We consider the notions of agreement, diversity, and polarization in ordinal elections (that is, in elections where voters rank the candidates). While (computational) social choice offers good measures of agreement between the voters, such measures for the other two notions are lacking. We attempt to rectify this issue by designing appropriate measures, providing means of their (approximate) computation, and arguing that they, indeed, capture diversity and polarization well. In particular, we present "maps of preference orders" that highlight relations between the votes in a given election and which help in making arguments about their nature.

翻译：我们考虑序数选举（即选民对候选人进行排序的选举）中的一致性、多样性和极化概念。尽管（计算）社会选择理论为选民之间的一致性提供了良好的度量方法，但针对其他两个概念的度量方法尚显不足。我们试图通过设计适当的度量标准、提供其（近似）计算方法，并论证这些标准确实能够有效捕捉多样性与极化特征，来弥补这一缺陷。具体而言，我们提出了“偏好序地图”，用以突出特定选举中选票之间的关系，并辅助论证其自然属性。