Abstract: This work introduces permutation weighting: a weighting estimator for observational causal inference under general treatment regimes which preserves arbitrary measures of covariate balance. We show that estimating weights which obey balance constraints is equivalent to a simple two-class classification problem between the observed data and a permuted dataset (no matter the cardinality of treatment). Arbitrary probabilistic classifiers may be used in this method; the hypothesis space of the classifier corresponds to the nature...