We propose a new theoretical study of domain adaptation for majority vote classifiers (from a source to a target domain). We upper bound the target risk by a trade-off between only two terms: The voters’ joint errors on the source domain, and the voters’ disagreement on the target one. Hence, this new study is simpler than other analyses that usually rely on three terms. We also derive a PAC-Bayesian generalization bound leading to a DA algorithm for linear classifiers.