Method for evaluating the robustness of rankings generated by composite indices

Characteristics of the quality of many systems in the economics, politics, society is in the form of a composite index, take the form of a linear composite index that linearly aggregates over several dimensions using a weight vector. The construction of the complex indexes of a system can be considered as the task of extracting the useful signal from the background noise. The signal in this case is the weights of the linear convolution of the indicators, which should reflect the structure of the system being evaluated. Principal component analysis determines the structure of the principal components for successive observations differently. The reason for this may be the presence of fatal errors in the data used. A modification of the principal component method that takes into account the presence of errors in the data used determines the structure of the system unambiguously. If the nature of the aggregation method of variables and the choice of weights adequately reflect the system quality model, then to study the reliability of the composite index, it is necessary to investigate the stability of ratings over time. The consequence of stability is on average a slight change (increment) in the rating of objects for different measurements. This increment can be a posteriori estimated by a set of observations on the proposed dispersion criterion. The results of assessing the stability of different integral characteristics by this criterion are given. Complex indexes, calculated by the author's method, show good stability.