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fubarobfusco comments on Democracy and rationality - Less Wrong
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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?
This is the case that doesn't sound like an a-priori dictator to me, because you don't know who the dictator will be, and thus can't do anything to manipulate the outcome by dint of there being a dictator.
Under Arrow's terms, this still counts as a dictator, as long as the other ballots have no effect. (Not "no net effect", but no effect at all.)
In other words: if I voted for myself, and everyone else voted for Kanye, and my ballot happened to get chosen, then I would win, despite being 1 vote against 100 million.
It may not be the traditional definition of dictatorship, but it sure ain't democracy.