p51

On this type of view, contraction will not permit any action that was not previously permitted.24 Of course, you may well disagree with out judgments. You may think that in certain cases, an agent in M will not be rationally permitted to take risks like going to Restaurant A, whereas an agent in p will be so permitted. To deliver that verdict, you will need to adopt an ambiguity-averse decision theory. We think there are good independent reasons to reject ambiguity-averse decision theories, but we won’t try to defend that claim here.25 Instead, let’s think about what the anti-contraction argument looks like, for someone who adopts an ambiguity-averse decision theory. We have argued that there are no accuracy-based reasons not to contract. The ambiguity-averse decision theorist should agree with us on this count. What she thinks is something like this: “If I contract, I won’t be any less accurate than I am now. But I will be in a state that permits actions that, right now, look pretty bad to me. Better not do that!” If we use anambiguity-averse decision theory to avoid contraction, then we will have to separate the accuracy of your credences from their “guidance value”– roughly, how well they’ll do at getting you what you want.26 This isn’t the worst result. Since neither EGT nor EUT says that accuracy considerations require contraction, it’s not as though separating guidance value from accuracy will lead you to some sort of uncomfortable dilemma. But it is a nice feature of the accuracy frameworks on offer (both EUT and EGTcombinedwithtraditional or supervaluationist decision theory) that accuracy and guidance value go together– that what makes sense to believe for accuracy-based reasons also makes sense for guiding our actions. Arethere ways to rule out contraction, without separating accuracy and guidance value? One natural thought is that we could do this by amending the guessing framework, so that instead of only considering forced-choice scenarios, we also allowed the possibility of abstention. What if, in response to some questions, your doxastic state did not permit any guesses?27 This might free up some space for prohibiting contraction, and for accepting ambiguity-averse verdicts in cases like Three Restaurants, without separating epistemic and practical concerns. We will turn to examining that possibility– and more generally, the prospects for accuracy-based arguments against contraction– in the final section.BUILES ET AL. 13 8 THEPROSPECTS FORACCURACY-BASED ARGUMENTS AGAINST CONTRACTION First we’ll explain why wedon’t think adding abstention as an option to the guessing framework will do the trick. Then we’ll gesture towards some more general reasons why it’s challenging to find accuracybased arguments against contraction. The problem with allowing abstention is that, if we do, we lose the result that precise credences are self-recommending. To put it another way: we lose the result that your guesses elicit your credences or your comparative confidence judgments, the way the Brier Score was designed to elicit weather forecaster’s subjective probabilities. This is because, with abstention as an option, there will be cases where many different belief states, defined over the same algebra of propositions, deliver exactly the same guesses. Here is an intuitive argument for why this is true. The main idea behind EGT is that your goal, in guessing, is to make true guesses and avoid making false ones. If we only consider forced choices, then when faced with two very improbable options, it makes sense for you to guess in favor of the option in which you have higher credence. So, your guesses will always elicit your comparative confidence judgments. But when we allow abstention– if the choice is not forced– then there will be many questions which don’t elicit your comparative confidence judgments. For example, suppose you are asked to guess between: S: It will snow in New York in September. J: It will snow in New York in July. If you have precise credences in S and J, it’s safe to assume that your credence in S is higher than your credence in J. So in a forced choice between S and J, you will guess S. But if abstention is an option, and there’s disvalue to guessing falsely, you may well abstain– after all, both S and J are almost certainly false. So the difference between your credence in S and your credence in J won’t show up in your guesses: your guesses won’t elicit your credences. This also means that you won’t regard your own credences as the best for the purposes of guessing truly. This is because if the disvalue of guessing falsely is non-zero, there will be some number c such that, if you have credence less than c in P, you will not want to guess P, no matter what P is being compared with; it will always look better to abstain. So you won’t have any accuracy-based reason to stick with your current credences, rather than adopting new ones, which swap out your credence in P for some other sub-c value.28 This means that adding abstention is an option has the result that precise credences don’t even recommend themselves over alternative precise credences. It seems then that adding abstention as an option to the guessing framework is a bad idea. Still, it’s interesting to think about whether there is some plausible way of thinking about accuracy that yields the result that all probabilistic states– both precise and imprecise– are self-recommending.29 While we have no general argument that this can’t be done, we’ll conclude with some admittedly hand-wavy suggestions as to why such a project might be difficult. In general, belief states are self-recommending because they involve a commitment; they “take a stand”. In the case of binary belief, it’s clear why belief in P recommends itself from the point of view of accuracy. To believe P just is to believe that P is true, which means that if you want a true belief, and you believe P, you’ll think believing P is a good idea. We can also think of precise credal states as taking a stand. On the comparative picture, they’re states that are committed to regarding certain propositions as more likely than others. On other pictures they may be states that are committed to14 BUILES ET AL. regarding certain bets as preferable to others. Insofar as one is taking a stand, or making a commitment, that stand or commitmentwillnaturally rule out competing commitments, just as an intention to𝜙rules out intentions to act in ways that are incompatible with 𝜙-ing. But in general, while commitments rule out other commitments, a lack of commitment doesn’t obviously rule out anything at all. (Compare: lack of intention regarding whether to 𝜙 doesn’t rule out 𝜙-ing.) The more we think of imprecise credal states as states in which certain commitments are lacking, as the comparative confidence picture does, the harder it will be to motivate the idea that imprecise states recommends themselves over their precise members. So to rule out contraction, it might be better to think of imprecise credal states as expressing some form of commitment that rules out adopting their members. The practical motivation for imprecision we discussed in the previous section is an excellent example of this strategy: on ambiguity-averse decision theories, being in [0,1] involves certain practical commitments that being at 0.5 (or any other precise state) does not have. That’s why, on these theories, if you’re at [0,1] you will have practical reasons to stay there. An alternative approach might involve thinking of a state like [0,1] as expressing some form of evidential commitment- perhaps a commitment to the effect that the evidence available is deficient in certain respects. But it’s not clear what sort of commitment is expressed by [0,1] that will rule out 0.5 on accuracy grounds.30 Theconsiderations above are not of course a formal argument. Mathematics is full of complex structures and wiley tricks. We have no argument against the possibility of developing a new framework for thinking about accuracy which rules out both dilation and contraction,31 but philosophical reflection on the nature of imprecise states, we think, supports exactly the results delivered by the educated guess framework: the commitments involved in having precise credences result in a commitment to remain precise, but the lack of commitment involved in having imprecise credences doesn’t ground a commitment to remain imprecise.