Measuring Differences of Opinion: Axiomatic Foundation, Utility, and Truthtelling

Understanding how individuals and groups differ in their opinions and preferences is central to analyzing disagreement, measuring polarization, designing institutions, and predicting collective outcomes. Yet comparing preferences requires more than observing how each person ranks alternatives—it requires a method for comparing preference orderings themselves. This paper develops a formal framework to infer how individuals might rank different preference orderings based solely on their observed preferences. We introduce a set of natural and behaviorally plausible axioms—Independence (I), Disagreement Aversion (DA), and Symmetry (S)—and show that they uniquely characterize a class of hyperpreference relations and their associated utility representations. We apply this framework to the study of aggregation mechanisms, deriving necessary and sufficient conditions on utility structures that induce truthful preference reporting in equilibrium and guarantee efficiency. Our results yield new insights into strategyproof mechanism design under deep preference heterogeneity and clarify when differences of opinion can be meaningfully and reliably measured. KEYWORDS. Preference, Hyperpreference, Hyperutility, Strategy-proofness, Efficiency