A PROPOSAL ON REFORMATION OF THE ELECTION SYSTEM OF THE RUSSIAN FEDERATION

Introduction: the article analyzes the extent to which electoral systems meet different (mathematical and judicial) evaluation criteria. Purpose: to identify the fairest algorithm for mandate distribution when electing deputies and officials. Methods: apart from general scientific methods, we extensively used special scientific methods including comparative legal and systematic ones. Results: we have defined the range of mathematical criteria (the absolute majority rule, the Condorcet paradox, the principle of proportional representation of the parties, etc.) and legal criteria (the provisions of the principles of equal, free, and fair election). Preferential voting systems have been found to meet mathematical and judicial criteria most of all. A number of preferential voting systems meet the Condorcet paradox and ensure proportional representation of the parties. During such an election, free and equal participation of independent and party candidates is ensured. Many other systems of majoritarian, proportional, and mixed types do not meet the abovementioned criteria. Unfortunately, in particular cases the Condorcet paradox does not allow determining the candidate to be elected. Consequently, we suggest combining the algorithms developed by Tideman, Kemeny, Young, and Schulze in order to find the ‘strongest path’, or the most reliable way of determining the candidates’ positions in the election. Conclusions: the preferential voting system developed by us is universal and can be used while electing both officers (the president, the governor) and deputies. If it was implemented, electoral legislation would be standardized, as well as the operation of election committees. Such a unification would allow improving the level of citizens' electoral rights protection.

A simple construction of complete single-peaked domains by recursive tiling

Single-peakedness was introduced by Black (J Political Econ 56:23–34, 1948) as a sufficient condition to overcome Condorcet paradox. Since then it has been attracting interest from researchers in various fields. In this paper, we propose a simple recursive procedure of constructing complete single-peaked domains of tiling type explicitly for any finite alternative sets, by combining two results published in recent years, and some observations of known results and examples by the author. The underlying basic structure of tiling type and properties of single-peaked domains provided here give a good visualization and make further developments on single-peakedness more easy.

Voting Procedures: A Summary Analysis

Roughly two centuries ago the Marquis de Condorcet and Chevalier Jean-Charles de Borda originated a research tradition – by no means a continuous one – that over the decades has produced results casting doubt on many widely used collective decision-making procedures. The phenomenon known as the Condorcet effect or the Condorcet paradox is the well-known problem of the simple majority rule. The paradox bearing the name of Borda is less commonly known, but it also relates to a procedure that is widely used, namely the plurality principle. Either one of these paradoxes is serious enough to make these procedures suspect unless one is convinced that the situations giving rise to these paradoxical features are extremely rare. In this article we review some voting procedures that have been introduced in the literature. We aim at giving a synthesis of the assessments of procedures with respect to various criteria.