Language does not directly code facts about the world. Instead, speakers and listeners rely on shared assumptions to allow them to communicate more efficiently. Writers like Grice and Sperber & Wilson have proposed that communication is assumed to be "informative" or "relevant," but the predictions of these accounts are often informal or post-hoc. Here we propose a formal analogue to these accounts: that communicators choose what they want to say by how informative it would be about their intended meaning. We derive quantitative predictions about how this assumption would be used in language production and learning and test these predictions via two experiments. This work takes a first step towards formalizing the pragmatic assumptions necessary for effective communication in under-constrained, real-world situations.