In the literature on judgment aggregation, an important open question is how to measure the distance between any two judgment sets. This is relevant for issues of social choice: if two individuals hold different beliefs then we might want to find a compromise that lies somewhere between them. We propose a set of axioms that determine a measure of distance uniquely. This measure differs from the widely used Hamming metric. The difference between Hamming's metric and ours boils down to one axiom. Given judgment sets A and B, this axiom says that if the propositions in jointly imply that the propositions in A-B share the same truth value, then the disagreement between A and B over those propositions in A-B should be counted as a single disagreement. We consider the application of our metric to judgment aggregation, and also use the metric to measure the distance between preference rankings.