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The fundamental basis for territorial political representation is the presumption that people share greater common interests with others in closer geographic proximity than with people farther away. This principle is found in U.S. legal requirements that districts for the House of Representatives and state legislatures should not needlessly divide "communities of interest" and should be "reasonably compact." We propose a new objective standard to evaluate spatial fairness of redistricting plans: the extent to which a delineation minimizes total distance between all pairs of people assigned to the same district. To date, the legal standard of compactness has primarily been thought of in terms of the shapes of political districts, but boundary shape may have little correspondence with how populations are actually clustered and dispersed. Inter‐person separation, by contrast, provides a direct, intuitive metric for evaluating the congruence of districting plans with the territorial basis of political representation. To operationalize an inter‐person separation standard, we propose a model and present a heuristic method for delineating comparator districting schemes. We apply the standard to the current U.S. Congressional Districts in the states of Arizona and North Carolina to demonstrate how inter‐person separation could be used to develop and vet future redistricting plans. [ABSTRACT FROM AUTHOR]

Analysis results are often found to vary with the way we abstract geographical space. When continuous geographic phenomena are abstracted, processed, and stored in a digital environment, some level of discretization is often employed. Information loss in a discretization process brings about uncertainty/error, and as a result research findings may be highly dependent on the particular discretization method used. This article examines one spatial problem concerning how to achieve the maximal regional coverage given a limited number of service facilities. Two widely used geographical space abstraction approaches are examined, the point-based representation and the area-based representation, and issues associated with each representation scheme are analyzed. To accommodate the limitations of the existing representation schemes, a mixed representation strategy is proposed along with a new maximal covering model. Experiments are conducted to site warning sirens in Dublin, Ohio. Results demonstrate the effectiveness of the mixed representation scheme in finding high-quality solutions when the regional coverage level is medium or high. [ABSTRACT FROM AUTHOR]

This article introduces measures to quantify spatial autocorrelation for vectors. In contrast to scalar variables, spatial autocorrelation for vectors involves an assessment of both direction and magnitude in space. Extending conventional approaches, measures of global and local spatial associations for vectors are proposed, and the associated statistical properties and significance testing are discussed. The new measures are applied to study the spatial association of taxi movements in the city of Shanghai. Complications due to the edge effect are also examined. [ABSTRACT FROM AUTHOR]