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Uncertainty behind the Veil of Ignorance

Published online by Cambridge University Press:  17 February 2012



This article argues that the decision problem in the original position should be characterized as a decision problem under uncertainty even when it is assumed that the denizens of the original position know that they have an equal chance of ending up in any given individual's place. It supports this claim by arguing that (a) the continuity axiom of decision theory does not hold between all of the outcomes the denizens of the original position face and that (b) neither us nor the denizens of the original position can know the exact point at which discontinuity sets in, because the language we employ in comparing different outcomes is ineradicably vague. It is also argued that the account underlying (b) can help proponents of superiority in value theory defend their view against arguments offered by Norcross and Griffin.

Research Article
Copyright © Cambridge University Press 2012

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1 Harsanyi, John C., ‘Cardinal Utility in Welfare Economics and in the Theory of Risk-taking’, The Journal of Political Economy 61 (1953), pp. 434–5CrossRefGoogle Scholar.

2 When the probabilities of different outcomes are known to the decision-maker we have a decision under risk. When the decision-maker lacks such probability information we have a decision under uncertainty.

3 Parfit, Derek, On What Matters, 2 vols. (Oxford, 2011), vol. 1, pp. 350–1Google Scholar. Nagel also makes the same objection. See Nagel, Thomas, ‘Rawls on Justice’, The Philosophical Review 82 (1973), pp. 220–34CrossRefGoogle Scholar, at 11–12.

4 For a discussion of this distinction see Arrhenius, Gustaf, ‘Superiority in Value’, Philosophical Studies 123 (2005), pp. 97114CrossRefGoogle Scholar.

5 Parfit, Derek, ‘Overpopulation and the Quality of Life’, The Repugnant Conclusion: Essays on Population Ethics, ed. Ryberg, J. and Tännsjö, T. (Dordrecht, 2004), pp. 722CrossRefGoogle Scholar, at 17–18.

6 Griffin, James, Well-Being: Its Meaning, Measurement and Moral Importance, (Oxford, 1986), p. 86Google Scholar.

7 Griffin, Well-Being, p. 86.

8 Norcross, Alastair, ‘Comparing Harms: Headaches and Human Lives’, Philosophy and Public Affairs 26 (1997), pp. 135–67CrossRefGoogle Scholar, at 137.

9 My formulation of Norcross's sequence is slightly different from the original.

10 My argument in this section owes a great debt to Arrhenius, Gustaf and Rabinowicz, Wlodek, ‘Value and Unacceptable Risk’, Economics and Philosophy 21 (2005), pp. 177–97CrossRefGoogle Scholar; Qizilbash, Mozaffar, ‘Transitivity and Vagueness’, Economics and Philosophy 21 (2005), pp. 109–31CrossRefGoogle Scholar; Tuck, Richard, ‘Is There a Free Rider Problem?’, Rational Action: Studies in Philosophy and Social Science, ed. Harrison, R. (New York, 1979), pp. 147–56Google Scholar.

11 Epistemicists deny this. They argue that vague predicates have well-defined extensions and sharp boundaries, but their extensions are unknowable to us. For a defence of epistemicism see Williamson, Timothy, Vagueness (London, 1994)Google Scholar.

12 In this paragraph, I'm following Keefe, Rosanna and Smith, Peter, ‘Introduction’, Vagueness: A Reader, ed. Keefe, R. and Smith, P. (Cambridge, MA, 1997), pp. 157Google Scholar, at 2–3.

13 Qizilbash makes a similar observation. See Qizilbash, ‘Transitivity and Vagueness’, pp. 119–20.

14 The locus classicus is Fodor, Jerry A., The Language of Thought (Cambridge, MA, 1975)Google Scholar.

15 For the argument that the language of thought has to be vague see Sorensen, Roy A., ‘Vagueness within the Language of Thought’, The Philosophical Quarterly 41 (1991), pp. 389413CrossRefGoogle Scholar.

16 Dorsey, Dale, ‘Headaches, Lives and Value’, Utilitas 21 (2009), pp. 3658CrossRefGoogle Scholar, at 46.

17 Dorsey, ‘Headaches, Lives and Value’, p. 49.

18 I departed from Norcross's original formulation to emphasize this point.

19 Here's a brief illustration of why superiority does not entail the rejection of the continuity axiom. Suppose we have three intrinsically valuable goods a, b, and c with values 10, 3, and 1. Suppose that after the first unit of c, the value of each additional nth unit of c is 2−n. In this case, b is superior to c. No matter how many units of c we have their value will be less than 3. However, if there's a lottery giving us a with probability 0.5 and c with probability 0.5 we should pick this lottery over b for certain. We have superiority, but continuity isn't violated.

20 Preferences that do not satisfy the continuity axiom but are complete and transitive, and satisfy the independence axiom, can be represented by assigning a vector of expected utilities to each gamble where these vectors are ordered lexicographically. It's worth noting that attributing a lexicographic value function to the denizens of the OP doesn't entail that the principle which emerges out of the OP will be lexicographic too. Or more precisely, the rejection of continuity gives us lexically ordered principles, but it doesn't ensure that the principles themselves are lexical like the difference principle. For an overview of lexicographic decision theory, where the continuity axiom is dropped, and some applications, see Blume, L., Brandenburger, A. and Dekel, E., ‘An Overview of Lexicographic Choice under Uncertainty’, Annals of Operations Research 19 (1989), pp. 231–46CrossRefGoogle Scholar.

21 Alchian, A. A., ‘The Meaning of Utility Measurement’, The American Economic Review 43 (1953), pp. 2650Google Scholar, at 36–7; Chipman, J. S., ‘The Foundations of Utility’, Econometrica 28 (1960), pp. 193224CrossRefGoogle Scholar, at 221; Luce, R. D. and Raifa, H., Games and Decisions (New York, 1989), p. 27Google Scholar.

22 Kreps, D. M., Notes on the Theory of Choice (Boulder, CO, 1988), pp. 45–6Google Scholar.

23 We can get rid of vagueness in this sense by introducing a new vocabulary that does not contain vague predicates. However, that will mean eliminating our existing concepts and replacing them with other ones.

24 Rawls concedes that this is the case. See Rawls, John, Justice as Fairness: A Restatement (Cambridge, MA, 2001), p. 107Google Scholar.

25 Rawls, John, A Theory of Justice, rev. edn. (Oxford, 1999), p. 123Google Scholar.

26 Rawls, Theory, p. 131

27 Rawls, Theory, p. 134.

28 For Rawls's discussion of this point and a graph illustrating this possibility see Rawls, Justice as Fairness, pp. 107–9. There are a few other steps to his argument which I've ignored here.

29 This assumption departs from Rawls's characterization of the veil of ignorance. I make this assumption to emphasize the robustness of the argument we're developing here.

30 For a helpful discussion of supervaluationism see Keefe, Rosanna, Theories of Vagueness (Cambridge, 2000)Google Scholar.

31 For a very helpful discussion of such hybrid views see Casal, Paula, ‘Why Sufficiency Is Not Enough’, Ethics 117 (2007), pp. 296326CrossRefGoogle Scholar.

32 I am grateful to David Miller, Adam Swift, Nicholas Vrousalis, Andrew Williams, and two anonymous referees for this journal for their helpful comments on previous versions of this article.