Electoral Systems in the Digital Age: Underlying Challenges and New Opportunities Part I. A Review of the Problems, Classic Protocols of Collective Choice

Abstract

The article is devoted to the problem of democratic development of Ukraine. The reasons for the need for a radical transformation of the electoral process in Ukraine have been considered from a theoretical standpoint. The main goal and sub-goals of the research have been formulated. The classical mathematical models of electoral technologies, selected for comparison with modern approaches have been described. The basic principles of selection of methods for measuring the results of approval voting have been analyzed. The issues of constructing a verbal-numerical scale, assessing the consistency of voter decisions and applying statistical criteria to obtain a consolidated result have been considered. The models selected for calculating the final election rating are analyzed. Mathematical algorithms of multicriteria selection based on the qualimetric approach and pairwise comparison on four variants of scales are given. Protocols for determining consensus alternatives using the Topsis method, the Kemeni – Young median, the Schulze heuristic procedure, and the fuzzy set approach are described. The results of approbation of the selected protocols of approval of the voting system for the election model of 4 candidates on 7 questions of the ballot paper are given. The algorithm and the results of generating by the Monte Carlo method arrays of initial data with a size of 10,000 records, having a uniform and normal distribution with three variants of the bias parameter, are presented. To identify the sensitivity of the studied protocols to violations of the transitivity of individual preference profiles, the primary data arrays were transformed by replacing the nontransitive profiles with an equivalent number of transitive ones without presenting a preference to any alternative. Based on the assessment of the correlation of the final ratings, their sensitivity to the type of distribution and to violations of the transitivity of individual judgments, it was concluded that it is advisable to use the Kemeny median to determine the voting results. The use of the proposed method for transforming primary data also makes it possible to use the Condorcet, Dodgson, Saati and Schulze protocols. The results of this study indicate that there is a fundamental possibility of transition to a new digital paradigm of the electoral process based on the approving principle of voting.