Systems of personal pronouns (e.g.,`you' and `I') vary widely across languages, but at the same time not all possible systems are attested. Linguistic theories have generally accounted for this in terms of strong grammatical constraints, but recent experimental work challenges this view. Here, we take a novel approach to understanding personal pronoun systems by invoking a recent information-theoretic framework for semantic systems that predicts that languages efficiently compress meanings into forms. We find that a test set of cross-linguistically attested personal pronoun systems achieves near-optimal compression, supporting the hypothesis that efficient compression shapes semantic systems. Further, our best-fitting model includes an egocentric bias that favors a salient speaker representation, accounting for a well-known typological generalization of person systems (`Zwicky's Generalization') without the need for a hard grammatical constraint.