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MartinB 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).
The description of both problem 2 and 3 indicates a possible biasing in both participants. Its therefore reasonable to cool down first, and then check the evidence.
In problem 3 roommate might point out valid criticisms about biases one might have, while still being wrong on the question itself. Either way its not rational to argue when in heat.