¹ See, for example, Scanlon, T. M., What We Owe To Each Other (Cambridge, MA, 1998)Google Scholar.

² See, for example, Thomson, J. J., Rights, Restitution, and Risk (Cambridge, MA, 1986)Google Scholar; Lenman, J., ‘Contractualism and Risk Imposition’, Politics, Philosophy and Economics 7 (2008), pp. 99–122 CrossRefGoogle Scholar. For more recent attempts to reconcile non-consequentialism with the intuitive permissibility of acceptable levels of risk-imposition by defending versions of ex ante contractualism, see Kumar, R., ‘Risking and Wronging’, Philosophy and Public Affairs 43 (2015), pp. 27–51 CrossRefGoogle Scholar; Frick, J., ‘Contractualism and Social Risk’, Philosophy and Public Affairs 43 (2015), pp. 175–223 CrossRefGoogle Scholar. Considering whether such versions of contractualism adequately reconcile non-consequentialist judgements with permissive risk imposition is outside the scope of this article, since Kumar and Frick reject a central principle to be introduced shortly in favour of alternative principles. Instead, this article aims to show that a natural way of capturing the above aspects of common-sense morality are compatible in their current form, rather than to entertain alternative principles. This article treats the risk of some event occurring as the probability of that event occurring multiplied by the potential harm. It also adopts an epistemic understanding of probability, although nothing hinges on whether we have a frequentist or objective understanding of probability. For a survey of different characterizations of ‘risk’, see Hayenhjelm, M. and Wolff, J., ‘The Moral Problem of Risk Impositions: A Survey of the Literature’, European Journal of Philosophy 20 (2012), pp. 26–51 CrossRefGoogle Scholar.

³ Dougherty, T., ‘Aggregation, Beneficence and Chance’, Journal of Ethics and Social Philosophy 7 (2013), pp. 1–19 CrossRefGoogle Scholar.

⁴ For a similar argument for affirming an analogue of Risk Tolerance and rejecting an analogue of Many–Few which presupposes a consequentialist approach to the ethics of risk-imposition and aggregation of benefits, see Norcross, A., ‘Great Harms from Small Benefits Grow: How Death Can Be Outweighed by Headaches’, Analysis 58 (1998), pp. 152–8CrossRefGoogle Scholar. However, Norcross's argument is dialectically ineffective against non-consequentialists, since they will simply reject the consequentialist assumptions underpinning his argument. See Dougherty ‘Aggregation, Beneficence and Chance’, pp. 3–4.

⁵ This article follows Dougherty in assuming that our common-sense moral judgements are to be explained by Many–Few and Risk Tolerance. Consequently, if either principle is false, then so are the judgements which they explain.

⁶ Dougherty, ‘Aggregation, Beneficence and Chance’, p. 5.

⁷ Dougherty, ‘Aggregation, Beneficence, and Chance’, p. 5.

⁸ Dougherty's original argument involves eight premises. Since this discussion does not turn on those details of Dougherty's argument, for simplicity, they are suppressed.

⁹ Dougherty, ‘Aggregation, Beneficence and Chance’, p. 18.

¹⁰ For ease of exposition, I assume that ‘It is permissible that ϕ’ is equivalent to ‘It may be that ϕ’, where ‘permissible’ and ‘may’ have a deontic flavour, rather than epistemic or metaphysical. Nothing substantial hinges on this assumption, and we may read ◆ϕ as ‘It may be that ϕ’ if we so wish. Greek letters are metavariables ranging over sentences; quotation marks containing such sentences should be read as quasi-quotations.

¹¹ Thanks to Joseph Bowen for suggesting Insulin and Lifeboat.

¹² Dougherty, ‘Aggregation, Beneficence and Chance’, p. 10.

¹³ Thanks to an anonymous reviewer for pointing out that Constraint on Permissible Risk Imposition and Only Effects Matter are insufficient to explain the failure of agglomeration in other cases, such as when performing both of two harmless actions breaks a promise but performing either (but not both) of them does not. The reviewer suggests the following more general principle to capture such cases: performing two (or more) actions, each of which is permissible, may constitute performing a third, more complex action that is impermissible. While I agree with the reviewer's observation and suggestion, we should focus on Constraint on Permissible Risk Imposition in our current setting, since it better explains why the more general principle holds in cases involving agglomeration of risk impositions.

¹⁴ For example, if I have a 1/4 chance of causing serious harm by firing a gun at someone once, I almost double my chances of causing serious harm by firing my gun at two individuals.

¹⁵ Thanks to Joseph Bowen and an anonymous reviewer for both raising this objection.

¹⁶ For an objection along these lines, see Dougherty, ‘Aggregation, Beneficence and Chance’, pp. 8–11. Thanks to Tom Dougherty for encouraging me to engage with this objection explicitly.

¹⁷ Dougherty, ‘Aggregation, Beneficence and Chance’, p. 9.

¹⁸ Thanks to an anonymous reviewer for suggesting that I make explicit the quantificational structure of the disambiguations of Iterative Principle as follows:

¹⁹ Thanks to an anonymous reviewer for suggesting that I consider Generalized Only Effects Matter explicitly.

²⁰ I should like to thank Joseph Bowen, Karamvir Chadha, Matthew Clark, Daisy Dixon, Tom Dougherty, Jeff McMahan, Jessica Testro, and two anonymous referees for helpful comments and discussions on previous versions of this article. I should also like to thank the AHRC for financial support.