Optimization of the evolutionary matching method based on the probability of an erroneous decision

Roman Mirakhmedov, Zinaida Potapova

Abstract


The problem of obtaining demonstrably correct solutions to problems posed to experts is discussed and a methodology for solving local problems with a predetermined low error probability by a team of experts is presented. To build a theory of systems of evolutionary coordination, the following were used: Turchin’s theory of metasystem transitions; Condorcet's jury theorem; the Rasch model, which takes into account the connection between the probability of a correct decision and the actor’s preparedness and the difficulty of the task; ternary logic, which allows experts to accept the answer “I don’t know” in difficult cases; multi-stage work of actors acting as solution generators and expert evaluators of other people's solutions with coordination of their work by a genetic algorithm. A theoretical study of variations of the method of evolutionary coordination of solutions was carried out. The paper presents and substantiates mathematical models of variations of the method of evolutionary coordination of decisions, and proves a theorem about the tendency of the probability of an erroneous decision to zero when a number of conditions are met. The results of computer modeling of the decision-making process using the Monte Carlo method are presented. The results of computer modeling coincide with the results of the theoretical model within the limits of statistical errors. It is concluded that all the declared properties of systems of evolutionary coordination of decisions, if possible, to give either the correct answer with a given value of the probability of an erroneous decision, or the answer “I don’t know,” can be fulfilled by choosing a type of model, the number of actors and the rank of the actor in accordance with the local task.

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References


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