typo: let us consider utility(A)=10, utility(C)=9, utility(C)=0 for the first group of voters, and utility(A)=0, utility(C)=9, utility(C)=10 for the second group. should have said: et us consider utility(A)=10, utility(C)=9, utility(B)=0 for the first group of voters, and utility(A)=0, utility(C)=9, utility(B)=10 for the second group.