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Subjective values should be sharp


Elga (Philos Impr 10(5): 1–10, 2010) has argued that, even when no particular subjective probability is required by one’s evidence, perfectly rational people will have sharp subjective probabilities. Otherwise, they would be rationally permitted to knowingly turn down some sure gains. I argue that it is likewise true that, even when we do not possess enough practical reasons for a sharp evaluation (because of optionality or ignorance), perfectly rational people will have sharp subjective values. Those who would be most inclined to reject this argument are those who claim that we are rationally required by either our beliefs that objective values are unsharp (such as strong incomparability, vague value, or parity) or by our own ‘real’ values to have unsharp subjective values. Regarding the former claim, I show that we need not believe that all objective values are sharp to rationally have unsharp subjective values. Regarding the latter claim, I conclude that sharpened subjective values must be ‘real’ (i.e., practically authoritative) because otherwise perfect rationality would be impossible in principle.

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  1. 1.

    This debate is often framed as an investigation into the nature of ‘preferences’. Some notable theories include: Samuelson’s (1937) revealed preference view, Sen’s (1977) ranking of preference rankings, Broome’s (1991) objective goodness view, and Rabinowicz’s (2012) fitting attitudes account.

  2. 2.

    Assuming their expected values are analyzed in isolation of future and past choices; see Sects. 3.1 and 3.2.2.

  3. 3.

    To be clear, I do not assert that these purported nonstandard value relations rationally require agents to have unsharp subjective values (see Sect. 4.1), but this is a natural view for such theories. Martin Peterson (2007, 2014) uses this fact to argue that all such nonstandard value relations have money pump problems.

  4. 4.

    Since rationality only requires alignment between mental states, rationalityE is best understood as requiring one to have evaluations that fit what one believes about objective values (not that objective values directly impose rational requirements on one’s evaluations).

  5. 5.

    The example in Elga’s (2010) argument is a series of bets about an event for which one has unspecific evidence. That exact example does not apply to a defense of Sharp Values, but this is a parallel example.

  6. 6.

    No assumptions are needed regarding diminishing returns. However, it helpfully simplifies the case to stipulate that there are no increasing returns. Specifically, you do not value owning one diamond less than $19k and value owning both diamonds more than $39k.

  7. 7.

    This is very similar to Good’s principle (1952, p. 114) and to what Miriam Schoenfield (2017, p. 671) labels Permission, except for the key difference in both cases that unsharp credences only result from ignorance (insufficient evidence), whereas unsharp values might also result from optionality.

  8. 8.

    Thanks to an anonymous reviewer for pressing this point.

  9. 9.

    Gert (2014) offers a plausible account of what I am calling ‘optional value’. In Gert’s model, normative strength has two dimensions: Its justifying strength determines its maximum rationally permissible weight for an agent, and its requiring strength determines the minimum.

  10. 10.

    It is worth noting that, since unsharp credences are never the result of optionality, this response to the rebuttal using MMEU cannot be used to defend Elga’s (2010) conclusion.

  11. 11.

    For further discussion of the bootstrapping problem, see Holton (2009, pp. 139–148) and Bratman (1987).

  12. 12.

    Holton (2009, pp. 142–148) defends such a view regarding resolutions. He argues that one should only reconsider resolutions if doing so is permitted by some set of rules governing revisions that tend to have the best results. The toxin case might pose a problem for his view, since nothing has changed since the resolution was adopted, so it is doubtful that the rules would permit the revision.

  13. 13.

    In my version, this would be to assume that the agent is rationally permitted to act on any subjective value within the interval. But, to be clear, the evaluation one uses to deliberate regarding Offer A need not be the same as for Offer B. Otherwise, the strategy would just be Sharp Values. Rather, Weirich assumes the Permissive Principle applies to each decision with unsharp probabilities (values) in isolation.

  14. 14.

    Weirich’s proposal fails to refute Elga’s argument (regarding sharp subjective probabilities) for the same kind of reason as I offer here.

  15. 15.

    Other nonstandard value relations have been proposed, such as ‘imprecise equality’ (Parfit 2016) and ‘clumpy equality’ (Hsieh 2005).

  16. 16.

    Chang (1997) offers one of the most influential versions of the small improvement argument, but the argument goes back at least as far as de Sousa (1974, pp. 544–45), and the phenomenon was addressed at least as early as Leonard Savage (1954, p. 17).

  17. 17.

    See, e.g., Raz (1986, p. 326).

  18. 18.

    It is worth flagging that the defenders of parity sometimes differ regarding whether parity makes preferences or choices optional, but I assume here that parity makes preferences optional.

  19. 19.

    For the purposes of this essay, it is safe enough to treat ‘favoring’ and ‘evaluating’ similarly.

  20. 20.

    Gustafsson and Espinoza (2010, p. 754 fn) argue against a preferential version of the small improvement argument and simply assume that their argument applies mutatis mutandis for an objective version because they assume (the “received view”) that rationally required preferences and value judgments are very closely related. One could, instead, take their argument to be a good reason to believe that appropriate preferences and value judgments are not as closely related as the received view maintains.

  21. 21.

    I do not know of any published versions of this objection, but I find it to be the most common objection in discussion.

  22. 22.

    For an argument that “practical credences” are different than “theoretical credences”, see Wedgwood (2012).


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I would especially like to thank Peter Vallentyne, Paul Weirich, and the anonymous reviewers at Synthese for their comments on several revisions of this article. I am also grateful for helpful feedback (regarding this article or its predecessors) from Robert Johnson, Ruth Chang, Martin Peterson, Joshua Gert, Henrik Andersson, and the participants of the Formal Ethics 2019 conference.

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Correspondence to Jon Marc Asper.

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Asper, J.M. Subjective values should be sharp. Synthese 198, 6025–6043 (2021).

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  • Subjective value
  • Subjective probabilities
  • Preferences
  • Parity
  • Vague value
  • Incomparability
  • Sequential decisions
  • Money pumps