I propose a simple and formal method to reconstruct falsified election results, based on the hypothesis of the mutual independence of the overall turnout and the result of power. This method is a development of the classical method of S.A. Shpilkin, however, it does not require additional assumptions and has no free parameters. In addition, it uniformly reconstructs all key values and uses a simpler and clearer mathematical procedure. Comparison of official and true results of federal elections allows to perform a political science analysis of the development of the institution of electoral frauds in Russia in the 20th century and its impact on the political system.