Summer research project 2023

• Advisors: Ewan Davies and Ryan Job
• Researchers: Hannah Kim and Hyojin Seo

Objectives

• Understand the legislative districting problem

• Learn the Markov chain Monte Carlo (MCMC) algorithmic paradigm

• Study MCMC algorithms for redistricting

• Demonstrate knowledge with a case study or mathematical invesitgation

• Present findings as a poster, consider submission to CURC

Study plan

1. Learn Markov chains starting with this resource by Daryl DeFord (Week 1-2)
2. Implement simple Markov chains and some analysis with sagemath (Weeks 1-2)
3. Play with the sagemath code that enumerates all partitions of a 4x4 grid into 4 connected parts
   • Modify it to use a different planar graph on 15-20 vertices instead of the 4x4 grid
   • Modify the partition size requirements
   • Generate some pretty pictures of partitioned graphs
4. Read the chapter “Random Walks” from Political Geometry and think about how we might implement the flip chain from Section 3.3 of that chapter.

Resources

• Daryl DeFord’s introduction to Markov chains and redistricting
• Some final projects from a Math of Political Districting class at Claremont McKenna College taught by Sarah Cannon:
  • Reia Li and Rina Nagashima: Prison Gerrymandering in Arizona and Hawaii
  • Jonny Wise: Considering Competetiveness: A Fresh Look at Political Redistricting
• An online textbook: Political Geometry, edited by Duchin and Walch
• The ReCom Markov chains for redistricting
• A recent paper introducing a modified version of ReCom known as RevReCom
• DeFord’s GerryChain guide
• DeFord’s list of open problems from Jan 2021