A family of condorcet domains that are single-peaked on a circle

Arkadii Slinko ()
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Arkadii Slinko: The University of Auckland

Social Choice and Welfare, 2024, vol. 63, issue 1, No 3, 57-67

Abstract: Abstract Fishburn’s alternating scheme domains occupy a special place in the theory of Condorcet domains. Karpov (2023) generalised these domains and made an interesting observation proving that all of them are single-peaked on a circle. However, an important point that all generalised Fishburn domains are maximal Condorcet domain remained unproved. We fill this gap and suggest a new combinatorial interpretation of generalised Fishburn’s domains which provide a constructive proof of single-peakedness of these domains on a circle. We show that classical single-peaked domains and single-dipped domains as well as Fishburn’s alternating scheme domains belong to this family of domains while single-crossing domains do not.

Date: 2024
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DOI: 10.1007/s00355-024-01520-7

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