I often find it hard to apply the Equal Weight View (EWV) in practice. This makes it my task of counterexample generating a little harder than I feel it should be. I can come up with all sorts of cases where I think EWV gets the wrong result, but then I get worried that EWV doesn’t actually say what I think it says about that case. Here’s one example I was working with.
A and B are peers in the salient sense. They have a long track record of checking each other’s work, and they both get things right a high and equal proportion of the time. There is no external evidence that B is in any way epistemically compromised right now. They both try to work out 14 times 27, and A gets 378, while B gets 368. What should A’s credence be that the right answer is 368?
I think the EWV is committed to the answer being 0.5 or thereabouts. After all, A and B are peers, they are just as likely to get the answer right, and probably one of them did get the answer right. So the EWV-endorsed probability distribution, I would think, is that the answers 378 and 368 both get probability nearly 0.5, and the remainder goes to the possibility that they were both wrong.
This strikes me as implausible, since it is easy for A to see that 368 is the wrong answer by using the rule I’ll call D9.
D9. A number is a multiple of 9 iff the sum of the digits of its base-10 representation is a multiple of 9.
So I think this is a case where EWV is wrong, A shouldn’t assign equal weight to 378 and 368 being the correct answer. I can imagine some people denying this, and saying that 378 and 368 should be given equal weight. But I can also imagine some people denying that EWV really has that consequence.
If you’re an EWV-theorist, do you think EWV entails in this case that A should give equal credence to 378 and 368 being the correct answer? If the case is too vaguely described to answer that, consider some of the following variations.
Variation 1. A doesn’t commit to an answer before checking that it is consistent with D9. So that the answer 378 is consistent with D9 is part of her reason for believing the answer is 378. That means, I think, that Christensen’s Independence principle would rule out her going on to use D9 to conclude that B must have made a mistake.
Variation 2. B has never heard of D9. Perhaps this means A and B aren’t peers, because D9 is some evidence that A has and B lacks.
Variation 3. B doesn’t believe D9. Perhaps that’s because he thinks A is misremembering the rule (It’s really a rule for multiples of 11, not multiples of 9), or perhaps because he thinks there are restrictions on the rule (e.g., it is only guaranteed to work for numbers with an even number of digits).
Variation 4. B denies that all multiples of 27 are multiples of 9.
Variation 5. B denies that his answer is inconsistent with D9, since 3+6+8 = 18, while 3+7+8 = 19, so D9 actually supports his answer, not A’s.
I can sort of see how an EWV theorist would deny that EWV applies in variations 2 and 4, but in all the other cases, it seems to me that EWV implies, incorrectly, that A should give equal credence to 368 and 378 being the correct answer. But maybe that’s just because I haven’t understood EWV correctly. Anyone want to correct my understanding?
Posted by Brian Weatherson in Uncategorized