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I’ve never heard of this. Just off the first sentence on Wikipedia, I’d question the existence of independent alternatives. It looks like non-dictatorship is defined to be ordering invariant?
The issue is that, in the dictator voter proof of Arrow’s theorem, they prove that for every ordering of voting profiles between cases where the result of the vote is A and where the result of the vote is B there has to be a first profile where the result is not A. The profiles differ by just one vote, so they declare the relevant voter a dictator. The problem is that who this ‘dictator’ is depends on the order in which we change the votes. As such, we can literally argue that everybody is a dictator.
I do not think that this ‘non-dictatorship’ rule is a reasonable requirement for democratic systems.
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The issue is that, in the dictator voter proof of Arrow’s theorem, they prove that for every ordering of voting profiles between cases where the result of the vote is A and where the result of the vote is B there has to be a first profile where the result is not A. The profiles differ by just one vote, so they declare the relevant voter a dictator. The problem is that who this ‘dictator’ is depends on the order in which we change the votes. As such, we can literally argue that everybody is a dictator.
I do not think that this ‘non-dictatorship’ rule is a reasonable requirement for democratic systems.