Symmetry and asymmetry of electoral systems

The paper analyzes such a mathematical criterion for determining the fairness of electoral systems as the principle of reversal symmetry, proposed several years ago. The author has studied various circumstances that affect the asymmetry and, consequently, the unfairness of the electoral system. They, in particular, are the type of voting and the mathematical and, therefore, legal equivalence of the voters’ preferences. Otherwise, the elections may be won by candidates who are not supported by the majority of voters, which contradicts the basic requirements of democracy.