MATHEMATICAL METHODS AND MODELS FOR STUDYING CORRUPTION IN ORGANIZATIONAL SYSTEMS

Abstract

Context. In the process of functioning of various organizational expert systems – economic, social, militarized – the task of detecting, localizing and measuring the level of corruption in the system arises. These tasks are solved on the basis of various data obtained during observations and experiments on the system. However, there is no single method for processing information to solve these problems. This paper proposes such a technique, based on a comparison of assessments of the same indicators of evaluated objects, given by various experts. Objective. The purpose of the article is to develop a fully formalized method for detecting, localizing and measuring the level of corruption in an organizational system consisting of experts, based on the assessments given to objects. Method. The method proposed in the article consists in the presentation of an organizational system of m experts conducting an examination of the object with n indicators by means of a (m× n) -matrix B = bij . Here bij – is the assessment given by the i -th expert to the j-th indicator of the object. In this case a system with ideal (non-corrupted) experts corresponds to a matrix B with equal elements in any column and, accordingly, with matching lines. In a system with non-ideal (corrupt) experts, the matrix B does not have this property. This allows you to enter an indicator of the absolute level of corruption in the system as the sum of the distances between the results of the examination of various experts. Result. A general analytical expression is obtained for absolute level of corruption in systems with arbitrary B,m and n . The maximum possible value of this indicator is found. An algorithm for detecting corruption in organizational systems is given, based on a comparison of calculated absolute level of corruption and its maximum allowable level. The problem of detecting corruption in a complex system, where objects with several indicators pass the examination, is also solved. Examples of detecting and measuring corruption in real expert systems are given. Conclusions. A new approach to mathematical modeling of corruption processes in organizational expert systems, based on the use of a matrix of assessments of various indicators of evaluated objects by different experts of the system, is proposed. This approach, in contrast to the established practice, allows us to find uniform solutions of various problems of studying corruption in systems of this type. These are tasks of detecting, localizing and measuring corruption. The direction as a whole is proposed to be called corrumetry.