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RobinZ comments on Navigating disagreement: How to keep your eye on the evidence - Less Wrong
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Re: Problem 2: Take an even probability distribution involving your feelings and your roommate’s feelings on housework (and on who’s emotionally biased). You have no reason to treat your and your roommate's feelings as asymmetrically indicative (unless unbiased indicators have told you that you're especially above- or below- average at this sort of thing). It’s like the thermometers, again.
Re: Problem 3: Keep your belief in atheism. Your evidence against a Christian god is way stronger than any evidence provided by your roommate's assertion. Despite the superficial symmetry with Problem 2, the prior against the complex hypothesis of a Christian god is many orders of magnitude stronger than the prior against you being wilfully mistaken about the housework -- and these orders of magnitude matter.
(Though note that this reasoning only works because such "extraordinary claims" are routinely made without extraordinary evidence; psychology and anthropology indicate that p( your roommate's assertion | no Christian god) is relatively large -- much larger than a simplicity prior would assign to p(Christian god), or p(flying spaghetti monster).
Before reading your answers:
Problem 2: Given the stated conditions ("you feel strongly that you could never have such biases" is unlikely in my case, but taking it as fact), I would tentatively interpret my roommates remarks as indicating his frustration rather than my disposition. However, I would take the probability of being mistaken as high enough that I would attempt to find some way to defuse the situation that would work either way - most likely, arbitration from a mutually trusted party.
Problem 3: I would quickly review what I know about the debate, and conclude that I have received no additional evidence one way or the other. I would continue to be confident in my naturalist worldview.
After reading your answers:
Problem 2: I notice that you interpret "you feel strongly that you could never have such biases" differently to how I interpret it - I would not feel thus without an observed track record of myself supporting that conclusion. My actions are scarcely changed from those implied by your judgement, however.