In this paper we give the first explicit enumeration of all maximal Condorcet domains on $n\leq 7$ alternatives. This has been accomplished by developing a new algorithm for constructing Condorcet domains, and an implementation of that algorithm which has been run on a supercomputer. We follow this up by the first survey of the properties of all maximal Condorcet domains up to degree 7, with respect to many properties studied in the social sciences and mathematical literature. We resolve several open questions posed by other authors, both by examples from our data and theorems. We give a new set of results on the symmetry properties of Condorcet domains which unify earlier works. Finally we discuss connections to other domain types such as non-dictatorial domains and generalisations of single-peaked domains. All our data is made freely available for other researches via a new website.

翻译：本文首次明确枚举了所有在$n\leq 7\)个备选方案上的极大Condorcet域。我们通过开发一种构造Condorcet域的新算法，并在超级计算机上运行该算法的实现而完成此项工作。随后，我们首次调查了阶数至多为7的所有极大Condorcet域在社会科学及数学文献中研究的众多性质方面的特性。我们通过数据中的实例和定理，解决了其他作者提出的若干开放性问题。我们提出了一组关于Condorcet域对称性的新结果，统一了早期的工作。最后，我们讨论了与其他域类型的联系，例如非独裁域及单峰域的推广。我们通过新网站将所有数据免费提供给其他研究者使用。