Demographic statistics in defensive decisions


A popular informal argument suggests that statistics about the preponderance of criminal involvement among particular demographic groups partially justify others in making defensive mistakes against members of the group. One could worry that evidence-relative accounts of moral rights vindicate this argument. After constructing the strongest form of this objection, I offer several replies: (i) most demographic statistics face an unmet challenge from reference class problems, (ii) even those that meet it fail to ground non-negligible conditional probabilities, (iii) even if they did, they introduce new costs likely to cancel out any justificatory contribution of the statistic, but (iv) even if they didn’t, demographic facts are the wrong sort to make a moral difference to agents’ negative rights. I conclude that the popular argument should be rejected, and evidence-relative theories do not have the worrisome implication.

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  1. 1.

    See Leslie (2017) for discussion.

  2. 2.

    Summarized in Zimmerman (2018); developed in detail in Zimmerman (2008, 2014). He construes agents’ moral duties as requiring them to perform actions with sufficiently good prospective moral value; this is not a straightforward expected-value maximization standard. Zimmerman clarifies that “I take an agent’s prospectively best option to be that which it would be most reasonable for him to choose in light of his evidence, were he morally conscientious.” (2018, p. 454)

  3. 3.

    van der Vossen (2016, p. 143)

  4. 4.

    Frowe (2010, p. 269). Frowe advocates evidence-relativity only for defensive permissions, not moral rights generally, and is emphatic, however, that this sort of permission can come apart from the liability of the other party: if the defender’s beliefs are false, then her permissible defense will constitute a justified infringement of the other party’s rights against being harmed. So unlike the other views discussed, on Frowe’s analysis it does not follow from it being permissible for B to harm A that B would not thereby violate A’s rights.

  5. 5.

    The standard alternative is a kind of fact-relative view on which what agents owe each other is independent of what evidence they have, and (roughly) extensionally equivalent to what an omniscient, morally-motivated third party would advise them to do. On such views, if A is in fact not an unjust aggressor, imposing preemptive defensive harm would wrong them no matter how strongly misleading my evidence was. For a defense of fact-relative views of this kind, see Otsuka (1994) and McMahan (2005).

  6. 6.

    Anderson and Hawthorne (2018) interpret pragmatic encroachment as the thesis that S knows that P only if she is ‘practically adequate’ with respect to P, which they define as follows: “S is practically adequate with respect to P iff the top-ranked element(s) in S’s actual preference ranking do not differ from the top-ranked element(s) in her ranking conditional on P.” Fantl and McGrath (2002) and Hawthorne and Stanley (2008) can be read as offering variants of this condition for justified belief.

  7. 7.

    There are at least two problems with this step, one involving the mismatch between the property in the statistical claim and the property of interest to our agent, and one involving an unjustified assumption of probabilistic independence of evidence, but I’ll set those aside for now to give the objection as good a run as I can.

  8. 8.

    See discussions in Foot (1967), Quinn (1989) and Scanlon (2008, p. 91).

  9. 9.

    This asymmetry is even more pronounced if Defender chooses to waive her rights against suffering the aggressive harm; she can thereby make the harm she suffers non-wrongful. But she need not be so magnanimous, and, given that we are investigating the conditions of permissible defense against unjust threatened harms, I will assume that she does not waive her rights. (Thanks to Seth Lazar for discussion on this point.)

  10. 10.

    Quong (2009, p. 518)

  11. 11.

    Reichenbach (1949, p. 374): “If we are asked to find the probability holding for an individual future event, we must first incorporate the case into a suitable reference class. An individual thing or event may be incorporated into many reference classes, from which different probabilities will result. This ambiguity has been called the problem of the reference class.” As Hájek (2007) demonstrates, we must face this challenge regardless of which underlying theory of probability we assume. On most theories of probability, the probability of Fasimpliciter is undefined; to get a determinate value we must first select the single relevant reference class. So long as we remain ignorant of how G relates to the relevant reference class, we are not justified in assuming that the objective probability of Fa is anything like the probability of Fa conditional on a’s membership in G.

  12. 12.

    Some theorists disagree, holding that it is in fact never permissible to treat agency-involving properties as predictable, because doing so involves taking a ‘predictive stance’ toward an agent (see especially Basu 2019). Basu only explicitly discusses the wrongfulness of forming beliefs based on statistical evidence, but since using demographic statistics to set one’s credences involves taking group membership as predictively relevant, it seems this too violates Basu’s prohibition on treating other agents as “something whose behavior is to be predicted”, and so would also be impermissible on her account.

  13. 13.

    On the multiple variances between biological kinds and the folk notion of race, see for example Appiah (1996) and Glasgow (2003). Of course, even if race did correspond to some biological kind, we would still lack license to treat it as predictively relevant to violent behavior unless (implausibly) we had evidence that the heritable traits cause higher rates of violent aggression.

  14. 14.

    Whether we should take ‘race’ to refer to some real property is a matter of significant debate, but many even in the eliminativist camp will allow that there is a socially constructed property of ‘racial identity’, that can exert pressures on individuals to conform to the cultural expressions of the identity they are taken to have (see, e.g., Appiah 1996). ‘Identifying’ with a racial group is plausibly a two-dimensional process: in part it is a matter of the agent herself taking the racial identity to be part of her identity, but in part it is a matter of being taken by others to have that racial identity. For thorough discussion, see Gooding-Williams (1998) and Glasgow (2006).

  15. 15.

    In Bolinger (2018), I appeal to these kinds of reasons, and in particular the way that heuristics pattern and amplify risk exposure, to explain why inferences from visible social-group membership to stereotype-congruent conclusions are frequently rationally and morally impermissible.

  16. 16.

    In more technical terms, if agents rely on demographic statistics about G in determining their epistemic risk of error, they will more readily act preemptively against members of G, all else equal, in proportion to the strength of the conditional probability. The more widespread this attitude is, and the more visible and stable membership in G is, the more being a group member increases A’s objective ex ante risk of being mistaken for an aggressor. When these effects are especially stark [e.g. when being black doubles one’s risk of being mistakenly killed by police (Swaine et al. 2015)], A’s knowing that his group membership puts him at increased risk may trigger additional harms: it may take a psychological toll, and he may feel forced to engage in costly measures to unilaterally reduce his risk exposure (e.g. avoiding contact with police or legal institutions, adopting mannerisms and dress aimed at appearing non-threatening, etc.).

  17. 17.

    I’ve outlined the beginning of such an account elsewhere (see Bolinger 2017).


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Thanks to Rima Basu, Hannah Bourandt, Maegan Fairchild, Greg Keating, Seth Lazar, Kirsten Mann, Jonathan Quong, Mark Schroeder, Brian Weatherson, and James Willoughby, as well as the Moral Philosophy and Social Theory working group at Australian National University for helpful discussion on many of the questions covered in this paper. The funding was provided by ARC (Grant No. D170101394).

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Correspondence to Renée Jorgensen Bolinger.

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Bolinger, R.J. Demographic statistics in defensive decisions. Synthese (2019).

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  • Statistical evidence
  • Demographic statistics
  • Self-defense
  • Racial profiling
  • Moral encroachment
  • Social inference
  • Risk