Understanding buffering mechanisms for various perturbations is essential for understanding robustness in cellular systems. Protein-level dosage compensation, which arises when changes in gene copy number do not translate linearly into protein level, is one mechanism for buffering against genetic perturbations. Here, we present an approach to identify genes with dosage compensation by increasing the copy number of individual genes using the genetic tug-of-war technique. Our screen of chromosome I suggests that dosage-compensated genes constitute approximately 10% of the genome and consist predominantly of subunits of multi-protein complexes. Importantly, because subunit levels are regulated in a stoichiometry-dependent manner, dosage compensation plays a crucial role in maintaining subunit stoichiometries. Indeed, we observed changes in the levels of a complex when its subunit stoichiometries were perturbed. We further analyzed compensation mechanisms using a proteasome-defective mutant as well as ribosome profiling, which provided strong evidence for compensation by ubiquitin-dependent degradation but not reduced translational efficiency. Thus, our study provides a systematic understanding of dosage compensation and highlights that this post-translational regulation is a critical aspect of robustness in cellular systems.