On the Estimation of Efficiency of Voting Procedures

Abstract

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 $p_i$, where $\oot < m\l p_i\l M < 1$, $i = 1, 2, \ldots , n$. It is shown that, for the error probability of the optimal collegial decision, the estimates $$ {1-M\over M} \left(\matrix{ n \cr [n/2] \cr }\right)\prod_{i=1}^n\sqrt{p_i(1-p_i)}\l \bP_{\err}^{\rm opt} \l {m\over 2m-1}\, \left(\matrix{ n \cr [n/2] \cr }\right)\prod_{i=1}^n\sqrt{p_i(1-p_i)} $$ are valid.