Liberal values suggest that there are some choices that are purely personal and should be the perogative of the individual concerned. We say that a social order exhibits liberalism if for each individual i, there is a pair of alternatives x; y ∈ X over which she is decisive, that is, for which
x ≻i y ⇒ x ≻ y
(A dictator is decisive over all alternatives.) Show that is impossible to complete a Pareto order in a way that respects liberalism. This inconsistency between liberalism and the Pareto principle is known the Liberal Paradox. [It suffices that show that there are not even two persons who are decisive over personal choices. Consider a pair of alternatives for each person, and show that the implied Pareto order is intransitive.]