Hostname: page-component-7479d7b7d-68ccn Total loading time: 0 Render date: 2024-07-13T23:20:49.228Z Has data issue: false hasContentIssue false

A Reconsideration of the Harsanyi–Sen–Weymark Debate on Utilitarianism

Published online by Cambridge University Press:  16 August 2016

University of


Harsanyi claimed that his Aggregation and Impartial Observer Theorems provide a justification for utilitarianism. This claim has been strongly resisted, notably by Sen and Weymark, who argue that while Harsanyi has perhaps shown that overall good is a linear sum of individuals’ von Neumann–Morgenstern utilities, he has done nothing to establish any connection between the notion of von Neumann–Morgenstern utility and that of well-being, and hence that utilitarianism does not follow.

The present article defends Harsanyi against the Sen–Weymark critique. I argue that, far from being a term with precise and independent quantitative content whose relationship to von Neumann–Morgenstern utility is then a substantive question, terms such as ‘well-being’ suffer (or suffered) from indeterminacy regarding precisely which quantity they refer to. If so, then (on the issue that this article focuses on) Harsanyi has gone as far towards defending ‘utilitarianism in the original sense’ as could coherently be asked.

Research Article
Copyright © Cambridge University Press 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)


1 Bentham, J., An Introduction to the Principles of Morals and Legislation (Oxford, 1879), ch. 4Google Scholar, sec. 5.6; emphasis in original.

2 Mill, J. S., ‘Utilitarianism’, Utilitarianism; On Liberty; Essay on Bentham, ed. Warnock, M. (London, 1962), ch. IVGoogle Scholar.

3 Harsanyi, J. C., ‘Cardinal Utility in Welfare Economics and in the Theory of Risk-Taking’, Journal of Political Economy 61.5 (1953), pp. 434–5CrossRefGoogle Scholar, at 434; Harsanyi, J., ‘Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility’, Journal of Political Economy 63.4 (1955), pp. 309–21CrossRefGoogle Scholar; Harsanyi, J. C., Rational Behavior and Bargaining Equilibrium in Games and Social Situations (Cambridge, 1977)CrossRefGoogle Scholar.

4 Samuelson, P. A., ‘Bergsonian Welfare Economics’, Economic Welfare and the Economics of Soviet Socialism: Essays in Honor of Abram Bergson, ed. Roseelde, S. (Cambridge, 1981), pp. 223–66CrossRefGoogle Scholar, at 245.

5 Sen, A., ‘Welfare Inequalities and Rawlsian Axiomatics’, Theory and Decision 7 (1976), pp. 243–62CrossRefGoogle Scholar; Sen, A., ‘Non-linear Social Welfare Functions: A Reply to Professor Harsanyi’, Foundational Problems in the Special Sciences, vol. 2, ed. Butts, R. E. and Hintikka, J., (Dordrecht, 1977), pp. 297302 CrossRefGoogle Scholar.

6 Weymark, J. A., ‘A Reconsideration of the Harsanyi–Sen Debate on Utilitarianism’, Interpersonal Comparisons of Well-being, ed. Elster, J. and Roemer, J. E. (Cambridge, 1991), pp. 255320 CrossRefGoogle Scholar; Weymark, J. A., ‘Measurement Theory and the Foundations of Utilitarianism’, Social Choice and Welfare 25.2–3 (2005), pp. 527–55CrossRefGoogle Scholar.

7 Roemer, J. E., ‘Harsanyi's Impartial Observer is not a Utilitarian’, Justice, Political Liberalism, and Utilitarianism: Themes from Harsanyi and Rawls, ed. Fleurbaey, M., Salles, M. and Weymark, J. (Cambridge, 2008), pp. 129–35CrossRefGoogle Scholar.

8 Harsanyi, ‘Cardinal Utility in Welfare Economics and in the Theory of Risk-Taking’, Harsanyi, Rational Behavior and Bargaining Equilibrium in Games and Social Situations, pp. 48–50.

9 Rawls, J., A Theory of Justice (Oxford: Oxford University Press, 1972)Google Scholar.

10 E.g. Weymark, ‘A Reconsideration of the Harsanyi–Sen Debate on Utilitarianism’.

11 E.g. Mongin, P., ‘Consistent Bayesian Aggregation’, Journal of Economic Theory 66.2 (1995), pp. 313–51CrossRefGoogle Scholar; Broome, J., ‘Bolker–Jeffrey Expected Utility Theory and Axiomatic Utilitarianism’, The Review of Economic Studies 57.3 (1990), pp. 477502 CrossRefGoogle Scholar; see also Mongin, ‘Impartiality, Utilitarian Ethics, and Collective Bayesianism’ (Ely Lectures delivered at Johns Hopkins University, 2002) and references therein.

12 Diamond, P. A., ‘Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility: Comment’, Journal of Political Economy 75.5 (1967), pp. 765–6CrossRefGoogle Scholar; Sen, ‘Welfare Inequalities and Rawlsian Axiomatics’.

13 E.g. Adler, M. and Sanchirico, C., ‘Inequality and Uncertainty: Theory and Legal Applications’, University of Pennsylvania Law Review 155 (2006), pp. 279377 CrossRefGoogle Scholar, at 323.

14 Fleurbaey, M. and Voorhoeve, A., ‘Decide as You Would with Full Information! An Argument against ex ante Pareto’, Inequalities in Health: Concepts, Measures, and Ethics, ed. Eyal, N., Hurst, S., Norheim, O. and Wikler, D. (Oxford, 2013), pp. 113–28CrossRefGoogle Scholar.

15 Mongin, P. and d'Aspremont, C., ‘Utility Theory and Ethics’, Handbook of Utility Theory, vol. 1: Principles, ed. Barbera, S., Hammond, P. and Seidl, C. (Dordrecht, 1998), pp. 371481 Google Scholar, at 442.

16 Roemer, J. E., ‘Egalitarianism against the Veil of Ignorance’, The Journal of Philosophy (2002), pp. 167–84CrossRefGoogle Scholar.

17 If (but only if) the set of outcomes is sufficiently rich, one can instead take the i-cardinal structure to be given by an ordering of pairs (‘the difference between x 1 and x 2 is at least as great as the difference between x 3 and x 4’), and still end up with numerical scales that are unique up to positive affine transformation; see the discussion of ‘intrapersonal difference comparability’ in Bossert, W. and Weymark, J. A., ‘Utility in Social Choice’, Handbook of Utility Theory, vol. 2: Extensions, ed. Barbera, S., Hammond, P. and Seidl, C. (Heidelberg, 1977), pp. 10991177 Google Scholar, at 1127–8, and references therein.

18 We also need to impose requirements of mutual consistency between the i-ordinal and i-cardinal (resp., i-cardinal and co-cardinal) structures for a given quantity. Consistency between i-ordinal and i-cardinal structure: if a i b, c i d, e i f, g i hX and $C_{i}(a,c,e,g)=r\in \mathbb{R}$ , then Ci (b, d, f, h) = r. Consistency between i-cardinal and cocardinal structure: if Ci (a, b, c, d) = Cj (e, f, g, h), and if in addition (a, b; i) ~ (e, f; j), then (c, d; i) ~ (g, h; j).

19 But not inevitable: cf. the ‘extended preferences’ approach to grounding interpersonal comparisons, discussed in e.g. Harsanyi, Rational Behavior, secs. 4.2–4.4; J. Broome, ‘Extended Preferences’, Preferences, ed. Fehiga and Wessels, pp. 271–87; Adler, M., Well-being and Fair Distribution: Beyond Cost–Benefit Analysis (Oxford: 2012), ch. 3Google Scholar; H. Greaves and H. Lederman, ‘Extended Preferences and Interpersonal Comparisons of Well-being’ (forthcoming in Philosophy and Phenomenological Research, 2016).

20 For further discussion of weighted utilitarianism and interpersonal comparisons of utility in the context of Harsanyi’s theorems, see, e.g. Mongin and d’Aspremont, ‘Utility Theory and Ethics’, sec. 5.2. For Harsanyi-style theorems that aim to establish unweighted utilitarianism via the imposition of an additional axiom of ‘anonymity’, see Mongin and d’Aspremont, ‘Utility Theory and Ethics’, Proposition 5.3; d'Aspremont, C. and Mongin, P., ‘A Welfarist Version of Harsanyi's Aggregation Theorem’, Justice, Political Liberalism, and Utilitarianism (Cambridge, 2008), pp. 184–97CrossRefGoogle Scholar), Theorem 7.2.

21 Harsanyi, J. C., ‘Nonlinear Social Welfare Functions: Do Welfare Economists have a Special Exemption from Bayesian Rationality?’, Theory and Decision 6.3 (1975), pp. 311–32CrossRefGoogle Scholar; Harsanyi, J. C., ‘Nonlinear Social Welfare Functions: A Rejoinder to Professor Sen’, Foundational Problems in the Special Sciences, vol. 2, ed. Butts, R. E. and Hintikka, J. (Heidelberg, 1977), pp. 293–96CrossRefGoogle Scholar.

22 Sen, ‘Welfare Inequalities and Rawlsian Axiomatics’, p. 248.

23 Harsanyi, ‘Nonlinear Social Welfare Functions: A Rejoinder to Professor Sen’, p. 294.

24 De Finetti, B., Theory of Probability, vol. 1 (London, 1974), p. 76 Google Scholar.

25 Sen, ’Welfare Inequalities and Rawlsian Axiomatics’, pp. 249–50; emphasis in original.

26 Field, H., ‘Theory Change and the Indeterminacy of Reference’, Journal of Philosophy 70.14 (1973), pp. 462–81Google Scholar.

27 The terminology follows Field, ‘Theory Change and the Indeterminacy of Reference’.

28 Fine, K., ‘Vagueness, Truth and Logic’, Synthese 30.3 (1975), pp. 265300 CrossRefGoogle Scholar.

29 Williamson, T., Vagueness (London, 2002), ch. 5Google Scholar.

30 von Neumann, J. and Morgenstern, O., Theory of Games and Economic Behaviour (Princeton, 1944), p. 23 Google Scholar.

31 Broome, J., ‘Can there be a Preference-Based Utilitarianism?’, Justice, Political Liberalism and Utilitarianism: Themes from Harsanyi and Rawls, ed. Fleurbaey, M., Salles, M. and Weymark, J. (Cambridge, 2008), pp. 221–38CrossRefGoogle Scholar, at 222.

32 The difficulty of the question has often been noted in the literature on prioritarianism: see e.g. Broome, J., Weighing Goods (Oxford, 1991)Google Scholar; Parfit, D., ‘Another Defence of the Priority View’, Utilitas 24 (2012), pp. 399440 CrossRefGoogle Scholar; Greaves, H., ‘Antiprioritarianism’, Utilitas 27 (2015), pp. 142 CrossRefGoogle Scholar.

33 Variations on this theme are explored by Edgeworth, F. Y., Mathematical Psychics: An Essay on the Application of Mathematics to the Moral Sciences (London, 1881)Google Scholar, pp. 7ff., 60ff., 98ff.; Y.-K. Ng, ‘Bentham or Bergson? Finite Sensibility, Utility Functions and Social Welfare Functions’, The Review of Economic Studies (1975), pp. 545–69; and T. Tännsjö, ‘Utilitarianism or Prioritarianism?’ (n.d., unpublished). It is also the basic idea behind the Borda count.

34 For discussion of various results connecting separability conditions to additive representations and of the range of possible applications of those results, see e.g. Blackorby, C., Primont, D. and Russell, R. R., ‘Separability: A Survey’, Handbook of Utility Theory: vol. 1: Principles (Heidelberg, 1998), p. 49 Google Scholar, sec. 5; D. von Winterfeldt, W. Edwards, et al. (1986). Decision Analysis and Behavioral Research (Cambridge), pp. 331–4; Broome, Weighing Goods.

35 For overviews of attempts to articulate a causal principle as whole or part of metasemantic theory, see K. Neander, ‘Teleological Theories of Mental Content’, The Stanford Encyclopaedia of Philosophy (Spring 2012 edition), <>; Rupert, R. D., ‘Causal Theories of Mental Content’, Philosophy Compass 3.2 (2008), pp. 353–80CrossRefGoogle Scholar. On the ‘charity plus eligibility’ programme, see especially Lewis, D., ‘New Work for a Theory of Universals’, Australasian Journal of Philosophy 61.4 (1983), pp. 343–77CrossRefGoogle Scholar; Lewis, D., ‘Putnam's Paradox’, Australasian Journal of Philosophy 62.3 (1984), pp. 221–3CrossRefGoogle Scholar.

36 Weatherson, B., ‘The Role of Naturalness in Lewis's Theory of Meaning’, Journal for the History of Analytical Philosophy 1.10 (2013)CrossRefGoogle Scholar.

37 See especially Williamson, Vagueness, esp. chs. 7, 8.

38 Lewis, D. K., On the Plurality of Worlds (Cambridge, 1986), p. 61 Google Scholar.

39 For further discussion of the general issue of how to understand higher-order naturalness, see Sider, T., Writing the Book of the World (Oxford, 2011), ch. 7.11.1CrossRefGoogle Scholar; J. R. G. Williams, ‘Eligibility and Inscrutability’, The Philosophical Review (2007), pp. 361–99; J. Hawthorne, ‘Craziness and Metasemantics’, The Philosophical Review (2007), pp. 427–40; J. Hawthorne, ‘Quantity in Lewisian Metaphysics’, Metaphysical Essays, ed. J. Hawthorne (Oxford, 2006), pp. 236–7.

40 As noted already by W. Vickrey, ‘Measuring Marginal Utility by Reactions to Risk’, Econometrica (1945), pp. 319–33.

41 Mongin, ‘Impartiality, Utilitarian Ethics, and Collective Bayesianism’.

42 M. Fleurbaey and P. Mongin, ‘The Utilitarian Relevance of the Aggregation Theorem’ (n.d., unpublished manuscript).

43 For valuable discussions, I am grateful to Ted Sider, Robbie Williams, and participants in the 2014 Conference on Rational Choice and Philosophy at Vanderbilt University, especially Christian List and John Weymark. Thanks also to an anonymous referee for extremely helpful comments and suggestions.

44 Harsanyi’s own presentations of (especially) the Impartial Observer result are rather informal. The formulation outlined here is close to that provided by Weymark, ‘A Reconsideration of the Harsanyi–Sen Debate on Utilitarianism’.

45 I.e. the probability that π assigns to extended alternative (A, i) is given by the product π X (A) · π I (i).