We propose a framework for measuring attentional agency, which we define as a user's ability to allocate attention according to their own desires, goals, and intentions on digital platforms that use statistical learning to prioritize informational content. Such platforms extend people's limited powers of attention by extrapolating their preferences to large collections of previously unconsidered informational objects. However, platforms typically also allow users to influence the attention of other users in various ways. We introduce a formal framework for measuring how much a given platform empowers each user to both pull information into their own attention and push information into the attention of others. We also use these definitions to clarify the implications of generative foundation models and other recent advances in AI for the structure and efficiency of digital platforms. We conclude with a set of possible strategies for better understanding and reshaping attentional agency online.