Optimal statistical solution with qualitative measurements. Signal detection

The methods of statistical solution theory are extended to the case of qualitative measurements characteristic of expert estimation, classification, and managements characteristic of expert estimation, classification, and management decision making problems. Rules, optimal in terms of minimal mean risk, are designed for signal detection and the detection performance estimates are given. As a particular case a primitive voting model is described where the majority principle follows from mean risk minimization. The dependence of the voting threshold on a priori data, the number of voters, and conditional error probabilities are analyzed.