Redistricting to Maximize the Preservation of Political Boundaries

Redefining legislative districts is a task undertaken by the states after each census in order to ensure equitable representation. Many criteria have been proposed as objectives in forming districts but specific definitions of an optimal plan have not been enforced. In attempting to eliminate political concerns from the effort, the Michigan Supreme Court defined criteria based on the preservation of county and municipality borders. A quadratic programming formulation is given for this problem, and a heuristic solution procedure is proposed. In Reynolds v. Sims (377 U.S. 533, 583 (1964)), the U.S. Supreme Court ruled that the states should define the boundaries of legislative districts according to decennial census data in order not to violate the “one person, one vote ” rule. The state legislatures undertake this re-districting activity and generally develop politically partisan plans. Avoiding political considerations becomes very difficult because many objectives may be used to justify alternative plans. The following criteria are usually considered in evaluating redistricting plans: (1) population equality: the districts are selected so as not to deviate beyond some limit from a mean population; (2) compactness: the districts have regular shapes, being nearly square or nearly circular; (3) contiguity: the districts are constructed so that one may travel between any two points in a district without leaving the district; (4) political boundary integrity: the districts should preserve political boundaries as much as possible. Contiguity and some standard of population equality are given the heaviest weight in redistricting plans. Possible dilution of minority voting strength is also considered and can be challenged in court as unconstitutional or under the Voting Rights Act even when equipopulous districts have bee