On the Estimation of Efficiency of Voting Procedures

We consider the problem of a collegial decision on the basis of individual opinions of n experts deciding independently, the probability of a correct decision by the ith expert being equal to pᵢ, where < m pᵢ M < 1, i = 1, 2, … , n. It is shown that, for the error probability of the optimal collegial decision, the estimates 1-M M ( n [n/2] )∏ᵢ₌₁ⁿ√pᵢ(1-pᵢ) _ᵒᵖᵗ m 2m-1\, ( n [n/2] )∏ᵢ₌₁ⁿ√pᵢ(1-pᵢ) are valid.