Large language models are often ranked according to their level of alignment with human preferences -- a model is better than other models if its outputs are more frequently preferred by humans. One of the most popular ways to elicit human preferences utilizes pairwise comparisons between the outputs provided by different models to the same inputs. However, since gathering pairwise comparisons by humans is costly and time-consuming, it has become a very common practice to gather pairwise comparisons by a strong large language model -- a model strongly aligned with human preferences. Surprisingly, practitioners cannot currently measure the uncertainty that any mismatch between human and model preferences may introduce in the constructed rankings. In this work, we develop a statistical framework to bridge this gap. Given a small set of pairwise comparisons by humans and a large set of pairwise comparisons by a model, our framework provides a rank-set -- a set of possible ranking positions -- for each of the models under comparison. Moreover, it guarantees that, with a probability greater than or equal to a user-specified value, the rank-sets cover the true ranking consistent with (the distribution of) human pairwise preferences. Our framework is computationally efficient, easy to use, and does not make any assumption about the distribution of human preferences nor about the degree of alignment between the pairwise comparisons by the humans and the strong large language model.

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