Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.

We derive sufficient conditions for ranking performance evaluation systems in multi-task agency models (using both optimal and linear contracts) in terms of a second-order stochastic dominance (SSD) condition on the likelihood ratios. The SSD condition can be replaced by a variance-covariance matrix of likelihood ratios (VCM) condition when the utility function is square-root, the performance measures are normally distributed, and for LEN models. We identify existing results derived under the LEN assumptions that rely on the VCM condition and, thus, also hold for optimal contracts.