Condorcet domains satisfying Arrow's single-peakedness

摘要

Condorcet domains are sets of linear orders with the property that, whenever the preferences of all voters belong to this set, the majority relation of any profile with an odd number of voters is transitive. Maximal Condorcet domains historically have attracted a special attention. We study maximal Condorcet domains that satisfy Arrow's single-peakedness which is more general than Black's single-peakedness. We show that all maximal Black's single-peaked domains on the set of m alternatives are isomorphic but we found a rich variety of maximal Arrow's single-peaked domains. We discover their recursive structure, prove that all of them have cardinality 2(m-1), and characterise them by two conditions: connectedness and minimal richness. We also classify Arrow's single-peaked Condorcet domains for m <= 5 alternatives. (C) 2019 Elsevier B.V. All rights reserved.