▁is ▁clearly ▁not ▁dict atorial . ▁Many ▁other ▁rules ▁are ▁neither ▁manip ul able ▁nor ▁dict atorial : ▁for ▁example , ▁assume ▁that ▁the ▁alternative ▁ ▁wins ▁if ▁it ▁gets ▁two ▁third s ▁of ▁the ▁votes , ▁and ▁ ▁wins ▁otherwise . ▁ ▁A ▁game ▁form ▁showing ▁that ▁the ▁con verse ▁does ▁not ▁hold ▁ ▁Consider ▁the ▁following ▁rule . ▁All ▁candidates ▁are ▁elimin ated , ▁except ▁the ▁candidate ▁or ▁candidates ▁that ▁are ▁placed ▁in ▁top ▁position ▁in ▁vot er ▁ 1 ' s ▁ball ot . ▁Then , ▁among ▁the ▁non - el imin ated ▁candidates , ▁one ▁is ▁elected ▁using ▁the ▁B ord a ▁count . ▁This ▁whole ▁process ▁is ▁dict atorial , ▁by ▁definition . ▁However , ▁it ▁is ▁manip ul able , ▁for ▁the ▁same ▁reasons ▁as ▁the ▁usual ▁B ord a ▁count . ▁Thus , ▁the ▁Gib b ard – S atter th wa ite ▁theorem ▁is ▁an ▁imp lication ▁and ▁not ▁an ▁equivalence . ▁ ▁Cor ollary ▁ ▁We ▁now ▁consider ▁the ▁case ▁where ▁by ▁assumption , ▁a ▁vot er ▁cannot ▁be ▁ind ifferent ▁between ▁two ▁candidates . ▁We ▁denote ▁by ▁ ▁the ▁set ▁of ▁strict ▁total ▁orders ▁over ▁ ▁and ▁we ▁define ▁a ▁strict ▁voting ▁rule ▁as ▁a ▁function ▁. ▁The ▁definitions ▁of ▁possible ▁out comes , ▁manip ul able , ▁dict atorial ▁have ▁natural ▁adapt ations ▁to ▁this ▁framework . ▁ ▁For ▁a ▁strict ▁voting ▁rule , ▁the ▁con verse ▁of ▁the ▁Gib b ard – S atter th wa ite ▁theorem ▁is ▁true .