LEGAL EVALUATION OF THE CONSISTENCY OF INDIVIDUAL PREFERENCES ASKED IN THE FORM OF CHOICE FUNCTIONS

Fisun K. A. Doctor of Economics, Associate Professor, National Academy of the National Guard of Ukraine, е-mail: fisun.konstantsn.1958@gmail.com, ORCID ID: 0000-0002-2928-4313 Vavzhenchuk S. Ya. Doctor of Law, Associate Professor, Taras Shevchenko National University in Kiev е-mail: aadvokat@gmail.com; ORCID ID: 0000-0002-6968-6720 Tkachenko Yu.V. Ph.D., AssociateиProfessor, Management and Law Institute,Yaroslav Mudryi National Law University E-mail: yuriy.tkachenco@gmail.com, ORCID ID: 0000-0002-7155-8410 Cherkashina M. V. Ph.D., Associate Professor, National Academy of the National Guard of Ukraineб E-mail: rfhbnt@gmail.com, ORCID ID: 0000-0001-9543-5047

Ключевые слова: групповой выбор, индивидуальные предпочтения, коэффициент согласия, медиана, мера близости, технологии обработки, финансовая информация. Формул 23, рис. 0, табл.: 1, библ.: 29 Introduction. The procedures for obtaining collective decisions pose a number of questions for the process organizers: the types of measurement scales in which individual and group opinions are implemented; selection of a rule for harmonizing individual assessments; selection of requirements for a group profile; assessment of the consistency profile of individual preferences [1-3; 23-25].Obtaining quantitative estimates of the consistency of the entire profile of individual preferences is the subject of research by many authors working in the field of expert estimates and methods of statistical analysis [5; 10; 15; 16-21].The use of one or another coefficient of consistency depends on the type of rating scale and the opinion of the person making decisions regarding the «fairness» of taking into account the preferences of all participants in the group selection process [4; 9]. The formation of a reasonable set of collective agreement measures and the determination of their relationship enables managers to conduct expert assessments to use not only their opinions and preferences, but also justify the calculations of the applied coefficients. This determines the need for research in the analysis of aggregation of qualitative data.
Analysis of recent studies. There are several basic approaches to solving the problem of reconciling various individual assessments into group assessments or obtaining a collective opinion. The axiomatic approach requires the coordination of certain principles of group choice. Five principles of coordination for the formation of group choice are incompatible. This manifestation of the problem of collective decision is the «Arrow paradox» [1].
The metric approach [3; 10; 15; 17]. The opinion of each individual is equally taken into account in group preference, and the concept of «distance between a set of relations of experts» is introduced to determine the measure of proximity. The best group solution is based on the principles of discrete mathematics. The question of adequacy is being reduced.
The geometric approach [4; 13; 14]. The study of bulge structures can be defined in a variety of preferences. A distinctive feature is the consistent use of geometric concepts. However, the introduced group choice rules are completely abstracted from the specific physical content of the practical problem being solved. Expert opinions are considered as a choice of points in some formalized model of space.
Heuristic approach [7][8][9][10][11][12]. This approach assumes: an increase in the number of factors taken into account leads to an increase in the accuracy of calculations; the need to determine the «weight» of each factor; the final conclusion is made by the decision maker; the administrative structure apparatus participates in the development of assessments, or forms a description of the main provisions of the conditions of group choice. The emerging shortcomings of this approach are, first of all, determined by the adequacy of the questions posed to the expert and the need to find a specialist in the field of sequence of questions during the examination.
When processing quantitative data in order to obtain a collective solution, the use of metric models is considered one of the most correct approaches for matching various individual estimates [27; 28]. The main assumption of these models is that individuals are equal and their opinions are equally taken into account in group preference. Group preference is «the closest» to all individual preferences received at the same time. To determine the measure of proximity, one or another distance is introduced between a set of individual preferences.
The need for a preliminary analysis of individual preferences in order to obtain a quantitative assessment of the consistency of the totality of preferences involves the calculation of the coefficient of consistency. These coefficients are often investigated during group examination [10; 14; 23; 24], multi-round processes for finding collective solutions [6; 22; 24]. The question of the relationship between different indicators of measures of agreement, using different measurement scales is also relevant.
The purpose of the study: to investigate and develop compliance measures when individual preferences are defined as a choice function and a group decision is defined as a choice function using an analogue of the Hamming metric.
The results of the study. The proposed coefficients of the measure of agreement ) H ( T , ) H ( G for the selection functions, to some extent simplify the verification of the consistency of the collective assessment and, for the simplified version, coincide with finding the median, Candell's coefficient of agreement, respectively.
Group selection mathematical models. When processing qualitative data in order to obtain the «the best» collective solution, the use of mathematical models is considered one of the most correct approaches for matching various individual estimates [9; 18].
It is characteristic of this approach that each individual assessment is equally taken into account in group preference. Group preference is «the closest» to all individual preferences received at the same time. To determine the proximity measure, one or another distance is introduced between a set of individual preferences [16; 23].
Often when obtaining a group decision, there is a need for a preliminary analysis of individual preferences in order to obtain a quantitative assessment of the consistency of the entire set of preferences. This paper explores two possible measures of agreement. In the framework of the statement of the group choice problem, when individual preferences are set in the form of selection functions and the group solution is determined as a choice function, an analog of the Hamming metric is used to find the median as a group choice function [2; 14; 24]. Using this metric, two coefficients that determine the consistency in the space of individual selection functions are introduced. One of the coefficients is directly related to finding the median [14]. The second is an analogue of the Candell's coefficient of agreement for binary preference relations [2].
We denote by In the first statement of the group choice problem, individual opinions are defined as preference relations belonging to a certain class of binary relations. A group solution is found as mapping a profile of individual preferences into a certain group preference, also belonging to a certain class of binary relations. This mapping is a group preference function. A group preference function (GSR) is a mapping that maps to any profile a group preference from a certain class of binary relations on A. Let us designate this statement of the group choice problem as « ФГП ИП  » (individual preferences are mapped to the group preference function). The mapping of individual opinions into a group is carried out using a predefined rule for obtaining group opinions.
In the second statement of the group choice problem, individual opinions are set in the form of FC. A group solution is found as mapping an individual FC profile to a group selection function (GSR).This mapping is carried out according to the group selection rule (GSR), which is defined as a mapping  that maps to any   preference relations, and the group decision is defined as the mapping R into the group choice function, i.e. profile R is mapped to FC from an arbitrary class  . Similarly to the above, this mapping is carried out according to the group selection rule for relations (GSR).We will designate this statement of the problem as « GPF IP  » (individual preferences are displayed in the group preference function).
A fourth setting is possible, when the individual opinions are FC, i.e. « GPF IP  » (individual selection functions are reflected in the group selection function). In the literature on the theory of collective choice, this statement of the group choice problem is not considered. It is believed that, determining the opinions of individuals in such a general form as FC, it is inexpedient to seek a group solution in the form of GSR.
The procedures for developing a solution in the framework of the first and third formulations of the group choice problem have been known for a long time, however, a special interest in them arose after the work of K. Arrow, who fully used the ideas and methods of modern discrete mathematics. Among a large number of methods for the analysis and synthesis of complex systems, management, of considerable theoretical and practical interest are those that take into account the peculiarities of people's behavior when making decisions.
Defining a metric for a selection function. We introduce the following notation for FC h : For the selection functions ' h and k h , the notation will be S , x ' C and S , x ) k ( C , respectively.
We define [2] the distance d between two arbitrary FC ' h and k h , as: The restrictions on the set  S for FC ' h and k h are denoted by S h and S ' h , respectively, then  (1)). Then the number of GSR coinciding with the median . Using the distance d (2), we construct the agreement measures of individual selection functions as quantitative estimates that make it possible to judge the proximity of two or more individual FCs on each  S . At the stage of the preliminary analysis, checking the consistency of individual opinions will allow more reasonably choosing the final group decision.
Let S h and S ' h be two arbitrary FCs defined for any  S . Moreover, the number of alternatives in S is S , that is, For the elements of the selection matrices S h and S h , the relation holds: It is assumed that the FC does not impose conditions that combine the choice of different sets of H . Therefore, the consistency of individual FCs is determined separately for each  S . We Based on the expression (5) we obtain the calculated formula for the coefficient: We rewrite in final form: Expression (7) Suppose that a preference relationship from profile R belongs to a relationship class The measure of consent will be defined as (18) for each  S . Using (3), we write expression (8) in the following form: From the expression (9)   . The feasibility of using this coefficient is applicable for multilevel expert assessment procedures.  These coefficients allow you to form a sequence of choices and directions for the development of the process of harmonizing the «common opinion». It is assumed that the formation of group choice is an iteration.
Conclusions. In the statement of the problem, which was considered in this article, the coordination of the final solution is determined by the selection of the group of «best» alternatives from the set of compared ones. Such a decision is often sufficient when processing the results of a collective examination. In addition, the group choice determined on the set of binary relations is not always unambiguous. For example, when using the majority rule. The proposed coefficients of the measure of agreement, for the selection functions, to some extent simplify the verification of the consistency of the collective assessment and, for the simplified version, coincide with finding the median, Candell's coefficient of agreement, respectively.
Directions for further research: the imposition of restrictions on structural conditions.