Recent advances in language modeling have enabled new conversational systems. In particular, it is often desirable for people to make choices among specified options when using such systems. We address the problem of reference resolution, when people use natural expressions to choose between real world entities. For example, given the choice
Should we make a Simnel cake or a Pandan cake?' a natural response from a non-expert may be indirect:let's make the green one'. Such natural expressions have been little studied for reference resolution. We argue that robustly understanding such language has large potential for improving naturalness in dialog, recommendation, and search systems. We create AltEntities (Alternative Entities), a new public dataset of 42K entity pairs and expressions (referring to one entity in the pair), and develop models for the disambiguation problem. Consisting of indirect referring expressions across three domains, our corpus enables for the first time the study of how language models can be adapted to this task. We find they achieve 82%-87% accuracy in realistic settings, which while reasonable also invites further advances.