Redistricting reformulated: A maximum interaction/minimum separation objective

Alternative objective functions to the population centroid type commonly employed in computerized political districting algorithms are suggested and discussed. Districtings based on maximum overlap of individuals' "action spaces" or on minimum aggregate length of interpersonal separations better represent the spatio-political notion of "compactness" than do those based on centroid measures. The traditional analogy between the warehouse location problem and the optimal districting problem may thus be an inappropriate one. The proposed reformulated optimal districting problem with a spatial interaction or interpersonal separation objective may be formally stated as a quadratic integer program. The solution to the program is seen, however, to be only one of several possible "optimal" political partitionings. Regardless of the specific compactness measure chosen, separate "mean" and "modal" districtings may exist.