Speaker: Arkadii Slinko (Department of Mathematics, UOA)
Title of presentation: “Generalisation of the Danilov-Karzanov-Koshevoy construction for Peak-Pit Condorcet domains”
Date, Time and Venue: Wednesday, 4 March 2020, 14:30-15:30, 260-5115 [Business School Building, Level 5]
Abstract: Danilov, Karzanov and Koshevoy (2012) geometrically introduced an interesting operation of composition on Condorcet domains and using it they disproved a long-standing problem of Fishburn about the maximal size of connected Condorcet domains. We give an algebraic definition of this operation and investigate its properties. We give a precise formula for the cardinality of composition of two Condorcet domains and improve the Danilov, Karzanov and Koshevoy result showing that Fishburn’s alternating scheme does not always produce a largest connected Condorcet domain.