Title : Condorcet Domains and Median Graphs
Speaker: Arkadii Slinko
Affiliation: The University of Auckland
Time: 4:00 pm Monday, 21 March, 2016
Location: Clock Tower 032
Condorcet domains are sets of linear orders with the property that, whenever the preferences of all voters belong to this set, the majority relation has no cycles. We observe that, without loss of generality, 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 individuals whose preferences belong to this domain. We show that every closed Condorcet domain is naturally endowed with the structure of a median graph and that, conversely, every median graph is associated with a closed Condorcet domain (which may not be a unique one). Maximality of a Condorcet domain imposes additional restrictions on the underlying median graph. We prove that among all trees only the chains can induced by maximal Condorcet domains, and we characterise the chains that in fact do correspond to maximal Condorcet domains.

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