Maximal Condorcet domains. A further progress report

Condorcet domains are sets of preference orders such that the majority relation corresponding to any profile of preferences from the domain is acyclic. The best known examples in economics are the single-peaked, the single-crossing, and the group separable domains. We survey the latest developments in the area since Monjardet's magisterial overview (2009), provide some new results and offer two conjectures concerning unsolved problems. The main goal of the presentation is to illuminate the rich internal structure of the class of maximal Condorcet domains. In an appendix, we present the complete classification of all maximal Condorcet domains on four alternatives obtained by Dittrich (2018).