Universality of electoral systems

The paper analyzes such a mathematical criterion of the best electoral system as universality, proposed several years ago. The author proves that this criterion is a mathematical expression of the principle of free elections. The author has studied various circumstances affecting the universality of the electoral system. Such a circumstance, in particular, is the type of voting that allows or does not allow all possible options for expressing the political will of the voter. Otherwise, it is allowed to recognize the ballot as invalid and, consequently, ignore the will of the citizen. Ultimately, this will lead to a violation of the principles of equal and fair elections.