Mona Simion on resistance to evidence

More preparation for the formal (or fine-grained) epistemology meets mainstream (or coarse-grained) epistemology conference! In my previous post, I asked what a certain Bayesian approach might say about certain questions from the recent mainstream epistemology literature on inquiry. Now I want to ask what that same approach might say about what Mona Simion calls 'epistemic duties to believe', and particularly what it says about the sorts of violations of those norms that Simion gathers together under the heading of 'resistance to evidence'.

This is a natural application of the approach I described in the previous post, since that approach grows out of Good's justification of the Principle of Total Evidence (PTE), which seems like a credal analogue of the norm Simion calls The Duty to Believe (DTB). Here's the Principle of Total Evidnence:

PTE: At any given time, a subject's credence function should be acquired from her previous ones by conditionalizing on her total evidence (that is, the strongest proposition she has as evidence).

Here's Simion's norm:

DTB: A subject $S$ has an epistemic duty to form a belief that $p$ if there is sufficient and undefeated evidence for $S$ supporting $p$.

Bluebell fulfilling her positive epistemic duties by attending to all avaiable evidence out the window

1. The Good-Myrvold approach to gathering and incorporating evidence

In the previous post, I presented Good's approach as concerning inquiry. I presented him as interested in the following question: suppose (i) you know you'll respond to any evidence you get by conditionalizing on it; (ii) you know that a certain evidence-gathering episode will teach you which proposition from a certain partition is true; (iii) that evidence-gathering episode will cost you nothing; then, when should you choose to engage in it? And his answer is: in expectation, it's always better to engage in it than not. (As Brian Weatherson pointed out to me after my post, this result is actually already there in David Blackwell's 'Comparisons of Experiments' paper; and, as with so much in formal epistemology, it turns out Frank Ramsey was there before us with his unpublished note, 'Weight, and the Value of Knowledge'.) Good was interested in the pragmatic utility of evidence-gathering, but Wayne Myrvold has shown how to adapt his argument to concern purely epistemic utility. But, while I presented the approach as concerning when to gather evidence, it can equally be applied to tell us when we should incorporate evidence we've already gathered. Indeed, it likely applies better in the latter case, since that is much more likely to be cost-free. And so, Good's theorem goes, in expectation, it is always pragmatically better to incorporate evidence than not, and so the Principle of Total Evidence follows, as Good wanted; and, replacing pragmatic value with epistemic value, it is always epistemically better to incorporate evidence than not, and so the Principle of Total Evidence follows from epistemic considerations as well.

It's maybe worth saying here that this argument for the Principle of Total Evidence relies on a particular model of what's going on when you have evidence but you haven't incorporated it. It suggests that, at the point at which you are deciding whether or not to incorporate it, you remain uncertain which evidence you ended up gathering, and so it still makes sense to make the decision by maximizing expected utility from this position of uncertainty. It's as if you gathered the evidence, popped it in a cupboard, and forgot everything except the evidential situation in which you gathered it. But there are other ways of modelling the situation. According to one of them, the proposition you learned is there in full view, but you haven't changed your credences in response to it. In Section 6, I'll ask what happens if we use a model more faithful to that way of understanding things. In the end, not much turns on this for the situations that Simion considers; but it does make a difference when we ask how general the Principle of Total Evidence is: using the original model, resistance to evidence is sometimes rational, as we'll see in Section 5; using the alternative model from Section 6, it never is.

I won't rehearse all of Good's framework here, nor Myrvold's adaptation, but David Papineau pointed out to me after the last post that Good's result assumes that we update by conditionalizing on our evidence. Now, for Good's purposes, this is fine. All he really needs to show is that there is some available way to respond to the evidence, should you gather it, that is better, in expectation, than not gathering it and sticking with the credence function you currently have. But it's a legitimate question whether the best available way to respond is to conditionalize. And indeed it turns out that we can extend Good's theorem by showing that gathering-and-conditionalizing is the best combined available option; and we can extend Myvold's version in the same way. This is essentially what Peter M. Brown does in his pragmatic argument for conditionalization; and it follows from Hilary Greaves and David Wallace's epistemic argument for conditionalization. Brown's point is this: Good defines the pragmatic utility of a credence function relative to a decision to be the utility it will acquire for you if you use it to choose between the options available in that decision. So we can then take the pragmatic utility of gathering-evidence-and-updating-in-a-particular-way to be the pragmatic utility of the credence function you'll end up with if you do gather the evidence and update in that way. And then it's possible to show that, when evidence is available and cost-free, the thing that maximizes expected pragmatic utility is gathering the evidence and updating by conditionalizing. And similarly for Myrvold's approach: measure the epistemic utility of a credence function by a strictly proper epistemic utility function, then take epistemic utility of gathering-evidence-and-updating-in-a-particular-way to be the epistemic utility of the credence function you'll end up with if you do gather the evidence and update in that way. And again it's possible to show that, when evidence is available, the thing that maximizes expected epistemic utility is gathering the evidence and updating by conditionalizing. 

2. Simion's examples

So Myrvold's version of Good's approach gives a rather different route to the sort of positive epistemic norm concerning respect for evidence that Simion wants: where Simion appeals to an account of the proper functioning of our cognitive processes, this appeals to epistemic value and the best means to take in the pursuit of it. I'm not sure whether I want to say that Myrvold's result tells us that we have an epistemic duty to maximize expected epistemic utility, and therefore incorporate all the evidence we've gathered, but I certainly think it tells us we should incorporate that evidence, from an epistemic point of view, and we're irrational if we don't.

So let's ask now how this approach treats the examples that Simion uses to motivate her norm and her justification for it. Here's the first one:

Case #1: Testimonial Injustice. Anna is an extremely reliable testifier and an expert in the geography of Glasgow. She tells George that Glasgow Central is to the right. George believes women are not to be trusted, and therefore fails to form the corresponding belief.

I think the Bayesian's assessment of this case is a little different from Simion's, since the Bayesian deals with the agent's subjective prior credences, while Simion works with a notion of evidential probability. On perhaps the most natural reading, it isn't really a case of resistance to evidence, but rather a case of irrational prior credences. After all, let's take the evidence that George obtains in this situation to be that Anna says Glasgow Central is to the right. He might well incorporate that evidence exactly as the Bayesian says he should and yet retain a low or middling credence that Glasgow Central is to the right. After all, Simion says that George believes women aren't to be trusted, and so this is something that is encoded in the credence function he has when he meets Anna and hears her testimony. The Bayesian says he should conditionalize on his priors, but doing so will lead him to have something pretty close to his previous middling credence about the direction of Glasgow Central, since he'll think Anna's testimony is little indicator of the truth. So, for the Bayesian, George is certainly flawed, but it's not because he is resistant to the evidence Anna gives him in the sense that he fails to incorporate it, but because he has an irrational prior that leads him to have an irrational posterior after he does incorporate it in the required way. Of course, his irrational prior might be the result of resistance to evidence in the past. There are at least two ways George might have ended up with that prior. On the first, his ur-prior, the credence function he has at the beginning of his epistemic life, might have assigned very low credence to the reliability of women's testimony, and that will be judged irrational since it's taking an extreme stand on a proposition about which George had no evidence at that time, and if he assigns higher credence to the reliability of men's testimony, say, we will judge it further irrational because it differentiates between two cases when he has no evidence to justify such different treatment. On the second way he might have arrived at his irrational prior, his ur-prior might have assigned middling credence to the reliability of women's testimony, just as it did to the reliability of everyone else's testimony, but then as he went through life he incorporated any evidence he received that told against women's reliability and failed to incorporate any evidence he received in its favour, leaving him with the biased credence function he has when he meets Anna and hears her testimony. In that latter case, he showed genuine resistance to evidence, and the Principle of Total Evidence and its epistemic utility justification tells us what was wrong with him.

In the second half of the paper, Simion considers two alternative approaches to evidence to see whether they can explain her motivating cases, and she finds that, when you tweak them so that they can account for George's case, they end up also judging Alvin Goldman's benighted cognizer Ben negatively. As Simion tells his sad tale:

"This fellow lives on a secluded island where he's been taught that reading astrology is an excellent way to form beliefs, and where he has no access to any clue to the contrary. Plausibly, there is no evidence available to Ben for p: 'Astrology is an unreliable way to form beliefs,' nor is he in a position to know it."

How does our account treat such a case? Like Simion's, it doesn't judge Ben negatively. You can only be criticized for failing to update on evidence that is available to you, and no evidence against his view of astrology is available to Ben, since his island is secluded and contains no such evidence.

So it looks like the Myrvold-inspired account can justify the sort of positive epistemic norm that Simion wants. And similar stories can be told about her other motivating cases. In each case, either: (i) the subject has ignored evidence that is available to them; or (ii) they've incorporated it in a way that is irrational given their priors--they've failed to conditionalize on it; or (iii) they've incorporated it by conditionalizing, but their priors were irrational, and again this can be because (iiia) their ur-priors were irrational, or (iiib) because they ignored evidence in the past, or (iiic) because they incorporated evidence incorrectly in the past. 

3. When is evidence available to me?

As Simion notes, her approach needs an account of when evidence is available to a subject. She enumerates three ways in which it might be unavailable:

Qualitative Availability: You might not be the sort of subject who can access or process this sort of evidence. Simion gives the example of a three year old child who can receive certain sorts of evidence but cannot process them to draw the right conclusion. And presumably there are also cases in which we don't have the necessary sensory apparatus to access the evidence, such as if there is a sound above the range of the subject's hearing or a colour beyond their visual perception or something occluded behind an opaque barrier.

Quantitative Availability: You might be able to process various pieces of evidence individually, but there might be too many for you to attend to and process them all. Simion gives the example of things within one's visual field: each is available in some sense, but no subject could adequately process all of them.

Environmental Availability: Your social and physical environment might ensure that, while the evidence is present in some sense, it is not available to you. Simion gives the example of a letter under a doormat and a newspaper on the table, and says that, because we can't read everything, we have to pick the source with the most helpful evidence, which she takes to be the newspaper on the table--I'm definitely more intrigued by the letter under the doormat, but that doesn't seem like a substantial disagreement!

One advantage of the Good-Myvold approach is that we can give a reasonably unified account of when evidence is sufficiently available that we should gather or incorporate it. You should gather evidence, or incorporate evidence already gathered, if (i) doing so is an available action for you in the sense of decision theory, that is, if you choose to do it, there's a high probability you will in fact do it; and (ii) gathering it or incorporating it is cost-effective--that is, the expected pragmatic or epistemic gain of doing so isn't outweighed by the cost.

I think this speaks to a worry that Simion mentions Tim Williamson raised for her account (footnote 16). The problem is that many different pieces of evidence I might gather or incorporate will be equally available to me, and yet gathering or incorporating all of them will unavailable, or too costly, and so it can't be quite right that we have an epistemic duty to incorporate any evidence that is available to us. In the decision-theoretic approach we've been developing here, this conclusion falls out naturally: there might be lots of different evidence-gathering or evidence-incorporating episodes that have equal expected pragmatic or epistemic utility, and each might be cost-effective, but that means only that it's rationally permissible to pick any of them, not that it's rationally required to pick all of them; compare: if going to the Isle of Skye on holiday and going to the Isle of Mull on holiday both maximize expected utility, I'm permitted to do either, but I'm certainly not required to do both.

4. Gathering evidence and incorporating it: are these so different?

A point of disagreement with Simion, though I can't tell how serious it is. When considering whether an approach based on Tim Williamson's E=K account of evidence can deliver the sort of norm she seeks, Simion points to "one important distinction between epistemic shoulds [that such an approach would miss]: that between the synchronic 'should' of epistemic justification and the diachronic 'should' of responsibility in inquiry." On the account I've been sketching, there is no significant difference in kind between the two cases. Both involve considering different options you might take: in the inquiry case, it's a combination of gathering evidence and updating on whatever it teaches you in a particular way; in the incorporating case, it's just whether to updating on the evidence you already have in a particular way. And in both cases we judge the options by the pragmatic or epistemic value of the credence functions they'll land you with.

5. Is it ever rational to resist to evidence?

It's worth noting that, because of the sort of case I mentioned in the previous post, which John Geanokoplos and Nilanjan Das have studied in the pragmatic case, resistance to evidence is sometimes rational. I'll just given a brief reminder here.

Suppose there are just three possibilities: the weather is currently dry outside, or it's raining lightly, or it's raining heavily. As my friend returns from outside, he tells me which it is. But, growing up in Scotland as he did, my friend doesn't pay much attention to how wet it is, since he pretty much always just prepares for it raining heavily. I know that, if it's dry outside, he'll tell me, 'It's dry or raining lightly, not sure which'; and if it's raining lightly or heavily, he'll tell me, 'It's raining lightly or heavily, not sure which'. And suppose I start off with these credences before I hear his testimony: I have credence 1/10 it's dry, 1/2 it's raining lightly, and 2/5 it's raining heavily. Then, at least if we measure epistemic utility using the negative Brier score, ignoring this evidence is better, in expectation, than incorporating it and conditionalizing on it. The reason is that, if I conditionalize on the evidence I'll get if it's dry, updating to a credence of 1/6 that it's dry and 5/6 that it's raining lightly, the Brier score considers that misleading evidence, because it actually makes my credence function less accurate at that world; and while if I incorporate the evidence I'll get if it's raining lightly or if it's raining heavily, updating to a credence of 5/9 that it's raining lightly and 4/9 that it's raining heavily in both cases, the Brier score will count this as good evidence at both of those worlds because it increases my accuracy, it doesn't increase it by enough in either case to counteract the decrease in accuracy I'll suffer from conditionalizing on my friend's testimony if it's dry. So, in this case, resistance to evidence is rational. I don't choose to gather the evidence: my friend simply walks in and tells me. But, having been presented with it, I've epistemic reason not to incorporate it; I've reason to resist it.

6. Modelling resistance to evidence

As I mentioned above, the approach I've been sketching involves a particular modelling choice. On it, we assume that the person who is resistant to evidence has the evidence, but is still uncertain what it is and is choosing as if they haven't actually gathered it yet. I think this is a perfectly legitimate way to model the situation, but it does have the peculiar feature that they are treating themselves as if they still haven't gathered the evidence; or at least as if they have, and then they've put it into safe storage and forgotten what it is. But what if we model things a different way? What if we assume they can see the evidence they gathered and are choosing whether to incorporate it, and how. Then we might turn to a proposal that Hannes Leitgeb and I made in our 2010 papers on accuracy arguments for epistemic norms: when you have a credence function and a proposition that gives your total evidence, and you're figuring out what to do with the proposition, we argued that you should pick a posterior credence function by maximizing expected epistemic utility, but not in the standard way where you sum the credence-weighted epistemic utilities across all of the ways the world might be, but rather across all ways the world might be that are compatible with your evidence; that is, all the ways the world might be on which your evidence is true. And then, if you do that, we showed, your posterior should always be obtained from your prior by conditionalizing on your total evidence. And so, if we go this way, we have an argument for an unrestricted version of the positive epistemic norm given by the Principle of Total Evidence. In this case, we needn't worry about the sorts of case that Das considers. While it is still true that, if you have to choose whether or not to gather the evidence about whether it's dry, raining lightly, or raining heavily, you should choose not to, once you've in fact gathered that evidence, or had it imposed upon you, you should update on it by conditionalizing, as the Principle of Total Evidence tells you to.