¹ For example, Rawls, John, A Theory of Justice (Oxford, 1972)Google Scholar, esp. p. 26; Sen, Amartya, On Economic Inequality (Oxford, 1973), p. 16CrossRefGoogle Scholar; Williams, Bernard, ‘A Critique of Utilitarianism’, Utilitarianism: For and against, ed. Smart, J. J. C. and Williams, Bernard (Cambridge 1973), pp. 142–3Google Scholar; Scheffler, Samuel, The Rejection of Consequentialism (Oxford, 1982)Google Scholar.

² Nagel, Thomas, Mortal Questions (Cambridge, 1979), p. 124Google Scholar.

³ Parfit, Derek, ‘Equality and Priority’, Ratio 10 (1997), pp. 202–21, at 213CrossRefGoogle Scholar.

⁴ Parfit, Derek, ‘Another Defence of the Priority View’, Utilitas 24 (2012), pp. 399–440, at 401CrossRefGoogle Scholar.

⁵ Harsanyi, John, ‘Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility’, Journal of Political Economy 63 (1955), pp. 309–21CrossRefGoogle Scholar.

⁶ It is not always clear whether prioritarians have in mind axiological, deontological or fitting-feeling claims, but I do not think the axiological prioritarian is a straw man. Parfit clearly draws the distinction (in his terminology, between ‘telic’ and ‘deontic’ prioritarianism), stating that ‘for most of my discussion, this difference does not matter’ (Equality or Priority? (Lawrence, Ka., 1995), sect. VIII); in a later discussion, he defends ‘the telic priority view’, and his statement of that view explicitly includes the clause that ‘it would in one way make the outcome better’ (my emphasis) if one acted so as to give people ‘a greater sum of weighted benefits’ (Parfit, ‘Another Defence’, p. 402). Williams explicitly argues for deontological as opposed to axiological (‘teleological’) prioritarianism, in response to objections that he takes to affect only the latter (Williams, Andrew, ‘The Priority View Bites the Dust?’, Utilitas 24 (2012), pp. 315–31CrossRefGoogle Scholar).

An anonymous referee has suggested that the notion of better-simpliciter is unacceptably mysterious until and unless it has been given an analysis, perhaps in deontic terms (for example, ‘more choiceworthy’). I don't agree, but those who do are free to substitute their preferred analysis throughout (any such analysis had better not collapse the axiological/merely-deontological distinction altogether). I leave it to the reader to examine whether or not any of the details of the arguments in this article are affected by the particular substitution they prefer.

⁷ To avoid repeated use of the cumbersome term ‘weakly better’ (or the still more cumbersome ‘at least as good as’), I will generally write ‘better’ where the context makes clear whether it is weak betterness (≽_i, ≽) or strict betterness (≻_i, ≻) that is intended.

⁸ See Debreu, Gerard, ‘Topological Methods in Cardinal Utility Theory’, Mathematical Methods in the Social Sciences, ed. Arrow, Kenneth J. and Suppes, Patrick (Stanford, 1960), pp. 16–26Google Scholar.

⁹ Both the primitivist position and this sort of response to the positivist complaint are explicit in Sen, Amartya, ‘Welfare Inequalities and Rawlsian Axiomatics’, Theory and Decision 7 (1976), pp. 243–62, at 249–50CrossRefGoogle Scholar.

¹⁰ This weakening of the positivist position is most explicit in conceptual role semantics, but even those who reject that approach to semantics must acknowledge the point in some form.

¹¹ For example, Broome, John, Weighing Goods (Oxford, 1991), pp. 146–8 and sect. 10.3Google Scholar.

¹² von Neumann, John and Morgenstern, Oskar, Theory of Games and Economic Behaviour (Princeton, 1944)Google Scholar.

¹³ As is well recognized, if our starting point is an independent better-for-i ranking for each person i, this representation theorem does not yet give us any interpersonal unit comparisons, i.e. comparisons between the difference between A and B for person i ₁ and the difference between C and D for a distinct person i ₂: it merely gives us a separate unit-comparable utility scale for each person. This, of course, is why the issue of ‘interpersonal utility comparisons’ in particular has remained a vexed one after the advent of expected utility theory. Without undertaking a full survey of the possibilities, I will assume, with both the modern utilitarian and the modern prioritarian, that some solution to this problem is available.

¹⁴ In defence of my claim that modern prioritarianism has become this ‘Technical’ claim rather than the ‘Primitivist’ version, note e.g. that the criticism of prioritarianism made by Otsuka and Voorhoeve – based on the ‘moral shift’ (the appearance of the transform f) that prioritarians claim to occur between first-person (individual-betterness) and third-person (overall-betterness) judgements – very obviously applies only to Technical Prioritarianism, not to Primitivist Prioritarianism (Otsuka, Michael and Voorhoeve, Alex, ‘Why It Matters That Some Are Worse Off Than Others: An Argument Against the Priority View’, Philosophy and Public Affairs 37 (2009), pp. 171–99CrossRefGoogle Scholar). Meanwhile, of the six articles (four defending prioritarianism) that appear in a special issue of Utilitas (September 2012) discussing Otsuka and Voorhoeve's criticism, none mentions the possibility that the criticism misses its mark for this reason. A Technical rather than Primitivist theory is explicitly recommended to prioritarians by Rabinowicz, in response to the criticisms from Broome cited above (Rabinowicz, Wlodek, ‘Prioritarianism for Prospects’, Utilitas 14 (2002), pp. 2–21CrossRefGoogle Scholar). In contrast, in much of the older work it is less clear whether it is a Primitivist or a Technical claim that is intended (e.g. Nagel, Mortal Questions; Parfit, ‘Equality and Priority’). But sometimes it is clear that the Technical version is not intended: thus Sen, defending ‘social welfare functions’ that exhibit ‘non-linearity’ of the sort represented by the transform f in (2), writes that it would be ‘grotesque’ ‘to define a non-linear social welfare function on von Neumann–Morgenstern utilities’ (Sen, ‘Welfare Inequalities’, p. 250; emphasis in original). Similarly, when Broome argues against ‘prioritarianism’, he is certainly discussing Primitivist Prioritarianism, and does not countenance Technical Prioritarianism (Broome, Weighing Goods).

¹⁵ Harsanyi, ‘Cardinal Welfare’.

¹⁶ By definition. Here I follow Parfit's suggestion for regimenting the terms ‘priority’ and ‘equality’ (Parfit, ‘Equality and Priority’). The corresponding formal issue is whether or not the value function exhibits additive separability of persons (Broome, Weighing Goods, ch. 9).

¹⁷ Parfit, ‘Another Defence’, p. 423.

¹⁸ Otsuka and Voorhoeve, ‘Why It Matters’, pp. 190–2. Otsuka and Voorhoeve's discussion draws on Scanlon, T. M, ‘Preference and Urgency’, Journal of Philosophy 72 (1975), pp. 655–69, at 659–60CrossRefGoogle Scholar; Nagel, Thomas, The View from Nowhere (Oxford, 1986), pp. 166–70Google Scholar.

¹⁹ Porter, Thomas, ‘In Defence of the Priority View’, Utilitas 24 (2012), pp. 349–64CrossRefGoogle Scholar.

²⁰ Readers may be starting to suspect that my cautionist character has lost the plot. I emphasize that I am sympathetic to this judgement: I do not advocate his theory-building procedure. His raison d’etre is not to propose a tenable rival doctrine, but to raise, by way of an analogy that I will argue is quite precise, equally serious concerns about the prioritarian's theory-building method. Section V will examine the cautionist's mistakes, and will undertake the comparison between prioritarian and cautionist.

²¹ Debreu, ‘Topological Methods’; for an informal exposition, see Broome, Weighing Goods, ch. 4.

²² To elaborate: the Technical Cautionist is committed to the value function ∑_ig ^{− 1}(u ^VNM_i) because his defining claim, qua Technical Cautionist, is that u ^VNM_i = g(u^D_i). It follows from this that u^D_i = g ^{− 1}(u ^VNM_i); but all agree that the overall value function is ∑_iu^D_i, by definition of Debreu utility.

²³ This is where the issues that Parfit touches on in the above quote in section II.3 (Parfit, ‘Another Defence’, p. 423) fit into the discussion; pace Parfit, they are not relevant to the question of axiology.

²⁴ In recommending to prioritarians that they embrace Ex Post (Technical) Prioritarianism, Rabinowicz notes that since the issues of priority to the worse off and of prudential risk aversion are conceptually entirely distinct, it is not immediately inevitable that these two degrees will coincide (Rabinowicz, ‘Prioritarianism for Prospects’). This observation is correct: there is some argument to be had here (it is the argument over the Ex Ante Pareto Principle). But we must not overstate the degree of comfort that the Technical Prioritarian can take from this observation: to note that priority of the worse off and prudential risk aversion are conceptually distinct is not to supply any positive reason for thinking that the second is smaller than the first.

²⁵ Greene, Joshua and Baron, Jonathan, ‘Intuitions about Declining Marginal Utility’, Journal of Behavioural Decision Making 14 (2001), pp. 243–55CrossRefGoogle Scholar. Greene and Baron's experiment shows, for various sorts of utility, that subjects report having intuitions of declining marginal utility not only with respect to independent scales (such as years of life), but also with respect to that same sort of utility: intuitions whose content is in fact incoherent.

²⁶ Parfit, ‘Another Defence’, p. 403; emphasis added.

²⁷ Harsanyi, ‘Cardinal Welfare’; Otsuka and Voorhoeve, ‘Why It Matters’.

²⁸ An example is the value function V = (∑_iu ^VNM_i)(1 − G), where G is the ‘Gini coefficient’, a measure of inequality. See e.g. Matthew Adler and Chris Sanchirico, ‘Inequality and Uncertainty: Theory and Legal Applications’, University of Pennsylvania Law Review 155 (2006), pp. 279–377, at 301–2.

²⁹ Parfit, ‘Another Defence’, p. 423. Parfit writes ‘expectable’, but makes clear that he means what others mean by ‘expected’.

³⁰ For useful discussions and/or comments on a previous draft of this article, I am grateful to Constanze Binder, John Broome, William MacAskill, Toby Ord, and audiences in seminars at Yale, Bristol, the London School of Economics and Erasmus University (Erasmus Institute for Philosophy and Economics).

³¹ Parfit, ‘Another Defence’; Porter, ‘Priority View’. In the article cited, Parfit writes that ‘we ought . . . to accept’ what he calls ‘the equal chances view’, i.e. the view that ‘when we could save the life of only one of two people, who do not differ in relevant ways, we ought to give these people equal chances of being the person whose life we save’ (‘Another Defence’, p. 431), and that ‘prioritarians should accept’ the view that ‘in deciding what we ought to do, we ought to take into account not only the goodness of outcomes, but also the goodness of people's prospects, in the sense of their chances of receiving benefits or burdens, and their expectable levels of well-being’ (‘Another Defence’, p. 432). On a superficial reading, these views seems more in keeping with Ex Ante than with Ex Post Prioritarianism. However, the context suggests that Parfit intends to limit the relevance of individuals’ status quo ex ante expected goodness to the deontic, rather than the telic, part of his overall moral theory. For instance, one page later, in discussing his ‘Expanded Nine’ case, Parfit writes: ‘When we assess the goodness of these outcomes, it makes no difference whether it is Jack or Jill who might have these longer or shorter lives, so these three acts would have outcomes that would be expectably equally good. But these acts differ in their effects on people's prospects.’ He concludes from this that, according to a principle (his PP3) that prioritarians ‘may believe’, ‘if other things are equal, we ought to do’ one of the three acts under discussion rather than either of the other two (my emphasis).

³² ‘Ex ante’ views in general, if not this specific form, have been defended by Diamond, Peter A., ‘Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility: Comment’, Journal of Political Economy 75 (1967), pp. 765–6CrossRefGoogle Scholar; Epstein, Larry G. and Segal, Uzi, ‘Quadratic Social Welfare Functions’, Journal of Political Economy 100 (1992), pp. 691–712CrossRefGoogle Scholar.

³³ Fleurbaey, Marc, ‘Assessing Risky Social Situations’, Journal of Political Economy 118 (2010), pp. 649–80CrossRefGoogle Scholar.

³⁴ This point was made in McCarthy, David, ‘Utilitarianism and Prioritarianism II’, Economics and Philosophy 24 (2008), pp. 1–33CrossRefGoogle Scholar.

³⁵ I am grateful to Toby Ord for this example.

³⁶ Marc Fleurbaey and Alex Voorhoeve, ‘Decide as You Would with Full Information! An Argument against Ex Ante Pareto’, Health Inequality: Ethics and Measurement, ed. Nir Eyal et al. (Oxford, forthcoming). The principle in question is Fleurbaey and Voorhoeve's ‘Principle of Full Information, Part I’.

³⁷ For example, Fleurbaey, ‘Assessing Risky Social Situations’.

³⁸ Fleurbaey, ‘Assessing Risky Social Situations’.