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

Published online by Cambridge University Press:  16 August 2016

HILARY GREAVES
HILARY GREAVES*
Affiliation:
University of Oxfordhilary.greaves@philosophy.ox.ac.uk
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Abstract

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.

Type
Research Article
Information
Utilitas , Volume 29 , Issue 2 , June 2017 , pp. 175 - 213
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Copyright
Copyright © Cambridge University Press 2016 

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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 h ∈ X 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.

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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).