Peer disagreement and models of error

You and I are epistemic peers and we calculate a 15% tip on a very expensive restaurant bill for a very large party. As shared background information, add that calculation mistakes for you and me are pretty much random rather than systematic. As I am calculating, I get a nagging feeling of lack of confidence in my calculation, which results in $435.51, and I assign a credence of 0.3 to that being the tip. You then tell me that you you’re not sure what the answer is, but that you assign a credence of 0.2 to its being $435.51.

I now think to myself. No doubt you had a similar kind of nagging lack of confidence to mine, but your confidence in the end was lower. So if all each of us had was their own individual calculation, we’d each have good reason to doubt that the tip is $435.51. But it would be unlikely that we would both make the same kind of mistake, given that our mistakes are random. So, the best explanation of why we both got $435.51 is that we didn’t make a mistake, and I now believe that $435.51 is right. (This story works better with larger numbers, as there are more possible randomly erroneous outputs, which is why the example uses a large bill.)

Hence, your lower reported credence of 0.2 not only did not push me down from my credence of 0.3, but it pushed me all the way up into the belief range.

Here’s the moral of the story: When faced with disagreement, instead of moving closer to the other person’s credence, we should formulate (perhaps implicitly) a model of the sources of error, and apply standard methods of reasoning based on that model and the evidence of the other’s credence. In the case at hand, the model was that error tends to be random, and hence it is very unlikely that an error would result in the particular number that was reported.