Robustness as a Selection Criterion for Scoring Rules in Composite Indicators

Composite indicators are widely used for measuring well-being, environment, social life, economy and other complex phenomena. Well-established international organizations or major corporations interested in investing in extensive research compile such indices. To illustrate, one of the most prestigious university rankings, the Times Higher Education World University Ranking, directly influences the position of higher education institutions, amount of funding, and their reputation among both students and staff. Despite their significance across various fields, composite indicators face criticism from the academic community. The problem of choosing the optimal scoring rule is not yet solved. Since we do not want the result to vary significantly depending on the subset of data we take, we check robustness of different scoring rules, which connect arithmetic and geometric mean and several popular ordinal scoring rules. Based on the metrics proposed, we select the most robust positional rule and compare those theoretical rules with the robustness of actual rules and the most robust rules shown in the literature. We expand the range of rules explored in the literature and focus on investigating positional scoring rules. We use data on composite indicators with different number of dimensions: Human Development Index, Education Index, Environmental Performance Index. This approach is used to make the result as general as possible.