Fifield, Benjamin, Kosuke Imai, Jun Kawahara, and Christopher T. Kenny. (2020). ``The Essential Role of Empirical Validation in Legislative Redistricting Simulation.'' Statistics and Public Policy, Vol. 7, No. 1, pp 52-68.

As granular data about elections and voters become available, redistricting simulation methods are playing an increasingly important role when legislatures adopt redistricting plans and courts determine their legality. These simulation methods are designed to yield a representative sample of all redistricting plans that satisfy statutory guidelines and requirements such as contiguity, population parity, and compactness. A proposed redistricting plan can be considered gerrymandered if it constitutes an outlier relative to this sample according to partisan fairness metrics. Despite their growing use, an insufficient effort has been made to empirically validate the accuracy of the simulation methods. We apply a recently developed computational method that can efficiently enumerate all possible redistricting plans and yield an independent sample from this population. We show that this algorithm scales to a state with a couple of hundred geographical units. Finally, we empirically examine how existing simulation methods perform on realistic validation data sets.

Fifield, Benjamin, Michael Higgins, Kosuke Imai, and Alexander Tarr. (2020). ``Automated Redistricting Simulator Using Markov Chain Monte Carlo.'' Journal of Computational and Graphical Statistics, Vol. 29, No. 4, pp. 715-728.

McCartan, Cory, and Kosuke Imai. (2023). ``Sequential Monte Carlo for Sampling Balanced and Compact Redistricting Plans.'' Annals of Applied Statistics, Vol. 17, No. 4 (December), pp. 3300-3323.

Fifield, Benjamin, Christopher T. Kenny, Cory MaCartan, and Kosuke Imai. ``redist: Computational Algorithms for Redistricting Simulation.'' available through The Comprehensive R Archive Network and GitHub.