Metrizable preferences over preferences

Gilbert Laffond (), Jean Lainé and Remzi Sanver
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Gilbert Laffond: Istanbul Bilgi University

Social Choice and Welfare, 2020, vol. 55, issue 1, No 8, 177-191

Abstract: Abstract A hyper-preference is a weak order over all linear orders defined over a finite set A of alternatives. An extension rule associates with each linear order p over A a hyper-preference. The well-known Kemeny extension rule ranks all linear orders over A according to their Kemeny distance to p. More generally, an extension rule is metrizable iff it extends p to a hyper-preference consistent with a distance criterion. We characterize the class of metrizable extension rules by means of two properties, namely self-consistency and acyclicity across orders. Moreover, we provide a characterization of neutral and metrizable extension rules, based on a simpler formulation of acyclicity across orders. Furthermore, we establish the logical incompatibility between neutrality, metrizability and strictness. However, we show that these three conditions are pairwise logically compatible.

Date: 2020
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DOI: 10.1007/s00355-019-01235-0

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