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Condorcet domains, median graphs and the single-crossing property

Puppe, Clemens; Slinko, Arkadii


Condorcet domains are sets of linear orders with the property that, whenever the preferences of all voters of a society belong to this set, their majority relation has no cycles. We observe that, without loss of generality, every such domain can be assumed to be closed in the sense that it contains the majority relation of every profile with an odd number of voters whose preferences belong to this domain. We show that every closed Condorcet domain can be endowed with the structure of a median graph and that, conversely, every median graph is associated with a closed Condorcet domain (in general, not uniquely). Condorcet domains that have linear graphs (chains) associated with them are exactly the preference domains with the classical single-crossing property. As a corollary, we obtain that a domain with the so-called `representative voter property' is either a single-crossing domain or a very special domain containing exactly four different preference orders whose associated median graph is a 4-cycle. Maximality of a Condorcet domain imposes additional restrictions on the associated median graph. We prove that among all trees only (some) chains can be associated graphs of maximal Condorcet domains, and we characterize those single-crossing domains which are maximal Condorcet domains. ... mehr

Volltext §
DOI: 10.5445/IR/1000061997
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Volkswirtschaftslehre (ECON)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2016
Sprache Englisch
Identifikator ISSN: 2190-9806
KITopen-ID: 1000061997
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 32 S.
Serie Working paper series in economics ; 92
Schlagwörter Social choice, Condorcet domains, acyclic sets of linear orders, median graphs, single-crossing property, distributive lattice, Arrovian aggregation, strategy-proofness, intermediate preferences
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