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Symmetric Maximal Condorcet Domains

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Abstract

We introduce the operation of composition of domains and show that it reduces the classification of symmetric maximal Condorcet domains to the indecomposable ones. The only non-trivial indecomposable symmetric maximal domains known are the domains consisting of four linear orders examples of which were given by Raynaud (1981) and Danilov and Koshevoy (Order 30(1), 181–194 2013). We call them Raynaud domains and we classify them in terms of simple permutations, a well-researched combinatorial object. We hypothesise that no other indecomposable symmetric maximal domains exist.

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Acknowledgements

We are grateful to the Associate Editor and the referees for a very thorough reading of the paper. Alexander Karpov gratefully acknowledges the support by the Basic Research Program of the National Research University Higher School of Economics. Arkadii Slinko was supported by the Faculty Development Research Fund 3719899 of the University of Auckland.

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Karpov, A., Slinko, A. Symmetric Maximal Condorcet Domains. Order 40, 289–309 (2023). https://doi.org/10.1007/s11083-022-09612-8

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