▁interval ▁[ 0 , 1 ] ▁using ▁yes / no ▁questions . ▁This ▁might ▁require ▁an ▁infinite ▁number ▁of ▁questions . ▁ ▁A ▁R MS ▁for ▁three ▁agents ▁can ▁be ▁constructed ▁as ▁follows . ▁Let ▁x , ▁y , ▁s , ▁and ▁t ▁be ▁parameters ▁satisfying : ▁▁▁▁▁▁▁ ▁Con struct ▁a ▁set ▁of ▁three ▁measures ▁with ▁these ▁two ▁properties : ▁ ▁The ▁density ▁of ▁each ▁measure ▁is ▁always ▁strictly ▁between ▁/ 2 ▁and ▁ ▁( so ▁for ▁a ▁given ▁piece , ▁the ▁agents ' ▁valu ations ▁differ ▁by ▁ ▁a ▁factor ▁of ▁less ▁than ▁ 2 ). ▁▁ ▁The ▁values ▁of ▁the ▁pieces ▁determined ▁by ▁x ▁and ▁y ▁are ▁as ▁in ▁the ▁table : ▁{ | ▁class =" wik itable " ▁| - ▁! ▁Agent ▁!! ▁[ 0 , x ] ▁!! ▁[ x , y ] ▁!! ▁[ y , 1 ] ▁| - ▁| ▁A ▁|| ▁t ▁|| ▁t ▁|| ▁s ▁| - ▁| ▁B ▁|| ▁s ▁|| ▁t ▁|| ▁t ▁| - ▁| ▁C ▁|| ▁t ▁|| ▁s ▁|| ▁t ▁| } ▁ ▁Then , ▁every ▁env y - free ▁division ▁among ▁Alice ▁Bob ▁and ▁Carl ▁must ▁have ▁cut s ▁at ▁x ▁and ▁y ▁( there ▁are ▁exactly ▁two ▁such ▁divisions ), ▁since ▁all ▁other ▁options ▁lead ▁to ▁env y : ▁▁ ▁If ▁cut s ▁are ▁made ▁to ▁the ▁left ▁of ▁x ▁and ▁to ▁the ▁right ▁of ▁y , ▁then ▁Alice ▁and ▁Bob ▁both ▁ins ist ▁on ▁getting ▁the ▁middle ▁piece . ▁ ▁If ▁cut s ▁are ▁made ▁to ▁the