A hyperpreference rule is a rule which maps any preference (input) on the set of alternatives, to a preference over preferences (output). Such a rule is termed separable if it is obtained by weighting each type of disagreement on each pair of alternatives. Given two preferences, the most preferred is the one that minimizes the sum of weights obtained from the disagreements between preferences and the input. A hyperpreference rule is neutral when relabeling alternatives has no impact on the rule. Deprived of all constraints of transitivity and completeness on the preferences on the set of alternatives, I show that a neutral separable hyperpreference rule is characterized by a unique parametric semi-metric called LG metric. I provide an axiomatization of the family of LG metrics, which is essentially a generalization of the Kemeny metric over the whole set of reflexive binary relations.
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. The results provide new insights into the design of strategyproof mechanisms under preference heterogeneity.