▁case ▁of ▁totally ▁conflic ting ▁belief s ▁when ▁interpreted ▁in ▁this ▁way . ▁Assume ▁that ▁Alice ▁pre fers ▁film ▁X ▁with ▁probability ▁ 1 . 0 , ▁and ▁that ▁Bob ▁pre fers ▁film ▁Z ▁with ▁probability ▁ 1 . 0 . ▁When ▁trying ▁to ▁combine ▁their ▁prefer ences ▁with ▁D emp ster ' s ▁rule ▁it ▁turns ▁out ▁that ▁it ▁is ▁undefined ▁in ▁this ▁case , ▁which ▁means ▁that ▁there ▁is ▁no ▁solution . ▁This ▁would ▁mean ▁that ▁they ▁can ▁not ▁agree ▁on ▁seeing ▁any ▁film ▁together , ▁so ▁they ▁do ▁not ▁go ▁to ▁the ▁cinema ▁together ▁that ▁evening . ▁However , ▁the ▁semantics ▁of ▁interpre ting ▁preference ▁as ▁a ▁probability ▁is ▁vague : ▁if ▁it ▁is ▁referring ▁to ▁the ▁probability ▁of ▁seeing ▁film ▁X ▁ton ight , ▁then ▁we ▁face ▁the ▁F alla cy ▁of ▁the ▁ex cluded ▁middle : ▁the ▁event ▁that ▁actually ▁occurs , ▁seeing ▁none ▁of ▁the ▁films ▁ton ight , ▁has ▁a ▁probability ▁mass ▁of ▁ 0 . ▁ ▁Example ▁producing ▁counter - int uit ive ▁results ▁in ▁case ▁of ▁high ▁conflict ▁An ▁example ▁with ▁exactly ▁the ▁same ▁numerical ▁values ▁was ▁introduced ▁by ▁Z ade h ▁in ▁ 1 9 7 9 , ▁to ▁point ▁out ▁counter - int uit ive ▁results ▁generated ▁by ▁D emp ster ' s ▁rule ▁when ▁there ▁is ▁a ▁high ▁degree ▁of ▁conflict . ▁The ▁example ▁goes ▁as ▁follows : ▁ ▁Suppose ▁that ▁one ▁has ▁two ▁equ i - re li able ▁do ctors ▁and ▁one ▁doctor ▁bel ieves ▁a ▁patient ▁has ▁either