Symmetric Maximal Condorcet Domains

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.