Large language models perform surprisingly well on many zero-shot classification tasks, but are difficult to fairly compare to supervised classifiers due to the lack of a modifiable decision boundary. In this work, we propose and evaluate a method that transforms binary classification tasks into pairwise comparisons between instances within a dataset, using LLMs to produce relative rankings of those instances. Repeated pairwise comparisons can be used to score instances using the Elo rating system (used in chess and other competitions), inducing a confidence ordering over instances in a dataset. We evaluate scheduling algorithms for their ability to minimize comparisons, and show that our proposed algorithm leads to improved classification performance, while also providing more information than traditional zero-shot classification.