A composition of Condorcet domains
Dominic Keehan, Arkadii Slinko
TL;DR
This paper investigates the structure of maximal Condorcet domains, revealing that many are formed through a specific composition of smaller domains, and provides conditions for such compositions to be maximal.
Contribution
It introduces a new composition method for Condorcet domains and establishes sufficient conditions for their maximality, advancing understanding of their structure.
Findings
9 out of 18 maximal domains are composed from smaller domains
Conditions identified for the composition to result in a maximal Condorcet domain
Provides a framework for constructing larger maximal domains from smaller ones
Abstract
Inspecting known maximal Condorcet domains on 4 variables classified by Tobias Dittrich we find that 9 out of 18 of them are created using a certain composition of smaller domains. In this paper we describe this composition. We give sufficient conditions for the composition of two Condorcet domain to be a maximal Condorcet domain.
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