Mathematical modeling of the collective solution accuracy

Currently, the problem of collective decision-making is one of the most relevant in the organization of effective management in social and economic systems. One of the main issues in the theory of expert assessments is the assessment of the group solution quality. The article discusses the matters of assessing the socio-economic indicator by independent experts. The centered random variables sums value of individual estimates is accepted as the error of group estimation. The situation is examined when the values of the indicator have an arbitrary distribution with known and unknown parameters. Two algorithms have been developed to determine the required amount of experts depending on the accuracy and reliability of the assessment. The first algorithm is used to find the confidence interval of mathematical expectation when the variance of the indicator is not specified. In this event, an iterative process is undertaken to ascertain the volume of representativeness for the confidence interval of variance with a given accuracy and reliability. The second algorithm is employed to construct a confidence interval for variance when the number of experts is more than three. The important task of quantifying the proportion (percentage) of possible errors within a predefined interval in measuring the indicator has been solved. An econometric model is designed for the Laplace function. The case of determining the number of experts to evaluate an indicator having a uniform and exponential distribution over a given interval is considered. An example of the practical implementation of the devised method is shown.

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