Question: A group S of individuals is decisive over a pair of alternatives x, y X if x i y for every i S

A group S of individuals is decisive over a pair of alternatives x, y ∈ X if x ≻i y for every i ∈ S ⇒ x ≻ y
Assume that the social order is consistent with the Pareto order and satisfies the IIA condition. Show that, if a group is decisive over any pair of states, it is decisive over every pair of alternatives. (Assume that there are at least four distinct states, that is, |X| > 4.)

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