¹ For example, see Lang, Gerald, ‘Fairness in Life and Death Cases’, Erkenntnis 62 (2005), pp. 321–51CrossRefGoogle Scholar; Peterson, Martin, ‘The Mixed Solution to the Number Problem’, Journal of Moral Philosophy 6 (2009), pp. 166–77CrossRefGoogle Scholar; Huseby, Robert, ‘Spinning the Wheel Or Tossing a Coin?’, Utilitas 23 (2011), pp. 127–39CrossRefGoogle Scholar; Stone, Peter, ‘On Fair Lotteries’, Social Theory and Practice 34 (2008), pp. 573–90CrossRefGoogle Scholar; Saunders, Ben, ‘A Defence of Weighted Lotteries in Life Saving Cases’, Ethical Theory and Moral Practice 12 (2009), pp. 279–90CrossRefGoogle Scholar.

² Broome, John, ‘Fairness’, Ethics Out of Economics (Cambridge, 1999), pp. 111–22CrossRefGoogle Scholar.

³ Gerard Vong, ‘Weighing up Weighted Lotteries’ (unpublished manuscript).

⁴ Broome, John, ‘Uncertainty and Fairness’, The Economic Journal 94 (1984), pp. 624–32CrossRefGoogle Scholar.

⁵ Most writers who advocate lotteries in some cases advocate running a lottery in this case, including Hirose, Rakowski, Saunders and Timmermann. See Hirose, Iwao, ‘Weighted Lotteries in Life and Death Cases’, Ratio 20 (2007), pp. 45–56CrossRefGoogle Scholar; Rakowski, Eric, ‘Taking and Saving Lives’, Columbia Law Review 93 (1993), pp. 1063–1156CrossRefGoogle Scholar; Saunders, ‘A Defence of Weighted Lotteries’; Timmermann, Jens, ‘The Individualist Lottery: How People Count, but Not Their Numbers’, Analysis 64 (2004), pp. 106–12CrossRefGoogle Scholar. This is deontically stronger than merely claiming running a lottery is fair as on a number of plausible philosophers' views fairness is neither a necessary nor a sufficient condition for moral rightness.

⁶ Precisely how much stronger a claim has to be in order to make running a lottery between them absurd and impermissible is a matter for contentious debate. In fact, as Parfit has suggested is true of some reasons, there may be no truth about some claims’ relative strength. On this, see Derek Parfit, On What Matters (Oxford, 2011), vol. 1, pp. 130-41. However, to illustrate the absurdity of running a lottery with a clear-cut case, consider the following. We only have one dose of a medicine that can be used to treat one of two patients. The medicine can be used to prevent the premature death of one person or stop the mild headache of the other person. On the assumption that claim strength in this case depends solely on the size of the benefit they will receive, the person who will die if untreated has a much stronger claim than the person suffering a headache. It is absurd to think one should run a lottery to decide whom to benefit in this case. One ought just to benefit the person who will die if untreated.

⁷ Thanks to Johann Frick for this suggestion.

⁸ Here, I assume fairness has a non-comparative, absolute element. On such a view, fairness does not merely require comparatively equal satisfaction of equally strong claims, so that giving all claimants a 0 per cent chance of benefiting is equally fair as giving all claimants a 100 per cent chance of benefiting. Instead, fairness requires giving potential beneficiaries what they have a claim on and, in cases of scarcity, best approximating the fairest situation where all claimants get a 100 per cent chance of benefiting, where this is understood non-comparatively. For the purposes of this article, I remain neutral on which is the best approximation (i.e. the most fair) of the fairest situation. For more on the comparative/absolute distinction, see Feinberg, Joel, ‘Noncomparative Justice’, Philosophical Review 83 (1974) pp. 297–338Google Scholar; Temkin, Larry, ‘Justice, Equality, Fairness, Desert, Rights, Free Will, Responsibility, and Luck’, Responsibility and Distributive Justice, ed. Knight, C. and Stemplowska, Z. (Oxford, 2011), pp. 51–76CrossRefGoogle Scholar.

⁹ One can imagine cases in which the benefits that people have claims on are accompanied by extra benefits to which they do not have claims. For example, imagine that the available buoys are manufactured by different manufacturers. One manufacturer runs a special, unexpected promotional campaign that rewards people saved through the use of their life buoys in a limited time period with a special luxury holiday. On the assumption that such a promotional holiday is a benefit rather than a burden, it is a benefit beneficiaries have no claim on and therefore is not relevant to satisfying their benefit claims. In such cases, whether or not such a benefit gets better or worse is irrelevant to the satisfaction of their benefit claims, though it may be relevant for what we ought to do all things considered.

¹⁰ Thanks to John Broome, Roger Crisp, David Faraci, Johann Frick, Daniel Halliday, Brad Hooker, Julian Savulescu, Jack Woods, and audiences at Bowling Green State University, Fordham University, the Princeton Philosophical Society and the Oxford University Applied Ethics Discussion Group for comments on earlier versions of this article.