Adapting Integer Programming Techniques to Circuit Restructuring

David Carlson

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For as long as the United States Courts of Appeals have been part of the federal judicial system, commentators, judges, and policymakers have disagreed over their geographic boundaries.  These disagreements are closely intertwined with discussions about the courts’ core characteristics, such as how many states they encompass, the workload of their judges, the number of judges on each court’s bench, and whether a circuit may contain only part of a state.  The debates exploded alongside the federal courts’ caseload in the twentieth century’s later half, when this “crisis of volume” prompted at least a dozen major studies and a rush of proposed solutions.

As commentators struggled with these issues, their analyses were typically either highly theoretical, limited to a geographically compact subset of the country, or both.  For example, one study examined several ideas for the systematic structural reform at a highly theoretical level,1 while the Commission on Structural Alternatives for the Federal Courts of Appeals discussed several specific proposals to reform the Ninth Circuit as well as theoretical proposals for structural reform of the federal appellate system as a whole.2  Simultaneously juggling every circuit’s boundaries is a daunting task.  Fortunately, constructing such examples using computerized optimization techniques, such as integer programming, is now possible.

In order to study proposed structural reforms of the federal Courts of Appeals by using integer programming, I used commercially available modeling software to write models of the federal appellate court system.  I wrote the model in AMPL 10.1, a programming language developed by Bell Laboratories for mathematical modeling.  I solved the models using AMPL’s implementation of ILOG’s CPLEX solver, a computer program for solving a variety of optimization problems.  I ran each model on a 2.40GHz desktop computer with 2 GB of RAM.  The baseline model applied the following “generally accepted” rules: 3

1)    Circuits in the continental United States must be geographically contiguous.

2)    No single state may be split between two or more courts of appeals.

3)    Regional courts of appeals must contain at least three states.

4)    Each court of appeals must have enough judges to ensure that adjusted case filings per three-judge panel do not exceed 500.

5)    Each court of appeals should seat between 7 and 17 judges.

6)    Where possible, states and districts should remain in their current courts of appeals.

When situations arose where complying with these rules was impossible, I broke rules, starting at the bottom of the list, until I found a solution.  After running this baseline model, I ran three alternative versions that allowed two-state circuits, splitting states between two circuits, or both.  In creating the models, I approximated caseload figures by using information in Judicial Business of the United States Courts, a compilation that the Administrative Office of the U.S. Courts publishes.  For the Note on which this Editorial is based, I used figures from the 12-month period ending September 30, 2008.  Adapting the models to use data from different periods would not be difficult—in many situations, it would be as simple as substituting an updated data table.

Several results were immediately apparent from my initial work.  Most significantly, California, New York, and Texas all generate enough cases that even if they were in circuits by themselves, those circuits still could not comply with both the caseload limit and judge maximum.  In addition, although Florida is not large enough to single-handedly break both rules, there is no way to construct a three-state contiguous circuit containing Florida that complies with both the caseload and judge restrictions.  In addition, six of the current circuit courts of appeals have larger caseloads than the caseload and judge limits which the traditional rules imposed can accommodate.


Regardless of what circuit court criteria one prefers, the models that this Editorial and the full Note on which it is based discuss were all successful in two key ways.  First, each illustrates a “perfect” circuit map based on the parameters given to it.  Second, by providing concrete examples, the models highlight issues and approaches not otherwise apparent.  Perhaps the most novel suggestion to arise from the models’ results is that of creating a new circuit in the South, primarily to relieve the current Eleventh Circuit of the necessity of addressing cases from both Georgia and Florida, both of which independently generate enough cases to dominate a circuit built according to the “generally accepted” rules. This is by no means the only interesting result to come from the models.

On the other hand, the most glaring problem in the models’ results is the lack of explicit standards stating when it is appropriate to switch a state from one circuit to another to reduce caseload pressures and when a circuit split is preferable to jointly reorganizing two or more circuits.  Clearly, such changes impose significant costs.  Similarly, the models do not explicitly consider the legal and administrative disruptions that would be inherent in any changes to the circuits’ boundaries.  However, these topics are beyond the scope the Editorial and the Note on which it is based, and the literature has not extensively discussed these topics.  Although the Commission on Structural Alternatives for the Federal Courts of Appeals briefly considered circuit realignment that would involve splitting the current Ninth and slightly altering the arrangement of the current Tenth Circuit, these ideas have not been developed further.4  Accordingly, no such explicit standard is included.

Ultimately, none of the models is perfect.  All would impose significant transition costs on the federal court system, and the models are simply not capable of considering those costs.  However, the models are nevertheless successful in demonstrating the practical effects of proposed changes to ideal circuit criteria, in highlighting potential theoretical and real-world issues with those proposed changes, and at helping identify new possibilities and problems.


David Carlson is a 2011 J.D. Candidate at Cornell Law School.

This Legal Workshop Editorial is based on Mr. Carlson’s Note: David Carlson, Note, Adapting Integer Programming Techniques to Circuit Restructuring, 96 CORNELL L. Rev. ___ (forthcoming 2010).

Copyright © 2010 Cornell Law Review.

  2. See Commission on Structural Alternatives for the Federal Courts of Appeals, Final Report (1998), at 33–57, 59–60 {hereinafter White Report}.
  3. See White Report, supra note 2; Commission on Revision of the Federal Court Appellate System, The Geographical Boundaries of the Several Judicial Circuits: Recommendations for Changes (Dec. 1973), reprinted in 62 F.R.D. 223, 229–30 (1974).
  4. See White Report, supra note 2, at 54–57. See generally Thomas E. Baker, A Generation Spent Studying the United States Courts of Appeals: A Chronology 34 U.C. Davis L. REV. 395 (2000) (summarizing several studies and proposals),

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