but as a part of a messy one.

    Whether a similarly conciliatory spirit can save something from other explanations we rejected along the way—say, those in terms of moral encroachment, or in terms of the knowledge account—will depend on the fate of the more principled arguments we used against them.

  72. 72.

    Let us again stress that an account that combines a role for Sensitivity and a role for incentives does especially well—better than all alternative accounts, as far as we can tell—in explaining and vindicating intuitions about DNA cases.


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For comments on previous versions we thank Dan Baras, Tali Fisher, Jamie Fritz, Georgi Gardiner, Clayton LittleJohn, Berislav Marušić, Oded Na’aman, Ittay Nissan-Rozen, Erik J Olsson, Jim Pryor, Daniel Telech, Gideon Yaffe, and audiences at the Eastern APA, Cornell, Dartmouth, Oxford, The Hebrew University, Brandeis, King’s College, Hamburg, and Bochum.


David Enoch’s research was supported by the Israeli Science Foundation, Grant Number 439/15. Levi Spectre’s research was supported by the Swedish Riksbankens Jubileumsfond as part of the ‘Knowledge Resistance: Causes, Consequences, and Cures’ research project (Reference Number: M18‐0310:1).

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Enoch, D., Spectre, L. Statistical resentment, or: what’s wrong with acting, blaming, and believing on the basis of statistics alone. Synthese (2021).

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  • Statistical evidence
  • Epistemic impurism
  • Pragmatic encroachment
  • Moral encroachment
  • Resentment