A Strict-Contiguity Criterion for Preventing County Splits in Redistricting

The splitting of political subdivisions (in particular, counties) is a contentious aspect of the redistricting process. Though sometimes necessary, county-splitting districts are generally thought to be undesirable, and are typically prohibited by legislation unless required, e.g., to achieve equality of district populations. Some county-splitting districts are clear examples of gerrymandering, taking awkward non-compact shapes and stretching across several counties. However, even reasonably compact districts can exhibit county splits, and we provide five examples of reasonably compact districts exhibiting county splits. Thus there is a need for a criterion, unrelated to compactness, for evaluating whether a county-splitting district should be allowed. To disallow splits, we introduce a strict contiguity constraint specifying that a county can be used on a path between two precincts in a district only if the fraction of the county population assigned to the district exceeds a user-specified parameter $\rho \in (0,1]$. We provide a mathematical formulation of redistricting with strict contiguity and illustrate its numerical solution. Our definition of strict continuity is not limited to county splits; it can apply to any grouping of geographical units, or in a redistricting setting other than within the U.S.