Date of Award
2026
Degree Type
Dissertation
Degree Name
Doctor of Philosophy in Computer Science
Department
Computer Science and Statistics
First Advisor
Edmund A. Lamagna
Abstract
Gerrymandering undermines democratic representation by manipulating electoral district boundaries to dilute the political influence of targeted communities. While Markov Chain Monte Carlo (MCMC) based redistricting algorithms have become a standard computational tool for detecting partisan gerrymandering, their effectiveness in addressing racial gerrymandering and their scalability on modern computing systems remain limited. This dissertation advances the theory and practice of algorithmic redistricting by optimizing MCMC-based approaches across three dimensions: racial fairness, computational efficiency, and interpretability.
First, this work introduces the Partial Map MCMC algorithm, a novel redistricting method designed specifically to address racial gerrymandering under the legal framework of Section 2 of the Voting Rights Act. Unlike standard MCMC approaches that perturb an entire districting plan, Partial Map MCMC restricts stochastic updates to carefully selected subsets of districts with high minority population density while holding the remainder of the map fixed. Extensive simulations on Alabama’s congressional districts, motivated by the 2023 United States Supreme Court decision in Allen v. Milligan, demonstrate that the proposed method dramatically increases the likelihood of generating legally compliant majority-minority districts. The algorithm produces two Black-majority districts in the vast majority of sampled plans, substantially outperforming conventional MCMC redistricting methods, while maintaining acceptable compactness, improved convergence behavior, and competitive partisan balance.
Second, the dissertation presents a systematic evaluation of parallel MCMC strategies for redistricting, including embarrassingly parallel MCMC, multi-proposal MCMC, and multi-jump multi-proposal MCMC. Using real redistricting datasets and high-performance computing environments, these approaches are compared against sequential MCMC in terms of runtime performance, CPU utilization, memory usage, convergence diagnostics, and effective sample size. The results show that chain-level parallelism provides the most reliable and scalable performance improvements in highly constrained redistricting state spaces, whereas proposal-level parallelism exhibits diminishing returns.
Finally, this work explores the application of MCMC redistricting algorithms in educational and game-based settings by modeling board-game districting environments as graph-partitioning problems. These experiments illustrate how MCMC ensembles can be used to analyze strategic bias, district stability, and outcome distributions, bridging recreational games, computational redistricting, and civic education.
Collectively, this dissertation contributes new algorithmic techniques, empirical insights, and computational frameworks that improve the fairness, efficiency, and transparency of MCMC-based redistricting. The results support the use of targeted and parallel sampling methods as effective tools for evaluating and mitigating gerrymandering in both legal and educational contexts.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Recommended Citation
Kekulandara, Madhukara, "OPTIMIZING MARKOV CHAIN MONTE CARLO ALGORITHMS FOR FAIRNESS, SCALABILITY, AND INTERPRETABILITY IN ELECTORAL REDISTRICTING" (2026). Open Access Dissertations. Paper 4570.
https://digitalcommons.uri.edu/oa_diss/4570