Modeling Region Affiliation with Fuzzy Membership Based on Spatial and Social Interactions

A key challenge in regionalization is that regions, such as urban function zones or climate zones, often have indeterminate boundaries, making it difficult to exactly quantify their geographic extent. Political redistricting, as a regionalization task, deals with this problem acutely, as requirements to preserve communities of interest (COIs) do not define such communities, introducing inherent vagueness in their boundaries. To address this issue, this work introduces a network approach that models COIs by integrating spatial-social interactions and evaluates district assignment by quantifying the degree to which a geographic area is connected to all other areas within each district. Furthermore, we draw on a splatial framework to understand the different spaces in which modern human communities interact, allowing us to more comprehensively model the community interactions that constitute COIs by using both spatial and social interactions, as measured with human mobility flows and social network connections. By comparing how district membership aligns across these two interaction types with the fuzzy membership methodology, it can reveal distinct spatial patterns, while combining them can reduce ambiguity in region membership. To demonstrate its utility, the proposed methodology is applied to a 2020 congressional district plan for the State of Wisconsin. Beyond redistricting, this work also contributes to the geography literature by providing a spatial interaction-based framework for quantifying regional affiliations in boundary areas.