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IIA, rationality, and the individuation of options

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Abstract

The independence of irrelevant alternatives (IIA) is a popular and important axiom of decision theory. It states, roughly, that one’s choice from a set of options should not be influenced by the addition or removal of further, unchosen options. In recent debates, a number of authors have given putative counterexamples to it, involving intuitively rational agents who violate IIA. Generally speaking, however, these counterexamples do not tend to move IIA’s proponents. Their strategy tends to be to individuate the options that the agent faces differently, so that the case no longer counts as a violation of IIA. In this paper, we examine whether this strategy succeeds. We argue that the ways of individuating options required to save IIA from the most problematic counterexamples—in particular, cases where agents violate IIA due to nonconsequentialist moral beliefs—do so only at the expense of severely compromising its central function within decision theory.

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Notes

  1. IIA has a descriptive variant, which claims that agents do obey IIA as we have stated it. This descriptive variant has been widely criticized by psychologists and behavioral economists: see, e.g., Tversky (1972), Tversky and Shafir (1992). Those critical of the descriptive variant often nevertheless presuppose that violations of it are irrational; i.e., presuppose the normative variant.

  2. This statement of IIA is wide-scope. IIA requires that your choice function makes the same selection from the smaller set and the larger set (when the selection from the larger set is in the smaller set), but it says nothing about whether it is the selection from the smaller set or that from the larger set that you should revise. It merely requires you to line the two up.

  3. For similar formulations, see, e.g., Rubinstein (1998: 11) and Sen (1969: 384) and the references therein (384, n. 1).

  4. Does this assume a crude behaviorism about preference, whereby there is nothing more to preference than what is revealed in behavior? Not necessarily. After all, it’s not like agents actually do face hundreds of choices between pairwise comparisons, such that we can actually observe their choices to read off preferences and then construct a utility function. But there is something that at least many decision theorists find desirable about linking preference to hypothetical choice, perhaps under some set of idealized conditions. The tempting thought is that it is hard to say what makes it the case that an agent prefers option A to option B (say, when the agent is in some choice situation where neither option is the agent’s actual choice or first preference) without appeal to what the agent hypothetically would pick if A and B were the only two options. A view like this allows us to think of an agent as maximizing the same utility function across different possible choice situations, always picking the top-ranked option of those that are available—rather than as having a different utility function for each potential choice situation, in such a way as to compromise the explanatory power of the utility-maximizing model, and to make it less clear what generates the ranking of options (beyond that of the top choice) in particular choice situations. Moreover, an account that links preference to hypothetical choice allows rational constraints on preference to have consequences for the rationality of particular choices, which is also a desirable feature of such an account.

  5. See Rubinstein (1998: ch. 1).

  6. See Sen (1993); Kamm (1996: ch. 12, 2007: ch. 9); Tungodden and Vallentyne (2005); Temkin (2012: 389).

  7. For different voicings of the strategy in question, see Broome (1991: 100–104); Neumann (2007); Temkin (2012: 389).

  8. Is decision theory inherently consequentialist, in that it takes rational agents to be utility-maximizers? No. Even assuming that rationality requires utility maximization, this “entailment” involves an equivocation about ‘utility.’ Decision theory constructs utility functions out of preferences. It does not require that these preferences be a function of the objective goodness of outcomes, which is the utility of consequentialism. For example, decision theory could allow an agent to have a preference against lying, regardless of the goodness of the outcome. This would then be reflected in the agent’s utility function. In this respect the usage of ‘utility’ in decision theory is different from that in consequentialist moral philosophy. The two might be extensionally equivalent if one has a preference theory of well-being, but that is a substantive (and, in our view, implausible) theory of well-being which decision theorists are not committed to.

  9. Sen (1993: 501).

  10. Sen himself acknowledges that one could describe the options this way; see Sen (1993: 501, n. 17).

  11. Note that it isn’t enough to capture the de dicto strategy simply to use relative terms like “second-largest” in individuating options. We could do that on the de re method too—as we illustrated above, there is a de re reading of “I want to second-largest slice”.

  12. This is a further claim to that expressed in the previous sentence, and the further claim is needed in order for the strategy to succeed in resisting Sen’s counterexample. It is not enough simply to point out that the chooser has a choice function which consistently picks the second-largest slice (read de dicto) from any set. That makes the chooser’s coherence vivid, but as long as the options themselves are still individuated de re (for example, as Large, Medium, and Small), this choice function will still result in violations of IIA, since IIA ranges over options. That was the whole point of Sen’s counterexample.

  13. US: “wrench”.

  14. On a plausible reading, this is the way that Broome (1991: 100–102) and Temkin (2012: 387–390) deal with cases like this one, although one can also read them as endorsing something closer to the de dicto strategy that we just rejected. We think it is important to carefully distinguish these two strategies for dealing with the example.

  15. For similar cases, see Kagan (1991: 16); Parfit (1982); Kamm (1996: ch. 12, 2007: 298–299). Each offers a structurally similar case. Only Kamm recognizes the potential violation of IIA (Kamm 2007: 485–486); her treatment is brief and the potential counterexamples she poses can perhaps be explained away by arguments like those offered by Temkin (2012: 389). For somewhat different cases involving moral beliefs that could be taken to lead to violations of IIA, see Tungodden and Vallentyne (2005); Temkin (2012: ch. 13).

  16. See Rulli (n.d.).

  17. One might object that the moral beliefs required to generate the verdict in the Factory case are actually themselves incoherent (thanks to an anonymous reviewer for this objection). According to Sarah, opening the low-standards factory in the absence of a high-standards option is permissible because it is better than opening no factory at all. But if that’s right, then how could it be the case that, when the high-standards factory is an option, opening the low-standards factory is impermissible but opening no factory at all is permissible? After all, it is still the case that opening the low-standards factory is better than opening no factory at all. However, this objection itself rests upon the consequentialist assumption that only the results of the action matter in determining its moral status. On a non-consequentialist view, the addition of the high standards factory option could introduce morally relevant factors not reducible to the goodness of consequences that explain the moral order of the options. So, on the best way to think of Sarah’s non-consequentialist view, it is not just the fact that the low-standards factory is better than opening no factory at all that makes it permissible to open the low-standards factory. Rather, it is this fact together with the fact that there is no option to open a high-standards factory. We do not see any independent motivation (other than that of saving IIA) for claiming that this view is incoherent.

  18. See Rulli (n.d.).

  19. Note that this is so despite the failure of the crude thought that decision theory is in itself consequentialist due to the assumption of utility-maximization (compare fn. 8 above).

  20. Some (including, on some readings, Broome 1991) may think that any feature of the options which can rationally influence agents’ preferences ought to be built into the descriptions of them. If this is correct, then trivially there can be no counterexamples to IIA. But you can read this section, and the next, as challenging this contention. Even though we agree that the believed moral status rationally influences Sarah’s preferences, we argue that the believed moral status cannot be built into the description of the options without compromising IIA’s central decision-theoretic role, and committing us to a controversial moral psychology.

  21. And it is Sarah’s lights that matter, since on this strategy we are individuating the options by their moral status by Sarah’s lights—not by their actual moral status.

  22. Thanks to Shengwu Li for the example.

  23. See, prominently, Smith (1994: ch. 3).

  24. Admittedly, this problem is also faced when individuals believe themselves to be facing different options due to differences in descriptive beliefs, as in the Ming vase case. However, in this case, we can still work out whether the members of the group have the same underlying preferences by asking what their preferences would be given various stipulations about the descriptive facts, stipulations which all can agree are coherent possibilities. But in the normative case, for the reasons given in the previous section, we cannot do this—since the agents disagree on which normative situations are even possible (for example, Sarah and Hasan disagree on whether it’s possible for the choice of the low-standards factory to be permissible in the presence of the high-standards option). Moreover, even if there were a way around this problem, it is intuitively problematic to think that Sarah and Hasan both get their underlying preference as long as we act on the correct moral theory: that they both simply have a preference for doing what is permissible, and this gets fulfilled as long as the ultimate decision is actually permissible. By contrast, it is not so intuitively problematic to think that two individuals who both want an actual (non-fake) Ming vase get what they most fundamentally want as long as they get an actual Ming vase (even if one had thought the vase was a fake). Again, what explains this asymmetry is that normative beliefs condition preference at a more fundamental level than descriptive beliefs do.

  25. This does not mean that Sarah’s beliefs commit her to denying the supervenience of the normative on the non-normative. A non-normative fact has changed; it is the fact that the high-standards factory is now an option. But, as already argued at the end of Sect. 4, this cannot itself be grounds for saying that the option to open the low-standards factory has changed. Such a move would make rob IIA of any applicability.

  26. Attributed to him by Kamm (2007: 485–486).

  27. Consequently, one should not formulate IIA itself by saying that it bans changes of preference without good reason (c.f. Broome 1991: 101–103). As Broome himself is famous for arguing in later work (e.g. Broome 2013: chs. 5–6), failures to track one’s reasons are not necessarily failures of rationality understood as internal incoherence.

  28. Our point here is of a piece with Sen (1993). Kelly (2004) very nicely makes a similar point with respect to honoring sunk costs.

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Acknowledgments

For helpful comments and discussion, we’re grateful to an audience at the London School of Economics, as well as to several anonymous referees, Richard Bradley, Tamar Gendler, Shelly Kagan, Jessie Munton, Aaron Norby, Mike Otsuka, John Pittard, Alex Voorhoeve, and especially Shengwu Li.

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Correspondence to Alex Worsnip.

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Tina Rulli and Alex Worsnip contributed equally to this manuscript.

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Rulli, T., Worsnip, A. IIA, rationality, and the individuation of options. Philos Stud 173, 205–221 (2016). https://doi.org/10.1007/s11098-015-0481-6

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