11. Recall that an electoral system satisfies non-imposition if, for every candidate, there exists a preference profile for which that candidate is the winner. Prove that if a system is Pareto efficient then it must also satisfy non-imposition, but that the converse is not true. 12. Prove that the Gibbard-Satterthwaite Theorem still holds if we replace the Pareto criterion by non-imposition.