Mathematical Models in the Social Sciences (SP26)

Welcome to the course webpage for Math 36, I look forward to a great semester! This will be our primary source for information about the schedule, assignments, and announcements. 

General Information

Textbook

We will primarily use two textbooks: 
- A Primer in Social Choice Theory (Revised Edition) by Wulf Gaertner. Available as an ebook from the Dartmouth library. 

- Political Geography edited by Moon Duchin and Olivia Walch. Available online from the Data and Democracy Lab.

Scheduled Lectures

We will meet on MWF from 2:10 to 3:15. I do not plan on using the X-hour. Our classroom is Haldeman 028 (located in the basement of Kemeny Hall). 

Instructor

Atticus McWhorter 
Office: 239 Kemeny Hall
Office Hours: MW 4-5, Th 12:30-1:30
Contact via email

Homework

There will be assignments announced in class, which will be submitted on Canvas. The assignments will be graded on completion, and are meant to serve as a litmus test for the difficulty of the Midterm problems. 

Midterm

There will be an in-class midterm exam on Friday, May 1. If you have a conflict with the midterm because of a religious observance (Star Wars day does not count), scheduled extracurricular activity, or similar commitment, please email Atticus as soon as possible. On the midterm exam, you may not give or receive help from anyone. The exam is closed book, no notes. All electronic devices must be left outside the classroom during the exam.  

Final Project

The final project is due June 5.

Grades

The course grade will be based upon attendance, scores on the midterm exam, and the final project as follows: 

  • Attendance: 20 points
  • Midterm Exam: 30 points
  • Final Project: 50 points

Academic Equity

Students who are eligible for classroom accommodations are encouraged to make an appointment to discuss with Atticus as soon as possible. Also, stop by the Academic Skills Center in Collis to register for support services. 

Tentative Schedule

Note: Future topics listed here are tentative and will likely move around as time permits.

  • Week 1: Introduction to Voting Systems
    • Monday 3/30: Course introduction, social choice motivation
    • Wednesday 4/1: Introduction to the axiomatic method: Monotonicity and Pareto Optimality
    • Friday 4/3: Formalization: Preferences 
  • Week 2: The Axiomatic Method
    • Monday 4/6: Formalization continued: Maximal sets and Choice Functions
    • Wednesday 4/8: Arrovian Welfare Axioms
    • Friday 4/10: Arrow's Impossibility Theorem
  • Week 3: Arrow Continued
    • Monday 4/13: An alternative proof
    • Wednesday 4/15: The majority rule
    • Friday 4/17: Single Peaked Preferences
  • Week 4: Strategic Voting
    • Monday 4/20: Other domain restrictions and introduction to strategic voting
    • Wednesday 4/22: The Gibbard-Satterthwaite Theorem
    • Friday 4/24: Strategy Proofness on Restricted Domains
  • Week 5: Strategic Voting
    • Monday 4/27: Condorcet winners and the median voter theorem
    • Wednesday 4/29: Midterm Review
    • Friday 5/1: MIDTERM EXAM
  • Week 6: Introduction to Redistricting
    • Monday 5/4: What makes a "good" district map
    • Wednesday 5/6: Legal and mathematical constraints, compactness measures
    • Friday 5/8: Efficiency gap and partisan symmetry
  • Week 7: Measuring Gerrymandering
    • Monday 5/11: The seats-votes curve
    • Wednesday 5/13: Motivating ensemble methods
    • Friday 5/15: Markov chains basics
  • Week 8: MCMC
    • Irreducibility and mixing
    • Random walks on redistricting plans
    • Generating ensembles of redistricting plans, outlier analysis
  • Week 9: MCMC for Redistricting
    • Monday 5/25: MEMORIAL DAY - NO CLASS
    • Wednesday 5/27:  Algorithm comparison and design
    • Friday 5/29: Recent case studies
  • Week 10: Advanced topics and Applications
    • Monday 6/1:  In-class project work
    • Wednesday 6/3: In-class presentations
    • Friday 6/5: FINAL PROJECT DUE