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Modeling the precautionary principle with lexical utilities

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Abstract

Confronted with the possibility of severe environmental harms, such as catastrophic climate change, some researchers have suggested that we should abandon the principle at the heart of standard decision theory—the injunction to maximize expected utility—and embrace a different one: the Precautionary Principle. Arguably, the most sophisticated philosophical treatment of the Precautionary Principle (PP) is due to Steel (2015). Steel interprets PP as a qualitative decision rule and appears to conclude that a quantitative decision-theoretic statement of PP is both impossible and unnecessary. In this article, we propose a decision-theoretic formulation of PP in terms of lexical (or lexicographic) utilities. We show that this lexical model is largely faithful to Steel’s approach, but also that it corrects three problems with Steel’s account and clarifies the relationship between PP and standard decision theory. Using a range of examples, we illustrate how the lexical model can be used to explore a variety of issues related to precautionary reasoning.

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Notes

  1. For variants of this position, see Ackerman (2009), Barker (2008), Howarth (2001), McCauley (2006) and Weitzman (2009).

  2. Proposals for interpreting the Precautionary Principle are discussed briefly in Sect. 2.

  3. See UNESCO (2005) and Harremoës (2001). We are grateful to a referee for emphasizing the importance of this work, which is largely disconnected from formal decision theory.

  4. See Mayer and Stirling (2002), Sandin (2004), Sandin and Peterson (2019), Steele (2006) and Thalos 2009, 2012).

  5. See Ackermann (2009), Ackermann and Heinzerling (2002), Hansson (1997), Gardiner (2004, 2006) and Chisholm and Clarke (1993).

  6. See Peterson (2006, 2017b), Boyer-Kassem (2017a; 2017b), Steel (2015) and Stefánsson (2019).

  7. See Fishburn (1974) for a survey of the lexical utilities approach, to be discussed below. Lexical models are also used in empirical models of precautionary decision-making; see Brandstätter et al. (2006).

  8. This observation is discussed in Sect. 3.1.

  9. Our interpretation of PP and the harm threshold, developed below, abandons no standard axiom other than Continuity. Other interpretations (Peterson 2006; Stefánsson 2019) require giving up other standard axioms on rational preferences, such as Transitivity and Completeness.

  10. Although ‘lexicographic utilities’ is standard terminology, we will refer to ‘lexical utilities’ and the ‘lexical model’ for stylistic simplicity. Other representations of the harm threshold are possible (see Bartha and DesRoches 2017), but lexical utilities provide a simple and natural approach.

  11. Christiansen also endorses as reasonable Steel’s requirement of proportionality: the precautionary measures “should correspond to the plausibility and severity of the threat” (Steel, 2015, p. 10). Agents should employ the least costly precautionary measures available. The proportionality requirement is not formally part of the tripod.

  12. Colyvan et al. (2010a, b) attempt to model precautionary reasoning about the environment using large utilities for the value of ecosystems, species, etc.

  13. Harsanyi’s famous counterexample to Maximin is often cited. As a resident of New York, you face a choice between continuing your terrible job in New York and flying immediately to Chicago to start a fabulous job. Maximin recommends staying in New York because of the tiny risk of being killed in a plane crash (Harsanyi, 1975, p. 595). This is widely regarded as an absurd prescription.

  14. For Peterson, the term “qualitative decision theory” also applies when we have merely ordinal rankings for our utilities. We omit such decision problems, though we believe that the approach developed in Sect. 5.2 could handle many of them.

  15. We do not believe that there is a version of PP generally applicable to decisions under ignorance. In Sect. 6, however, we briefly consider the prospects for extending our formulation of PP to settings in which agents have imprecise probabilities. The lexical utilities model can also be applied to sequential decisions, and to cases involving partial information, that go beyond what we are able to consider in this article.

  16. We take the Appendix to provide a “first-order” summary, as it omits details found elsewhere in the book (in particular, Steel’s consideration of proportionality and robust adaptive planning).

  17. We adapt this example from an earlier article, (Bartha and DesRoches 2017).

  18. The two states are meant to be independent of the two acts. OS as stated is compatible with either BP or ~ BP. Note also: the notation ~ OS, BP & OS, etc. assumes that states and actions may be represented as propositions. Our examples are simple enough that this should cause no confusion.

  19. This argument closely parallels a well-known objection to Pascal’s Wager; see (Hájek 2003).

  20. Here we suspend Steel’s injunction to ignore dismal scenarios.

  21. A summary of the contrast between the two modeling approaches is provided in (Steele and Stefánsson 2016).

  22. Partial and full linearity results depend upon structural assumptions, just as with standard decision theory (Fishburn 1971). We assume these conditions in the setting of decisions under risk. Fishburn singles out what we have called a binary lexical ordering (where there is a partition of one or more dimensions into “acceptable and unacceptable levels”) as a particularly simple form of lexicographic ordering (Fishburn, 1974, p. 1451).

  23. The lexical approach can be broadened to handle multiple harm thresholds, but we are unable to consider cases of this type in this article.

  24. Typically, we reserve the term “CQ context” for situations where we have only a rank ordering on probabilities (and possibly only an ordinal utility scale). However, we have defined CQ contexts to include situations where we have quantitative probability values and/or an interval utility scale. The results in this section are meant to be consistent with those in Sect. 5.1, where we have this precise information.

  25. In Sect. 8, we discuss the objection that this feature of reasoning with lexical utilities is absolutist.

  26. We omit the analysis, since the first-order decision table is identical to Table 5 and the recommendation is unchanged.

  27. See van Fraassen (1990), Joyce (2010), and Bradley (2019a).

  28. The classic discussion is (von Neumann and Morgenstern 1953). See also (Luce and Raiffa 1957), (Resnik 1987) and (Peterson 2017).

  29. As noted earlier, the linearity results are linked to technical assumptions about the agent’s preferences (Fishburn 1971, 1974).

  30. Representation with binary lexical utilities is broad enough to encompass standard decision theory (see note 31).

  31. Lexical utilities can represent continuous preferences if no outcomes are catastrophic (all utilities have the form (0, u)), or if all outcomes are catastrophic (all utilities have the form (-1, u)).

  32. See (Dreier 1996) and (Hájek 1997) for contrary views.

  33. See (Norcross 1997); a recent review of this literature is found in (Lazar 2018). While the example as formulated is not a counterexample to Continuity, it may be re-stated as one; see (Lazar 2018).

  34. If only nuclear holocaust counts as a disaster, then of course the recommendation is Don’t reduce GHG, but in this case there is no problem of incoherence.

  35. Complications arise if we broaden the range of policy options. Consider policy PN: stay at home N times, then use the car. PN+1 looks better than PN on the lexical framework. Addressing this problem is beyond the scope of this article, but similar difficulties arise within standard decision theory (Arntzenius et al. 2004).

  36. For instance, the lexical utilities approach also allows us to consider examples with multiple harm thresholds (omitted here to keep the discussion manageable).

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Acknowledgments

We would like to thank three anonymous reviewers for extremely helpful comments. An early version of this paper was presented at the 2019 PDX PhilSciNow workshop (Portland State University, Sept. 13–15, 2019). We would like to thank the audience for useful comments and criticisms. Finally, we are grateful to Daniel Steel (UBC, School of Population and Public Health) and Chris Stephens (UBC, Philosophy) for many helpful suggestions.

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  1. Department of Philosophy, University of British Columbia, Vancouver, BC, V6T 1Z1, Canada

    Paul Bartha

  2. School of Sustainability and School of Historical, Philosophical and Religious Studies, Arizona State University, PO Box 875502, Tempe, AZ, 85287-5502, USA

    C. Tyler DesRoches

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Correspondence to Paul Bartha.

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Bartha, P., DesRoches, C.T. Modeling the precautionary principle with lexical utilities. Synthese 199, 8701–8740 (2021). https://doi.org/10.1007/s11229-021-03179-4

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