The crudest form of electoral frauds is simply to make up results. This gives rise to a predominance of psychologically attractive values of electoral characteristics. I develop, ground and explore tests to identify such frauds. All these tests are strictly formal, base only on official data on the election results and do not use any assumptions about voters’ behavior or reference results. I pay special attention to the maximum possible simplification of both the tests themselves and the ways of presenting the results of their application. This should make them publicly available for use and verification. Fictitious results present in significant quantities for approximately 40% of the electoral cases of 2000-2018 federal elections in Russia. At least 10% of them are caught individually. About 20÷30 subjects of Russian Federation are affected by mass frauds of this type.

electoral statistics, electoral frauds, psychologically attractive values, round numbers, statistical hypotheses, maximum likelihood method

Mathematical modelling in actual problems of science and technics