▁result , ▁even ▁when ▁there ▁is ▁low ▁conflict . ▁ ▁Suppose ▁that ▁one ▁doctor ▁bel ieves ▁a ▁patient ▁has ▁either ▁a ▁brain ▁tum or , ▁with ▁a ▁probability ▁of ▁ 0 . 9 9 , ▁or ▁men ing itis , ▁with ▁a ▁probability ▁of ▁only ▁ 0 . 0 1 . ▁A ▁second ▁doctor ▁also ▁bel ieves ▁the ▁patient ▁has ▁a ▁brain ▁tum or , ▁with ▁a ▁probability ▁of ▁ 0 . 9 9 , ▁and ▁bel ieves ▁the ▁patient ▁suff ers ▁from ▁conc uss ion , ▁with ▁a ▁probability ▁of ▁only ▁ 0 . 0 1 . ▁If ▁we ▁calculate ▁m ▁( bra in ▁tum or ) ▁with ▁D emp ster ’ s ▁rule , ▁we ▁obtain ▁ ▁This ▁result ▁implies ▁complete ▁support ▁for ▁the ▁diagn osis ▁of ▁a ▁brain ▁tum or , ▁which ▁both ▁do ctors ▁believed ▁very ▁likely . ▁The ▁agreement ▁ar ises ▁from ▁the ▁low ▁degree ▁of ▁conflict ▁between ▁the ▁two ▁sets ▁of ▁evidence ▁compr ised ▁by ▁the ▁two ▁do ctors ' ▁opinions . ▁ ▁In ▁either ▁case , ▁it ▁would ▁be ▁reasonable ▁to ▁expect ▁that : ▁ ▁since ▁the ▁existence ▁of ▁non - zero ▁belief ▁prob abilities ▁for ▁other ▁diagn oses ▁implies ▁less ▁than ▁complete ▁support ▁for ▁the ▁brain ▁tum our ▁diagn osis . ▁ ▁D emp ster – S ha fer ▁as ▁a ▁general isation ▁of ▁Bay esian ▁theory ▁▁ ▁As ▁in ▁D emp ster – S ha fer ▁theory , ▁a ▁Bay esian ▁belief ▁function ▁▁ ▁has ▁the ▁properties ▁ ▁and ▁. ▁The ▁third ▁condition ,