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Comparing social preferences: incompleteness and intransitivity - Social Choice and WelfareA 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.

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