Daryl R. DeFord

Daryl R. DeFord

Assistant Professor of Statistics

Research

My main research interests fall into an area that is often referred to as quantiative or computational social science as I'm particularly interested in discrete and probabilistic problems that arise in the study of social data. My PhD work focused on models for dynamics on social networks, including economic networks, and I've continued to work in this area, as well as on theoretical questions in graph theory. Currently, much of my work is motivated by political redistricting and applications of computational sampling methods to both detecting gerrymandering and analyzing the policy impacts of redistricting rules. I also have related interests in the analysis of voting data and the properties of alternative election systems.

(Google Scholar) (arXiv) (MathSciNet)

Research Articles

Data Science of Redistricting and Elections

  1. The Marked Edge Walk: A Novel MCMC Algorithm for Sampling of Graph Partitions, with A. McWhorter, arXiv: 2510.17714, (2025).
  2. A Cycle Walk for Sampling Measures on Spanning Forests for Redistricting, with G. Herschlag and J. Mattingly, arXiv: 2509.08629, (2025).
  3. Free Elections in the Free State: Ensemble Analysis of Redistricting in New Hampshire, with A. McWhorter, arXiv: 2509.07328, (2025).
  4. Bounds and Bugs: The Limits of Symmetry Metrics to Detect Partisan Gerrymandering, with E. Veomett, Election Law Journal, (2025).
  5. Repetition effects in a Sequential Monte Carlo sampler, with S. Cannon and M. Duchin, arXiv: 2409.19017, (2024).
  6. Multi-Balanced Redistricting, with E. Kimsey and R. Zerr, Journal of Computational Social Science, (2023).
  7. Implementing partisan symmetry: Problems and paradoxes, with N. Dhamankar, M. Duchin, V. Gupta, M. McPike, G. Schoenbach, K. W. Sim, Political Analysis, 31 (3), 305-324, (2023).
  8. Partisan Dislocation: A Precinct-Level Measure of Representation and Gerrymandering, with N. Eubank and J. Rodden, Political Analysis, 30(3), 403-425, (2022).
  9. Empirical Sampling of Connected Graph Partitions for Redistricting with L. Najt and J. Solomon, Physical Review E, 104, 064130, (2021).
  10. ReCombination: A family of Markov chains for redistricting, with M. Duchin and J. Solomon, Harvard Data Science Review, 3(1), (2021).
  11. Colorado in Context: Congressional Redistricting and Competing Fairness Criteria in Colorado, with J. Clelland, H. Colgate, B. Malmskog, and F. Sancier-Barbosa, Journal of Computational Social Science, 5(1), 189-226, (2021).
  12. A Computational Approach to Measuring Vote Elasticity and Competitiveness, with M. Duchin and J. Solomon, Statistics and Public Policy, 7(1), 69-86, (2020).
  13. Mathematics of Nested Districts: The Case of Alaska, with S. Caldera, M. Duchin, S. Gutenkust, and C. Nix, Statistics and Public Policy, 7(1), 39-51, (2020).
  14. Complexity and Geometry of Sampling Connected Graph Partitions, with L. Najt and J. Solomon, arXiv:1908.08881, (2019).
  15. Redistricting Reform in Virginia: Districting Criteria in Context, with M. Duchin, Virginia Policy Review, 12(2), 120-146, (2019).

    16. Statistics, Optimization, and Computation

  16. Algorithmic Accountability in Small Data: Sample-Size-Induced Bias Within Classification Metrics, with J. Briscoe, G. Kepler, and A. Gebremedhin, AISTATS25, (2025).
  17. Does the first-serving team have a structural advantage in pickleball?, with S. Ethier, AMS Contemporary Mathematics Series, (to appear 2024).
  18. Maximum a Posteriori Inference of Random Dot Product Graphs via Conic Programming with D. Wu and D. Palmer, SIAM Journal on Optimization (SIOPT), (2022).
  19. Medial Axis Isoperimetric Profiles, with P. Zhang and J. Solomon, SGP'20 Computer Graphics Forum, 39(5), 1-13, (2020).
  20. Total Variation Isoperimetric Profiles, with H. Lavenant, Z. Schutzman, and J. Solomon, SIAM J. Appl. Algebra Geometry, 3(4), 585-613, (2019).
  21. Cyclic Groups with the same Hodge Series, with P. Doyle, Revista de la UMA, 59(2), 241-254, (2018).
  22. Random Walk Null Models for Time Series Data, with K. Moore, Entropy, 19(11):615, (2017).
  23. Fourier transforms on SL_2(Z/P^nZ) and related numerical experiments, with B. Breen, J. Linehan, and D. Rockmore, arxiv: 1710.02687, (2017).
  24. Empirical Analysis of Space-Filling Curves for Scientific Computing Applications, with A. Kalyanaraman, Proceedings of the 42nd International Conference of Parallel Processing, 170-179, (2013).

    25. Network Science and Combinatorial Graph Theory

  25. Ranking Trees Based on Global Centrality Measures, with A. Barghi, Discrete Applied Mathematics, 343, 231-257, (2024).
  26. Stirling Numbers of Uniform Trees and Related Computational Experiments, with A. Barghi, Algorithms, 16(5), (2023).
  27. On the Spectrum of Finite Rooted Homogeneous Trees, with D. Rockmore, Linear Algebra and Applications, 598, 165-185, (2020).
  28. Spectral Clustering Methods for Multiplex Networks, with S. Pauls, Physica A, 121949, (2019).
  29. A new framework for dynamical models on multiplex networks, with S. Pauls, Journal of Complex Networks, 6(3), 353-381, (2018).
  30. Multiplex Dynamics on the World Trade Web, Proc. 6th International Conference on Complex Networks and Applications, Studies in Computational Intelligence, Springer, 1111-1123, (2018).
  31. A Random Dot Product Model for Weighted Networks, with D. Rockmore, arXiv:1611.02530, (2016).
  32. Enumerating Tilings of Rectangles by Squares, Journal of Combinatorics, 6(3), 339-351, (2015).
  33. Pulsated Fibonacci Sequences, with K. Atanassov and A. Shannon, Fibonacci Quarterly (Conference Proceedings), 52(5), 22-27 (2014).
  34. Enumerating Distinct Chessboard Tilings , Fibonacci Quarterly (Conference Proceedings), 52(5), 102-116, (2014).
  35. Seating Rearrangements on Arbitrary Graphs, Involve, 7(6), 787-805, (2014).
  36. Counting Rearrangements on Generalized Wheel Graphs, Fibonacci Quarterly, 51(3), 259-273, (2013).

    37. Expository Redistricting Articles

  37. Redistricting Graphics , MAA Focus, 4(3), 35, (2024).
  38. Random Walks and the Universe of Districting Plans, with M. Duchin, Book Chapter in Political Geography, Birkhauser, (2022).
  39. Aftermath: The Ensemble Approach to Political Redistricting, with J. Clelland and M. Duchin, MAA Math Horizons, 27(3), 34-35, (2020).

Expert Reports for Redistricting Litigation

  1. Expert Report for Wisconsin (2024)
    • Analysis of the Wright Petitioners' state legislative maps in litigation before the Supreme Court of Wisconsin.
  2. Expert Report (and rebuttal report) for Pennsylvania (2022)
    • Analysis of proposed Congressional redistricting plans for Pennsylvania on behalf of Citizen Mathematicians and Scientists in litigation before the Commonwealth Court.
  3. Expert Report (and Rebuttal Report) for Wisconsin (2021 and 2022)
    • Analysis of proposed Congressional and State Legislative redistricting plans for Wisconsin on behalf of Citizen Mathematicians and Scientists in litigation before the Supreme Court of Wisconsin.
  4. Analysis of Prospective Districts in Colorado (2021)
    • Reports comparing Colorado's Staff maps for Legislative and Congressional districts to a large ensemble of randomly generated maps. Uses 2020 precinct data and election data from 2016-2020.

Technical Reports and Amicus Briefs

  1. Amicus Brief of Computational Redistricting Experts, with A. Becker and D. Gold, Merrill v. Milligan, United States Supreme Court, (2022).
  2. Applying GerryChain: A User's Guide for Redistricting Problems (2021)
    • Description of modeling methodology for applying the ensemble method using GerryChain to analyze political redistricting problems. This guide was created by a team of research fellows that I supervised through the 2021 UW Data Science for Social Good program.
  3. Comparison of Districting Plans for the Virginia House of Delegates, with M. Duchin and J. Solomon, MGGG Technical Report, (2019).
  4. Amicus Brief of Mathematicians, Law Professors, and Students, with M. Duchin and G. Charles et al., Rucho v. Common Cause, United States Supreme Court, (2019).
  5. Study of Reform Proposals for Chicago City Council, with M. Duchin et al., MGGG Technical Report, (2019).
  6. Introduction to Discrete MCMC for Redistricting (with Scrabble) (2019).
    • A friendly and interactive introduction to discrete MCMC methods, concluding with applications to political redistricting. Many of the motivating examples are explained with Scrabble tiles. Accompanying Sage-interact widgets embedded on a webpage here and also on GitHub.
  7. Building Ensembles of Graph Partitions (2019).
    • This is a guide to GerryChain that walks through the engineering challenges inherent in generating ensembles of districting plans. Contains numerous examples and code snippets. Frequently updated.
  8. Geospatial Data Preparation for GerryChain (2019)
    • Beginning to end description of the data preparation process for building an annotated dual graph for GerryChain.
  9. An Application of the Permanent-Determinant Method: Computing the Z-index of Arbitrary Trees, WSU Technical Report Series #2013-2, (2013).

Media Coverage

  1. Ask Dr. Universe: What is the hardest math equation in the world? (Melissa Mayer WSU Communications, 2025).
    • Brief interview about hard math problems in an educational series for children.
  2. New Faculty Members Bring Expertise Spanning Virology to Volcanoes (Larry Hertz Vassar Communications, 2025).
    • Brief introduction as a new faculty member at Vassar College.
  3. Due to the ‘Utah Paradox,’ there’s a flaw in the GOP’s partisan bias map test (Sean Higgins KUER, 2025).
    • Article containing some quotes from me about Utah's SB1011 and the concept of the Utah Paradox introduced in this paper.
  4. DeFord receives University of Chicago Outstanding Educator Award (WSU CAS Staff, 2024).
    • Announcement and brief interview about a teaching award.
  5. Using statistics to help predict upsets in the NCAA Tournament (B. Jones, KREM, 2024).
    • Short video segment commenting on statistical models for predicting NCAA tournament winners and why upsets by lower seeded teams seem relatively common.
  6. Taking the First Serve (F. Cerabino, The Pickler, 2023).
    • Discussion and commentary on my preprint with Professor Stewart Ethier about first-server advantages in pickleball.
  7. How Math Has Changed the Shape of Gerrymandering (M. Orcutt, Quanta, 2023)
    • Article about mathematical advances for studying political redistricting that discusses my work on ReCom in Virginia and Colorado. Interesting followup blog post by Dr. Dan Nexon with lots of comments here.
  8. Redistricting tools and gerrymandering (S. Whitlock, AAAS SciLine, 2022)
  9. New districts for 2022 midterms, in part thanks to math (A. Zimmerman, KOAA News, 2022)
    • Brief article and video interview with one of my collaborators Beth Malmskog about our work in Colorado.
  10. Pennsylvania Supreme Court relies on Daryl DeFord's Research (T. Wagoner, WSU, 2022)
    • Brief article highlighting the PA Supreme Court's reliance on my analysis in their opinions selecting a Congressional map in 2022.
  11. Redistricting process was independent and fair (C. Perez, The Gazette, 2022)
    • Guest opinion piece referencing our contributions to Colorado's redistricting process.
  12. Can Math Make Redistricting More Fair? (D. Strain, CU Boulder Today, 2021)
  13. Data Science for Social Good Team Builds Tools to Support Fairness in Computational Redistricting (E. Keller, UW ESciences Institute, 2021)
    • Blog post from the UW EScience Institute about the Vote Redistricting summer program that was a part of the 2021 Data Science for Social Good. I was the faculty lead for this project.
  14. Open source tool can help identify gerrymandering in voting maps (S. Zaske, WSU News, 2021)
  15. People Who Can't Vote Still Count Politically in America. What if That Changes? (E. Badger, NYT Upshot, 2019)
    • Article on representation that discusses my unpublished analysis of potential impacts of CVAP-based population balancing.
  16. The Supreme Court's Math Problem (J. Ellenberg, Slate, 2019)
    • Article about the oral argument in Rucho v. Common Cause that discusses the `mathematician's brief' for which I did the computational work.
  17. Hannah Croasdale Award (A. Skinner, Dartmouth Graduate News, 2018)
    • This article from the Dartmouth graduate school describes the research experiences that led to me winning the Hannah Croasdale Award, in 2018. This is a college-wide award awarded annually to the graduating PhD recipient who best exemplifies the qualities of a scholar.
  18. Graduate Teaching Award (A. Skinner, Dartmouth Graduate News, 2017)
    • This article from Dartmouth focuses on my teaching experiences as a graduate student, for which I was awarded the 2017 Dartmouth Graduate Teaching Award, which is a college-wide recognition for exemplifying the qualities of a college educator.