An axiomatic characterization of the Borda mean rule

• Published in: Social choice and welfare Vol. 52; no. 4; pp. 685 - 707
• Main Authors: Brandl, Florian, Peters, Dominik
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer 01-04-2019; Springer Berlin Heidelberg; Springer Nature B.V
• Subjects: Alternatives; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Economics and Finance; Function; Game Theory; International Political Economy; Neutrality; Original Paper; Preferences; Property; Public Finance; Reinforcement; Social and Behav. Sciences; Social Policy; Symmetry
• ISSN: 0176-1714; 1432-217X
• DOI: 10.1007/s00355-018-1167-8

A social dichotomy function maps a collection of weak orders to a set of dichotomous weak orders. Every dichotomous weak order partitions the set of alternatives into approved alternatives and disapproved alternatives. The Borda mean rule returns all dichotomous weak orders that approve all alternatives with above-average Borda score and disapprove alternatives with below-average Borda score. We show that the Borda mean rule is the unique social dichotomy function satisfying neutrality, reinforcement, faithfulness, and the quasi-Condorcet property. Our result holds for all domains of weak orders that are sufficiently rich, including the domain of all linear orders and the domain of all weak orders.