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Douglas_Knight comments on Democracy and rationality - Less Wrong
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Comments (47)
Again, you're simply not understanding the theorem. If a system fails non-dictatorship, that really does mean that there is an a priori dictator. That could be that one vote is chosen by lot after the ballots are in, or it could be that everybody (or just some special group or person) knows beforehand that Mary's vote will decide it. But it's not that Mary just happens to turn out to be the pivotal voter between a sea of red on one side and blue on the other.
I realize that this is counterintuitive. Do you think I have to be clearer about it in the post?
I would say that Arrow simply excludes that possibility. As you said, he only considers systems that "consistently give the same winner...for the same voter preferences."
Nothing wrong with your analysis, but I think it's an important disclaimer.