Kyle Lee
DIMACS REU 2025 - Classical, Computational, and AI-Powered Social Choice
About Me
Welcome to my website! My name is Kyle Lee, and I am studying Social Choice Theory this summer with Professor Lirong Xia. My mathematical interests include Algebraic Number Theory, Enumerative Combinatorics, and Geometric Group Theory, and I am also interested in the intersection of these fields (and mathematics in general) with applicatory fields such as Computer Science and Economics. This is what makes Social Choice Theory fascinating to me: it is a rigorous and mathematically fulfilling field that has important direct application.
My other interests include literature, space photography, and card magic. I also love to play video games in my free time (my favorites are Disco Elysium and Hollow Knight). I am (as my fellow REU-mates might know) also a board games enthusiast!
As for some background, I am a NJ native that currently attends the University of Michigan pursuing a degree in Mathematics. You can reach me at leekylej@umich.edu and my office for the summer is located in the CoRE Building, Room 440.
Project Overview
We aim to take a multidiciplinary approach in studying Social Choice Theory... TBA
- TBA TBA
Progress Log
Week 1
I spent much of my time in week 1 getting situated and reading through the Handbook of Computational Social Choice: Chapters 1 and 2. After reading Most Equitable Voting Rules, a paper written by my mentor, Dr. Xia, I think I'm getting somewhat enamored by the inherent group symmetries of some of these Social Choice conditions: for example, it is fascinating that anonymity and neutrality can be expressed through invariance and covariance with respect to permutation over the agents or alternatives. I'm still trying to figure out what my project should ultimately be about, but this seems like a good start!
Week 2
I started this week by doing a good bit of reading to decide which specific project I was interested in. After speaking to Dr. Farhad Mohsin and briefly considering a machine learning–oriented project, I decided that this was not what I was particularly interested in. The same went for a more probabilistic project, although I found the results of the papers I scanned very interesting. Thus, it seems as if the best project for me is to attempt to expand the work of Professor Xia's group theoretic characterization of ANR Impossibility—perhaps by way of introducing and characterizing some notion of Pareto Efficiency, and focusing on the case in which the preference space and decision space mirror some notion of ranked choice voting. I concentrated my energy into understanding Theorem 1 of Professor Xia's paper comprehensively. This turned out to be a bit of a difficult task, as some definitions in the paper were quite challenging to parse.
Resources & Links
- Xia, L. (2023). Most Equitable Voting Rules. arXiv:2205.14838 [cs.GT]
- Xia, L. (2021). How Likely Are Large Elections Tied?. arXiv:2011.03791 [cs.GT]
- Mohsin, F., Kang, I., Chen, P.-Y., Rossi, F., & Xia, L. (2021). Group Decision Dynamics in NLP and Social Choice. NLP+CSS Workshop at EMNLP.
- Kang, I., Mohsin, F., Chen, P.-Y., Rossi, F., & Xia, L. (2022). Learning Individual and Collective Priorities over Moral Dilemmas with the Life Jacket Dataset. MPREF Workshop at AAMAS.
- Moulin, H. (1983). The Strategy of Social Choice. North-Holland.
- Brandt, F., Conitzer, V., Endriss, U., Lang, J., & Procaccia, A. D. (Eds.). (2016). Handbook of Computational Social Choice. Cambridge University Press.
Random Math Joke
Math jokes/brainrot