The clustering relation for minority voter populations

Let a voter distribution have a minority voter population, let $\mathsf{ClusP}$ denote its clustering measure, and let $\mathbb{E}(\mathsf{Rep}_\Delta)$ denote the expected representation of that minority population, averaged over districting plans. Clustering relation. For minority voter populations, there is a positive correlation between a measure of clustering and their expected representation. The paper motivates this relation through exhaustive computations on $5\times 5$ grids and proposes its extension to the general case using dual graphs; whether the relation holds in that generality remains open.