▁Indeed , ▁a ▁strict ▁voting ▁rule ▁is ▁dict atorial ▁if ▁and ▁only ▁if ▁it ▁always ▁selects ▁the ▁most - lik ed ▁candidate ▁of ▁the ▁dict ator ▁among ▁the ▁possible ▁out comes ; ▁in ▁particular , ▁it ▁does ▁not ▁depend ▁on ▁the ▁other ▁vot ers ' ▁ball ots . ▁As ▁a ▁consequence , ▁it ▁is ▁not ▁manip ul able : ▁the ▁dict ator ▁is ▁perfectly ▁def ended ▁by ▁her ▁s inc ere ▁ball ot , ▁and ▁the ▁other ▁vot ers ▁have ▁no ▁impact ▁on ▁the ▁outcome , ▁hence ▁they ▁have ▁no ▁in cent ive ▁to ▁devi ate ▁from ▁s inc ere ▁voting . ▁Thus , ▁we ▁obtain ▁the ▁following ▁equivalence . ▁ ▁In ▁the ▁theorem , ▁as ▁well ▁as ▁in ▁the ▁cor ollary , ▁it ▁is ▁not ▁needed ▁to ▁assume ▁that ▁any ▁alternative ▁can ▁be ▁elected . ▁It ▁is ▁only ▁assumed ▁that ▁at ▁least ▁three ▁of ▁them ▁can ▁win , ▁i . e . ▁are ▁possible ▁out comes ▁of ▁the ▁voting ▁rule . ▁It ▁is ▁possible ▁that ▁some ▁other ▁alternatives ▁can ▁be ▁elected ▁in ▁no ▁circumstances : ▁the ▁theorem ▁and ▁the ▁cor ollary ▁still ▁apply . ▁However , ▁the ▁cor ollary ▁is ▁sometimes ▁presented ▁under ▁a ▁less ▁general ▁form : ▁instead ▁of ▁assuming ▁that ▁the ▁rule ▁has ▁at ▁least ▁three ▁possible ▁out comes , ▁it ▁is ▁sometimes ▁assumed ▁that ▁ ▁contains ▁at ▁least ▁three ▁elements ▁and ▁that ▁the ▁voting ▁rule ▁is ▁onto , ▁i . e . ▁every ▁alternative ▁is ▁a ▁possible ▁outcome . ▁The ▁assumption ▁of ▁being ▁onto ▁is ▁sometimes ▁even ▁replaced ▁with