cp's OEIS Frontend

A369614 Maximal size of Condorcet domain on n alternatives.

%I A369614 #11 Mar 04 2024 13:37:34
%S A369614 1,1,2,4,9,20,45,100,224
%N A369614 Maximal size of Condorcet domain on n alternatives.
%C A369614 A Condorcet domain is a set D of permutations of [n] such that for any i, j, k from [n] there do not exist three permutations in D in which i, j, k are ordered in all three different cyclic permutations of the order (i, j, k). If these permutations are interpreted as voters' preferences, this condition prevents the Condorcet effect.
%C A369614 Condorcet domains are also known as acyclic domains, acyclic sets of linear orders, consistent profiles, or consistent sets.
%H A369614 Dolica Akello-Egwell, Charles Leedham-Green, Alastair Litterick, Klas Markström and Søren Riis, <a href="https://arxiv.org/abs/2306.15993">Condorcet Domains of Degree at most Seven</a>, arXiv:2306.15993 [cs.DM], 2023. See the <a href="http://abel.math.umu.se/~klasm/Data/CONDORCET/">website</a> presenting all maximal unitary Condorcet domains on 4, 5, 6, 7 alternatives.
%H A369614 Clemens Puppe and Arkadii Slinko, <a href="https://econpapers.wiwi.kit.edu/downloads/KITe_WP_159.pdf">Maximal Condorcet domains: A further progress report</a>, KIT Working Paper Series in Economics, 159 (2022).
%H A369614 Charles Leedham-Green, Klas Markström and Søren Riis, <a href="https://doi.org/10.1007/s00355-023-01481-3">The largest Condorcet domain on 8 alternatives</a>, Soc. Choice Welf., 62 (2024), 109-116.
%H A369614 Bernard Monjardet, <a href="https://doi.org/10.1007/978-3-540-79128-7_8">Acyclic domains of linear orders: a survey</a>, in "The Mathematics of Preference, Choice and Order: Essays in Honor of Peter Fishburn", edited by Steven Brams, William V. Gehrlein and Fred S. Roberts, Springer, 2009, pp. 139-160; preprint: <a href="https://shs.hal.science/halshs-00198635">halshs-00198635</a>.
%H A369614 Wikipedia, <a href="https://en.wikipedia.org/wiki/Condorcet_paradox">Condorcet paradox</a>.
%e A369614 For n <= 2, the set of all n! permutations is a Condorcet domain.
%e A369614 For n = 3, an example of a Condorcet domain of maximal size is the following set of permutations:
%e A369614   123
%e A369614   213
%e A369614   231
%e A369614   321
%e A369614 For n = 4, an example of a Condorcet domain of maximal size is:
%e A369614   1234
%e A369614   1324
%e A369614   1342
%e A369614   3124
%e A369614   3142
%e A369614   3412
%e A369614   3421
%e A369614   4312
%e A369614   4321
%Y A369614 Cf. A144685 (size of Fishburn's alternating domain), A144686 (maximal size of Condorcet domain containing a maximal chain), A144687, A289684.
%K A369614 nonn,hard,more
%O A369614 0,3
%A A369614 _Andrey Zabolotskiy_, Jan 27 2024