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The Equality of Lotteries

Published online by Cambridge University Press:  01 July 2008

Ben Saunders
Jesus College, Oxford


Lotteries have long been used to resolve competing claims, yet their recent implementation to allocate school places in Brighton and Hove, England led to considerable public outcry. This article argues that, given appropriate selection is impossible when parties have equal claims, a lottery is preferable to an auction because it excludes unjust influences. Three forms of contractualism are discussed and the fairness of lotteries is traced to the fact that they give each person an equal chance, as a surrogate for their equal claim to the good. It is argued that this can be a reason to favour an artificially-constructed lottery to a ‘natural’ lottery where there is suspicion that the latter may be biased.

Research Article
Copyright © The Royal Institute of Philosophy 2008

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1 A. O'Hear, ‘Editorial: The Equality Lottery’, Philosophy 82, No. 2 (April 2007), 209–10. For examples of mass media debate, see G. Paton ‘Schools can use lotteries for ‘fairer’ admissions, says minister’, The Daily Telegraph (Thursday 01/03/07) 15, and S. Laville and R. Smithers ‘War over school boundaries divides Brighton’, The Guardian (Thursday 01/03/07), 4.

2 The confusion surrounding equality of opportunity is well-exposed in Richards, J.R., ‘Equality of Opportunity’, Ratio X, No. 3 (December 1997), 253–79CrossRefGoogle Scholar. It is equality of opportunity, rather than lotteries per se, that seems to motivate O'Hear's complaint.

3 For others who stress the second-best nature of lotteries, see Broome, J. ‘Fairness’ in his Ethics Out of Economics (Cambridge: Cambridge University Press, 1999), 119–21CrossRefGoogle Scholar, and Stone, P.Why Lotteries Are Just’, The Journal of Political Philosophy 15, No. 3 (September 2007), 284 and 294.Google Scholar

4 Parfit, D., ‘Equality’, Ratio X, No. 3 (December 1997), 211Google Scholar and passim.

5 1 Kings 3:16–28

6 Broome, op. cit., 119.

7 Richards, op. cit., 217 offers the example of running shoes in a race. If only half the competitors have shoes, it seems fair to make all run barefoot.

8 For examples of such claims, see Williams, B., ‘The Idea of Equality’ in his Problems of the Self: Collected Papers 1956–72 (Cambridge: Cambridge University Press, 1973), 240–1CrossRefGoogle Scholar and Walzer, M., Spheres of Justice: A Defence of Pluralism and Equality (Oxford: Blackwell, 1983)Google Scholar, passim.

9 For discussion of Hohfeld's influential classification, see Thomson, J. J., The Realm of Rights (Cambridge, Mass.: Harvard University Press, 1990), ch.1Google Scholar and Sumner, L. W., The Moral Foundation of Rights (Oxford: Clarendon Press, 1987), ch.2Google Scholar.

10 Technically the ‘equal chance’ criterion assumes this is a fair lottery. A fair lottery is one where each side has an equal chance of winning. A just lottery is one that is appropriate to resolve a given conflict. A fair lottery need not be just, for instance if we were to toss a fair coin between two very unequal claimants. I do not here consider the merits of a weighted lottery, but possibly one may be just though not fair, as I use the term here.

11 Of course, a fair coin is generally preferable to a biased one, if only to remove any suspicion that the bias was known. In principle, however, if a third-party coin-tosser informed the claimants beforehand that he was using a biased coin, it should make no difference to the fairness of the lottery.

12 By a ‘natural lottery’ I mean letting goods fall where they lie, on the assumption that this is at least epistemically random. Thus, for example, if some good is falling towards us, we may agree that whoever it lands closest to should keep it, rather than adopting some further artificial chance mechanism. I do not mean a constitutive lottery, as Rawls intends by the term, see Rawls, J., A Theory of Justice revised edition (Oxford: Oxford University Press, 1999), 64Google Scholar and Hurley, S., Justice, Luck, and Knowledge (2003), ch.4Google Scholar. I address the question whether geographical proximity really can serve as a natural lottery below.

13 Stone, op. cit., 289–91. I will not, in the following, discuss Gauthier's version of contractarianism, which seems less plausible (to me) than the three I do discuss; but I see no reason why it cannot lead to lotteries, at least to adjudicate between parties with equal bargaining strength.

14 Harsanyi, J., ‘Cardinal Utility in Welfare Economics and in the Theory of Risk-taking’, Journal of Political Economy, 61, No. 5 (October 1953), 434–5CrossRefGoogle Scholar and ‘Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility’, Journal of Political Economy, 63, No. 4 (August 1955), 314–5. Stone, op. cit., 282, contrasts Harsanyi's contractarian account of justice to utilitarianism. I see utilitarianism as a first-order moral theory, and contractarianism a meta-theory by which it may be justified. C.f. Scanlon, T. M. ‘Contractualism and Utilitarianism’ in Utilitarianism and Beyond, Williams, B. and Sen, A. (eds.) (Cambridge: Cambridge University Press, 1982)Google Scholar.

15 Stone, op. cit., 290. Or, at least, no reason of justice. There are two possible reasons why a lottery may be favoured: a) because people value being treated fairly, and therefore even losers have a higher utility if they know a lottery was held and b) if what is to be chosen is a general social policy, rather than decision for a particular case, then one cannot be sure that a rule like ‘pick the white candidate’ will select one and only one person for the job, whereas allocating the good(s) by lottery is a perfectly general procedure.

16 Rawls, op. cit., for example, 11–2 and 153–4. Stone, op. cit., 291, claims contractors in such a framework would have no special reason to favour lotteries, though Rawls explicitly recommends lotteries in a number of places, e.g. Rawls, op. cit., 329 and ‘Outline of a Decision Procedure for Ethics’, The Philosophical Review, 60, No. 2 (April 1951), 193. I argue below that lotteries can indeed be recommended from Rawls’ original position.

17 Stone, op. cit., 291. He dismisses this response in footnote 29, but I confess to finding the reasoning obscure. Of course, that the chance of a benefit is itself a benefit is disputed. I cannot here argue for this belief, but point to the considerations in Richards, op. cit., 271–4.

18 A requirement Rawls, (1999) op. cit., 153–4, refers to as the ‘strains of commitment’. Note that this consideration comes in because Rawls explicitly uses the original position to determine general principles to regulate the basic structure of society. There is no suggestion that similar reasoning applied directly to particular problems will lead to satisfactory conclusions.

19 Scanlon, op. cit., and What We Owe to Each Other (Cambridge, Mass.: Belknap Press of Harvard University Press, 1998).

20 Stone, op. cit., 291–2. C.f. Scanlon, (1998) op. cit., 232.

21 In this, I follow Richards, op. cit., especially 274, who argues that opportunity is a good to be distributed and promoted.

22 I think many accepted distributive policies have, at least in part, this justification. For instance, majority rule is often defended as giving each person equal chance of satisfaction, e.g. Dahl, R.Democracy and its Critics (New Haven: Yale University Press, 1989), 144Google Scholar and Christiano, T., The Rule of the Many (Boulder, Colo.: Westview Press, 1996), 55Google Scholar.

23 The many debts I have incurred in thinking about related issues over the last few years are too numerous to mention here, though I must acknowledge the Arts and Humanities Research Council for supporting this earlier work. For stimulation and comments on this particular piece, I thank Conall Boyle, Robert Jubb, Peter Stone and participants in Julian Savulescu's Applied Ethics group (Oxford).