To create their rankings, university-ranking agencies usually combine multiple performance measures into a composite index. However, both rankings and index scores are sensitive to the weights assigned to performance measures. This paper uses a stochastic dominance efficiency methodology to obtain two extreme, case-weighting vectors using the Academic Ranking of Worldwide Universities (ARWU) and Times Higher Education (THE) data, both of which lead to the highest and lowest index outcomes for the majority of universities. We find that both composite scores and rankings are very sensitive to weight variations, especially for middle- and low-ranked universities.