An index is a function that given an election outputs a value between 0 and 1, indicating the extent to which this election has a particular feature. We seek indices that capture agreement, diversity, and polarization among voters in approval elections, and that are normalized with respect to saturation. By the latter we mean that if two elections differ by the fraction of candidates approved by an average voter, but otherwise are of similar nature, then they should have similar index values. We propose several indices, analyze their properties, and use them to (a) derive a new map of approval elections, and (b) show similarities and differences between various real-life elections from Pabulib, Preflib and other sources.

翻译：指数是一种函数，对于给定的选举输出一个介于0到1之间的值，表示该选举具有某一特定特征的程度。我们寻求能够捕捉批准选举中选民之间一致性、多样性和极化程度的指数，并使其相对于饱和状态进行归一化。所谓饱和归一化，是指如果两个选举仅在平均选民批准的候选人比例上存在差异，但其他本质特征相似，那么它们应具有相近的指数值。我们提出了若干指数，分析了它们的性质，并利用这些指数（a）推导出批准选举的新映射图，以及（b）展示来自Pabulib、Preflib及其他来源的各种现实选举之间的异同。