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Perplexed comments on Confidence levels inside and outside an argument - Less Wrong
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I'm afraid I don't know how to post links.
I think there is already a main-page article on this subject, but the general idea is that Arrow's theorem assumes the voting system is preferential (you vote by ranking voters) and so you can get around it with a non-preferential system.
Range voting (each voter gives each candidate as score out of ten, and the candidate with the highest total wins) is the one that springs most easily to mind, but it has problems of its own, so somebody who knows more about the subject can probably give you a better example.
As for the main point, I doubt you actually put 100% confidence in either idea. In the unlikely event that either approach led you to a contradiction, would you just curl up in a ball and go insane, or abandon it.
Ah. You mean this posting. It is a good article, and it supports your point about not trusting proofs until you read all of the fine print (with the warning that there is always some fine print that you miss reading).
But it doesn't really overthrow Arrow. The "workaround" can be "gamed" by the players if they exaggerate the differences between their choices so as to skew the final solution in their own favor.
All deterministic non-dictatorial systems can be gamed to some extent (Gibbard Satterthwaite theorem, I'm reasonably confident that this one doesn't have a work-around) although range voting is worse than most. That doesn't change the fact that it is a counter-example to Arrow.
A better one might be approval voting, where you have as many votes as you want but you can't vote for the same candidate more than once (equivalent to a the degenerate case of ranging where there are only two rankings you can give.
Thanks for the help with the links.