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homunq comments on Democracy and rationality - Less Wrong Discussion
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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.