The article analyzes the heuristic potential of leading cross-country indices and ratings for comparative and institutional analysis of the Russian Federation and other countries of the world. The author proves that numerous comparative cross-country ratings and indices that have become extremely popular in social sciences in recent decades have transgressed the research framework and could influence the economy of various countries, their educational and scientific systems, external image, political agendas and legitimacy of political regimes. The author carries out a correlation analysis of positions of 145 countries in 16 comparative rating studies highly cited in social and political science and calculates the coefficient of their correlation with the positions of the Russian Federation. Additionally, the author compares the scores of 144 countries in the array of 16 ratings with the relevant indicators of the Russian Federation, which allowed to distinguish a group of countries showing maximum institutional identity with Russia, according to the compilers of the ratings. The author states that discovered correlations lack empirical evidence and convincing interpretation. At the same time, they are largely affected by political and ideological factors, as well as the effect of "image evaluation". The author concludes that the analyzed cross-country indices have considerable heuristic potential, but the patterns and correlations based solely on statistical analysis of their data, and, particularly, qualitative assessments, do not fully meet the criteria of obtaining new scientific knowledge and should be considered mainly as hypotheses that require additional causal substantiation and empirical verification. The article shows that mandatory hierarchy of representation inherent in the cross-country ratings creates the basis for their politicization and contradicts the contemporary reality that strives towards polymodality of the world order.