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I'm pretty sure your characterization of the non-dictatorship rule is wrong. According to wikipedia, the rule states that there should be no voter whose preferences are always the same as those produced by the choice function:

> There is no individual, i whose strict preferences always prevail. That is, there is no i ∈ {1, …, N} such that ∀ (R1, …, RN) ∈ L(A)N, a ranked strictly higher than b by Ri implies a ranked strictly higher than b by F(R1, R2, …, RN), for all a and b.




It does not mean always as in "the same voter every time." What it means is that if more than two voters have a preference ranking which is digested by a social choice function, the outcome should not be exactly the same as any individual voter. I argue that doesn't make any sense, because there are plenty of situations where the best choice of ranking might coincide with the preferences of a particular voter, completely by coincidence.




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