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.