On the estimation of efficiency of voting procedures
Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 1, pp. 74-84
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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 $i$th expert being equal to $p_i$, where $\frac12$, $i = 1, 2, \ldots , n$. It is shown that, for the error probability of the optimal collegial decision, the estimates $$ \frac{1-M}M\binom{n}{[n/2]}\prod_{i=1}^n\sqrt{p_i(1-p_i)}\le\mathsf{P}^{\mathrm{err}}_{\mathrm{opt}}\le\frac m{2m-1}\binom{n}{[n/2]}\prod_{i=1}^n\sqrt{p_i(1-p_i)}. $$
are valid.
Keywords:
weighted voting, threshold function, optimal decision rule.
@article{TVP_1997_42_1_a5,
author = {Yu. A. Zuev},
title = {On the estimation of efficiency of voting procedures},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {74--84},
publisher = {mathdoc},
volume = {42},
number = {1},
year = {1997},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1997_42_1_a5/}
}
Yu. A. Zuev. On the estimation of efficiency of voting procedures. Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 1, pp. 74-84. http://geodesic.mathdoc.fr/item/TVP_1997_42_1_a5/