▁candidate ▁. ▁Now , ▁the ▁scores ▁are : ▁. ▁Hence , ▁ ▁is ▁elected . ▁V oter ▁ ▁is ▁satisfied ▁of ▁her ▁ball ot ▁modification , ▁because ▁she ▁pre fers ▁the ▁outcome ▁ ▁to ▁, ▁which ▁is ▁the ▁outcome ▁she ▁would ▁obtain ▁if ▁she ▁voted ▁sin cer ely . ▁ ▁We ▁say ▁that ▁the ▁B ord a ▁count ▁is ▁manip ul able : ▁there ▁exists ▁situations ▁where ▁a ▁s inc ere ▁ball ot ▁does ▁not ▁defend ▁a ▁vot er ' s ▁prefer ences ▁best . ▁ ▁Unfortunately , ▁the ▁Gib b ard – S atter th wa ite ▁theorem ▁states ▁that ▁a ▁voting ▁rule ▁must ▁be ▁manip ul able , ▁except ▁possibly ▁in ▁two ▁cases : ▁if ▁there ▁is ▁a ▁distinguished ▁vot er ▁who ▁has ▁a ▁dict atorial ▁power , ▁or ▁if ▁the ▁rule ▁limits ▁the ▁possible ▁out comes ▁to ▁two ▁options ▁only . ▁ ▁F ormal ▁statement ▁ ▁Let ▁ ▁be ▁the ▁set ▁of ▁alternatives ▁( which ▁is ▁assumed ▁finite ), ▁also ▁called ▁candidates , ▁even ▁if ▁they ▁are ▁not ▁necessarily ▁persons : ▁they ▁can ▁also ▁be ▁several ▁possible ▁dec isions ▁about ▁a ▁given ▁issue . ▁We ▁denote ▁by ▁ ▁the ▁set ▁of ▁vot ers . ▁Let ▁ ▁be ▁the ▁set ▁of ▁strict ▁weak ▁orders ▁over ▁: ▁an ▁element ▁of ▁this ▁set ▁can ▁represent ▁the ▁prefer ences ▁of ▁a ▁vot er . ▁A ▁voting ▁rule ▁is ▁a ▁function ▁. ▁Its ▁input ▁is ▁a ▁profile ▁of ▁prefer ences ▁ ▁and ▁it ▁yields ▁the ▁identity ▁of ▁the ▁winning ▁candidate . ▁ ▁We ▁say ▁that