PARADOX OF IMPOSSIBILITY OF FAIR ELECTIONS: HISTORICAL DISCOURSE (FROM NEW TIMES TO ARROW’S PARADOX)

The work is aimed at identifying and differentiating paradoxes that affect thе impossibility of democratic elections. The relevance of this topic is due to the fact that, different election systems give birth to their paradoxes and shortcomings. The thesis of the impossibility of democratic elections is based on the experience of many countries around the world that have faced this problem. Even Ukraine is a good example of many paradoxes that in the hands of political technologists are becoming tools to achieve the goal. The essence and significance of the election are determined. Different ways of voting depending on the type of electoral system are analyzed: majority, proportional and mixed. Auxiliary factors in determining the main issue of the work are theorems, scientific and artistic works, as well as examples that are based on practice. The following works of mathematicians and extras were studied: «When to rob and other life hacks» Steven Levitt and Stephen Dubner; «A Guide for Lovers of Mathematics» by Edward Scheinerman; «Collective Choice and Individual Values» by Kenneth Joseph Arrow, which shows both familiar and practicing paradoxes and methods of voting, and absurd, only theoretically defined, methods It is proved that elections are a mechanism by which the formation of the political elite of any country. The problem of democratic elections is a rather difficult issue for both Ukraine and other countries. The solution of this problem is impossible without the use of applied mathematics. Decision-making processes are at the core of any activity. In theatrical art — construction and organization of the process of staging «Hamlet», immersion in the culture of creativity; in biology — the discovery of the role of DNA in heredity; in the social sphere — the functioning and development of social processes and more. Therefore, the theory of choice exists as long as man exists. There are problems when choosing the optimal way of voting, none of these methods can be called perfect and completely democratic, each has its advantages and disadvantages.