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：本文首次显式枚举了所有在$n\leq 7$个备选方案上的极大Condorcet域。为此，我们开发了一种构建Condorcet域的新算法，并在超级计算机上实现了该算法。在此基础上，我们首次系统考察了所有阶数不超过7的极大Condorcet域的性质，涵盖社会科学与数学文献中研究的多种属性。通过数据实例与定理证明，我们解决了其他学者提出的若干开放问题。针对Condorcet域的对称性质，我们给出了一组新结果，统一了既有研究。最后，我们讨论了与其他域类型（如非独裁域及单峰域的推广）的联系。所有数据均通过新建网站向研究人员免费开放。