Podcast Summary: People I (Mostly) Admire

Episode: Is There a Fair Way to Divide Us? (Update)

Host: Steve Levitt (Freakonomics Radio)
Guest: Moon Duchin, Mathematician and Gerrymandering Expert
Release Date: October 18, 2025

Overview

This episode features a compelling conversation between economist Steve Levitt and mathematician Moon Duchin, focusing on the mathematics and politics of redistricting and gerrymandering. Duchin, renowned for bridging pure mathematics and practical policy, discusses how her expertise in geometry has led her to the frontlines of one of America's most contentious political processes: drawing fair electoral districts. The episode explores the mathematical, legal, and ethical dimensions of redistricting, why mathematical tools are needed, and the prospects for reforming how we draw the lines that divide and represent us.

Key Discussion Points and Insights

1. Moon Duchin's Journey from Geometry to Gerrymandering

• Teaching Sparks Application
  • Duchin began investigating redistricting when teaching an undergraduate class on math and voting (03:18). She was surprised by how “sneaky deep” and unsolved the mathematics of voting and districting were.
  • Quote:
    “I wasn't so much drafted as I drafted myself... I love learning things through teaching them and I love stretching across the math curriculum.” (03:18 — Moon Duchin)
• Early Realizations
  • The 2016 U.S. primary brought immediate relevance, inspiring her to connect abstract theorems to American redistricting practices (03:33).

2. The Mechanics and History of Gerrymandering

• Defining Gerrymandering

  • Gerrymandering is “basically abusive redistricting... where you use [line drawing] power to advance some agenda” (06:36).
  • Origin of the Term:
    • Named after Massachusetts Governor Elbridge Gerry, whose salamander-shaped district sparked a term still in use (07:17).
    • Quote:
      “It was called Garry’s Salamander and that’s what became Gerrymander.” (07:27 — Moon Duchin)

• Mathematical Impact

  • With 59% Democrats and 41% Republicans in a hypothetical state, district lines can be drawn to give either party disproportionate power—ranging from 0 to 8 seats for the minority.
    • Packing and cracking are key strategies: consolidating opposition votes into few districts (packing) and spreading them thinly over many (cracking) (10:44).

3. Rules and Constraints in Redistricting

• The “Big Six” Rules (11:27–13:38)
  • Universal:
    • Population balance
    • Racial fairness (Voting Rights Act, 14th Amendment)
  • Other common criteria:
    • Contiguity (districts as connected areas)
    • Compactness (regular, simple shapes)
    • Respect for political boundaries (cities, counties, towns)
    • Communities of interest (groups with shared cultural/economic interests)
  • Lack of Outcome Rules:
    • No direct requirement that seat allocation tracks vote shares, though some states like Ohio have tried proportionality rules (14:01).

4. Proportionality and International Comparisons

• Proportional Systems vs. U.S. System
  • Most countries use party-list proportional systems. Germany, for example, mixes district representation and party-list seats for proportionality (15:11–16:01).
  • The U.S. system values geographic representation, giving voice to local concerns (16:15).

5. The Segregation Paradox and Political Geography

• Distribution Effects

  • Contrary to “conventional wisdom,” minority groups gain more representation when geographically clustered rather than uniformly spread (18:06).
  • Quote:
    “If that minority population is advantageously arranged for representation, you’ll find by far the best representations as they get very clustered.” (18:06 — Moon Duchin)

• Massachusetts Example:

  • Despite being a blue state with 30% Republican voters, the Republicans are spread so evenly they win no congressional seats—illustrating the power of geography over simple vote share (20:15–21:24).

6. Why Fair Redistricting Is a Hard Math Problem

• Scale and Complexity

  • The space of possible districting plans is “a googol—one with 100 zeros” (22:03).
  • There is no recursive way to simplify the problem; exploring the space is more complex than even counting particles in the galaxy (23:19).

• Representative Sampling and Ensemble Method

  • Duchin’s research group uses advanced algorithms (e.g., Markov chains) to generate ensembles—a representative sample—of valid districting plans (25:35–28:58).
  • Quote:
    “We were able to implement [a new algorithm] to run really fast and to prove some theorems and get some mathematical control of what happens after a long time...” (27:37 — Moon Duchin)

• Practical Use:

  • If a proposed plan is an “extreme outlier” in the ensemble, it is likely gerrymandered (29:23).

7. Limitations of “Blind” Redistricting

• Blind/Apolitical Approaches May Not Be Fair
  • Blindly drawn plans can still yield partisan advantages based on political geography, as in Pennsylvania, where nonpartisan plans favored Republicans (30:50–31:34).
  • Visual appearance (compactness) is a weak proxy for fairness; attractive-looking districts can still be unfairly drawn (34:37).

8. Participatory and Process-Oriented Reform

• Consulting for “Doing It Right”
  • Duchin prefers helping commissions design fairer plans and standards, e.g., in Michigan for community input and Arizona for competitiveness (35:45–39:40).
  • Research shows many states could achieve proportionality or “efficiency gap” benchmarks through reasonable, non-sophisticated means.

9. Alternative Voting Systems

• Reforming the System
  • Duchin advocates exploring alternatives like multi-member districts and ranked-choice voting to reduce inherent representational biases (39:40–44:15).
  • Portland’s new multi-member districts stand as an effective proportional model.

10. Memorable Personal Anecdotes

• Rush Limbaugh Stories
  • Both Duchin and Levitt recount being mocked by Rush Limbaugh, ultimately viewing it as a badge of honor (44:34–49:34).
  • Quote:
    “At the end of the clip, he says, ‘Good night, Moon.’ It’s just chef’s kiss. Just beautiful.” (47:57 — Moon Duchin)

11. Math, Social Science, and Diversity

• Interdisciplinary Roots
  • Duchin’s background spans mathematics and women’s studies, which shaped her focus on the social implications of science (50:57).
  • On academic diversity: Both speakers discuss the value—and potential pitfalls—of efforts to increase diversity in academia, advocating for fair processes and informed choice (53:15–57:34).

12. Closing Thoughts: Applied Work and Academic Life

• Staying True to the Academy

  • Despite her work’s real-world influence, Duchin remains enthusiastic about academic life and the intellectual community of the campus (58:01).

• Current Focus

  • Duchin remains active in redistricting litigation (notably in Texas and Utah) and is writing a book titled “What Even Is Democracy?” (59:04).

Notable Quotes and Moments with Timestamps

• Defining Gerrymandering:
  “Gerrymandering is where you use [line-drawing] power to advance some agenda. Notice that's slippery.”
  — Moon Duchin (06:36)

• Importance of Geography:
  “You have shrimpers in Louisiana, you have loggers in Oregon, you have various kinds of local interests... Those interests might be at the substate level. You want some representation for geographically correlated local interests.”
  — Moon Duchin (16:15)

• Political Geography Paradox:
  "If that minority population is advantageously arranged for representation, you'll find by far the best representations as they get very clustered... It goes against the conventional wisdom."
  — Moon Duchin (18:06)

• The Mathematical Challenge:
  "There are probably thousands [of plans], he said. And all the math people like me fell out of our seats... Actually, probably the right scale to think about is a googol, a one with 100 zeros. That's probably how many districting plans there are to compare."
  — Moon Duchin (22:03)

• Innovation in Sampling:
  “So we came up with a big way to change plans one step at a time... You fuse two districts together that are neighbors and then draw a boundary in a totally new way...”
  — Moon Duchin (27:19)

• Blind isn't Always Fair:
  "You really have to get to this notion that something that's facially equal between groups might not be allocating resources in a way that's fair by other kinds of measurement."
  — Moon Duchin (31:01)

• The Irrelevance of Looks:
  “Over and over again... under pressure to make their districts look nice, they can gerrymander just as much. The shapes just don’t turn out to be as constraining as I expected.”
  — Moon Duchin (34:37)

• On Academic Life:
  "I step onto a college campus and I see the posters for talks... and I get all excited. I really love the life of a campus and all of the different kinds of intellectual projects." — Moon Duchin (58:01)

Important Segments (Timestamps)

| Topic | Start Time |
| --- | --- |
| How Duchin entered the redistricting field | 03:18 |
| Definition and history of gerrymandering | 06:36–08:59 |
| Vote share vs. seat allocation; packing/cracking | 09:42 |
| Core rules for drawing districts (“Big Six”) | 11:27 |
| Proportional systems and outcomes | 14:01–16:15 |
| Geography and the segregation paradox | 18:06 |
| The mathematical scale of redistricting | 22:03 |
| Introduction of Markov chains and ensemble methods | 25:35–27:36 |
| Use in real cases (Pennsylvania, etc.) | 29:23–34:00 |
| Irrelevance of “nice-looking” districts | 34:37 |
| Recommendations for voting system reform | 39:40–44:15 |
| Rush Limbaugh stories | 44:34 |
| Academic life, diversity, and social impact | 50:57, 53:15 |
| Closing thoughts, new projects | 59:04 |

Final Thoughts

This episode delivers an engaging and nuanced primer on how math and geometry are changing the fight for fair elections. Duchin’s accessible explanations reveal both the complexity and promise in the use of mathematical tools to diagnose and potentially curb gerrymandering. The conversation is wide-ranging, touching everything from technical details to personal anecdotes, and it offers hope that more transparent, fair, and scientifically informed processes might be within our reach.

For anyone interested in democracy, math in public policy, or how modern science can tackle social problems, this episode is indispensable.