Several of the classical results in social choice theory demonstrate that in order for many voting systems to be well-behaved the set domain of individual preferences must satisfy some kind of restriction, such as being single-peaked on a political axis. As a consequence it becomes interesting to measure how diverse the preferences in a well-behaved domain can be. In this paper we introduce an egalitarian approach to measuring preference diversity, focusing on the abundance of distinct suborders one subsets of the alternative. We provide a common generalisation of the frequently used concepts of ampleness and copiousness. We give a detailed investigation of the abundance for Condorcet domains. Our theorems imply a ceiling for the local diversity in domains on large sets of alternatives, which show that in this measure Black's single-peaked domain is in fact optimal. We also demonstrate that for some numbers of alternatives, there are Condorcet domains which have largest local diversity without having maximum order.

翻译：社会选择理论中的若干经典结果表明，为了使多数投票系统具有良好的性质，个体偏好的定义域必须满足某种约束，例如在政治轴线上呈现单峰性。因此，衡量良态域中偏好的多样性程度便具有研究价值。本文引入了一种衡量偏好多样性的平等主义方法，重点关注备选方案子集上不同子序的丰富程度。我们给出了"充裕性"与"丰饶性"这两个常用概念的通用推广形式，并对Condorcet域的丰富程度进行了详细考察。我们的定理揭示了大型备选集上域局部多样性的上限，表明在此度量下Black单峰域实际上是最优的。我们还证明了在某些备选方案数量下，存在达到最大局部多样性但未达到最大序数的Condorcet域。