Large language models (LLMs) that do not give consistent answers across contexts are problematic when used for tasks with expectations of consistency–e.g. question-answering, explanations, etc. Our work presents an evaluation benchmark for self-consistency in cases of under-specification where two or more answers can be correct. We conduct a series of behavioral experiments on the OpenAI model suite using an ambiguous integer sequence completion task. We find that average consistency ranges from 67% to 82%, far higher than would be predicted if a model’s consistency was random, and increases as model capability improves. Furthermore, we show that models tend to maintain self-consistency across a series of robustness checks, including prompting speaker changes and sequence length changes. These results suggest that self-consistency arises as an emergent capability without specifically training for it. Despite this, we find that models are uncalibrated when judging their own consistency, with models displaying both over- and under-confidence. We also propose a nonparametric test for determining from token output distribution whether a model assigns non-trivial probability to alternative answers. Using this test, we find that despite increases in self-consistency, models usually place significant weight on alternative, inconsistent answers. This distribution of probability mass provides evidence that even highly self-consistent models internally compute multiple possible responses.