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fortyeridania comments on Voting is like donating thousands of dollars to charity - Less Wrong
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That some people are "just wrong" is not at issue. Even mistaken people agree that some people are wrong. (They just think it's the right-thinking folks who are in error.)
Of course you don't. If half the population disagrees with you about an issue, you should interpret that as evidence that you are incorrect. How strong the evidence is, depends on how likely they are to possess information you don't, to be misled by things you've prepared yourself for, etc.
Agreed. I guess what makes checking the math work in the integral case is just that the better you are at checking the arguments, the less you have to worry about what other people think.