A 59/41 vote split can legally translate to anywhere from 0 to 8 of 10 seats, purely through line-drawing.
With winner-take-all districts, a minority party needs only just over 40 percent of the vote in each district it wants to win. Packing the majority into a couple of overwhelming districts and cracking the rest lets a minority-vote-share party capture most of the seats, entirely within the rules if the only constraint is equal district population.
gerrymandering-math
The space of possible districting plans is functionally infinite and has no exploitable substructure, which is why ad hoc human judgment (and even computers naively searching) cannot establish a fairness baseline.
Duchin estimates the number of valid plans for a state at roughly a googol (10^100), far beyond the number of particles in the galaxy. Worse, the problem doesn't decompose - knowing how to district a small state gives no leverage on a larger one - so there is no way to enumerate or exhaustively search the space, which is why courts historically had no baseline for what 'normal' districting looks like.
gerrymandering-math
Duchin's research group built a Markov-chain sampling method (ReCom) that generates a statistically representative sample of valid districting plans, giving courts a baseline distribution to test proposed maps against.
The method fuses two neighboring districts and redraws the boundary between them in one large step (unlike earlier methods that moved one precinct at a time), which explores the plan-space efficiently enough to run at scale and support rigorous outlier analysis in litigation.
gerrymandering-math
A blind, non-partisan redistricting process is not the same thing as a fair one.
In Pennsylvania, a map drawn with zero partisan data still handed Republicans several extra seats beyond proportionality, purely because Democratic voters are geographically concentrated in Philadelphia. Duchin's courtroom line - 'blind isn't always fair' - drew laughter until she explained that a facially neutral process can still allocate outcomes unevenly across groups.
fairness-vs-neutrality
Geographic clustering of a minority voting bloc is what makes proportional representation for that group achievable, contrary to the conventional 'Democrats huddle in cities and waste votes' narrative.
Duchin argues this conflates two senses of 'packed': density versus electoral inefficiency. If a minority group is spread perfectly uniformly across a state (as Republicans are across Massachusetts, where they hold roughly a third of the vote in nearly every town), no districting plan can ever give them representation - they lose every single seat. Clustering, not dispersal, is what makes districts winnable for a minority.
gerrymandering-math
Massachusetts has the most spatially uniform political geography of any US state, which mathematically guarantees an all-Democratic congressional delegation regardless of how lines are drawn.
Republicans reliably clear about 30 percent of the statewide vote but are distributed almost identically at the county, town, and (likely) household level, so no districting plan can concentrate them into a winnable seat. Massachusetts has sent a 9-0 Democratic delegation to Congress in recent cycles and hasn't elected a Republican to the House since 1992.
gerrymandering-math
Compact, normal-looking district shapes do not prevent gerrymandering.
Duchin initially expected that restricting district shapes to look 'nice' would limit legislatures' ability to gerrymander, but repeatedly found that legislatures under pressure to produce visually reasonable districts can still gerrymander just as effectively - shape constraints turned out to be far less binding than she expected.
gerrymandering-math
A test for whether a redistricting plan clears a proportionality bar - passing 3 of the last 4 major statewide elections - was achievable by an adequate supply of blindly-drawn plans even in gerrymandering hotspots.
Duchin and coauthor Gabe Schoenbach studied a rule proposed for the Freedom to Vote Act: check a plan's results against the last two presidential and two Senate elections and require it be close to proportional in 3 of 4. Even in North Carolina, Wisconsin, and Pennsylvania, plenty of neutrally drawn plans passed, and plans that hit the target on past elections tended to keep hitting it on future elections - suggesting the standard is both achievable and durable without requiring sophisticated partisan consultants.
fairness-vs-neutrality
Blind (non-race-conscious) redistricting is comparatively survivable for Democrats on average but can be devastating for racial and language minorities, given current Supreme Court hostility to race-conscious districting.
As courts increasingly disfavor any race-conscious line-drawing (even to remedy past discrimination), Duchin's modeling shows that a purely blind process, given how minority populations are actually distributed, would shut many racial and language-minority communities out of the chance to elect their preferred candidates - meaning 'neutral' is not neutral in its consequences.
fairness-vs-neutrality
Multi-member districts with ranked-choice voting can achieve proportional representation more directly than single-member first-past-the-post districts, without changing where anyone lives.
Duchin's modeling of a Massachusetts alternative voting-system study found that a well-designed ranked-choice system approached the proportionality of full party-list voting. Portland, Oregon's 2022 reform - four districts electing three members each - is cited as an especially effective real-world example, since electing several people from one district makes fractional proportional outcomes possible in a way a single-winner district cannot.
voting-system-design
Ranked-choice voting needs a well-designed 'menu curation' step (like a preliminary round) or it can produce chaotic ballots, as in a 2013 Minneapolis mayoral race with 35 candidates including one named Captain Jack Sparrow.
Duchin notes ranked choice works best paired with a mechanism (e.g., Alaska's top-four primary) that narrows the field before voters rank remaining candidates; without that curation step, ranked-choice elections can become unwieldy.
voting-system-design
Pushing talented young people toward academia because they show early aptitude may do them a disservice, since academics who identify and mentor promising students get first pick before other high-impact fields (politics, business) can recruit them.
Levitt raises this as a diversity-and-mentorship dilemma: professors and academics have disproportionate early influence over talented students' career paths, and steering them toward one's own field risks foreclosing other paths where their impact (and the social value of diversifying that field) might be larger. Duchin partially pushes back, arguing it would be patronizing to tell people their own stated career preference is wrong, and that the real fix is building fairer evaluation processes rather than pre-selecting people's paths for them.
representation-and-diversity
Diversity-minded hiring and prize committees can produce an unhealthy 'team play' dynamic that ends up tokenizing candidates rather than fairly evaluating them.
Duchin describes sitting on hiring and prize committees where some members push to ensure women, people of color, and other underrepresented groups are considered, while others push back defensively - both dynamics distort evaluation processes and prevent candidates from being assessed on merit rather than group identity.
representation-and-diversity
Books referenced
What Even Is Democracy? - Moon Duchin - Duchin's book-in-progress on the norms and goals of representation, informed by her math background and frontline redistricting work
Media referenced
Freakonomics - other - Levitt references the book he co-wrote and how getting a taste of the real world through it changed his relationship with academia
Atlas of Redistricting (FiveThirtyEight) - article - Dave Wasserman's project hand-drawing Democratic-gerrymander, Republican-gerrymander, and proportional maps for every state; Duchin and a coauthor tested whether his plans passed their proportionality benchmark
Companies
MGGG (Metric Geometry and Gerrymandering Group) - Duchin's research center at Tufts/Cornell studying redistricting math; mggg.org
New America - Advocacy group Duchin partnered with to study whether a different voting system would fix Massachusetts's lopsided congressional delegation
Techniques and frameworks
Ensemble method / Markov chain sampling of districting plans - Duchin's research group's core innovation: instead of drawing one map, generate a large representative sample of valid districting plans by algorithmically walking through the space of possibilities, then compare a proposed plan against that distribution
Recombination (ReCom) redistricting moves - The Markov-chain move Duchin's group designed: fuse two adjacent districts and redraw the boundary between them in one step, analogous to a riffle shuffle rather than moving cards one at a time - it explores the space of plans far faster than single-precinct swaps
Outlier analysis - Using the ensemble of randomly generated plans as a baseline distribution; if a proposed plan sits in the extreme tail (e.g., unusually favorable to one party), that is evidence of intentional gerrymandering, and courts have found this persuasive
Packing and cracking - The classic gerrymander mechanics: concentrate (pack) the opposing party's voters into a few districts you concede, then split (crack) the remainder just thinly enough across the districts you want to win
Summary
This encore episode revisits Steve Levitt's conversation with Moon Duchin, a Tufts mathematician whose abstract work in geometry became unexpectedly central to how US courts and independent commissions evaluate gerrymandering. Duchin explains that the core problem with judging whether a districting plan is fair is scale: the number of valid ways to divide a state into districts is astronomically large (on the order of a googol) and has no exploitable substructure, so neither courts nor computers can simply enumerate "normal" plans to compare against a proposed one. Her research group's answer was to build a Markov-chain sampling method - nicknamed for its "recombination" move of fusing two districts and redrawing the boundary between them - that generates a statistically representative ensemble of valid plans. Courts can then check whether a proposed map is an outlier relative to that distribution, which has become a genuinely persuasive form of evidence in redistricting litigation, including cases in Pennsylvania and elsewhere.
A recurring thread is that "neutral" and "fair" are not the same thing. Duchin recounts testifying in Pennsylvania that a map drawn with zero partisan data still favored Republicans by several seats, purely because of where Democratic voters happen to live (concentrated in Philadelphia); her line that "blind isn't always fair" drew laughter in the courtroom before she explained the distinction. She and Levitt also dig into the counterintuitive "segregation paradox": geographic clustering of a minority voting bloc, often assumed to be politically disadvantageous, is actually what makes proportional representation for that group possible. Massachusetts is the extreme counterexample - Republicans there are so uniformly spread across every town and county (holding roughly a third of the vote almost everywhere) that no districting plan, however drawn, can ever give them a winnable seat, which is why the state has sent an all-Democratic delegation to Congress for decades.
The conversation moves through several other findings from Duchin's work: that district shape constraints (avoiding "crazy" outlines like Pennsylvania's Goofy-kicking-Donald-Duck 7th district) do little to actually prevent gerrymandering; that a specific proportionality test proposed for the Freedom to Vote Act - matching past election results 3 of 4 times - turned out to be achievable even in gerrymandering hotspots like North Carolina and Wisconsin using blindly drawn plans; and that a purely blind, race-neutral process, while survivable for Democrats on average, would be far more damaging to racial and language minority communities given current legal hostility to race-conscious districting. Duchin also discusses her modeling work on alternative voting systems, finding that well-designed ranked-choice voting paired with multi-member districts (as in Portland, Oregon's reformed city council) can approach the proportionality of party-list systems without abandoning the geographic-representation logic Americans are used to.
The episode closes on two more personal threads. Levitt and Duchin swap stories of being mocked by name on Rush Limbaugh's radio show decades apart (Duchin over a college gender-neutral-bathroom initiative, Levitt over his prison-and-crime research), both treating it as an odd badge of honor. They also debate whether academia's ability to recruit talented students early - before other high-impact fields like politics get a chance - might do those students a disservice, and how diversity-minded hiring and prize committees can slide into an unhealthy, tokenizing "team play" dynamic rather than fair evaluation. In an added coda recorded for this update, Duchin reports she is now testifying in a Texas gerrymandering trial, tracking a "flawed and misguided" new Utah redistricting law, and writing a book, working title "What Even Is Democracy?"
Notable Quotes
"We don't have a baseline. We don't know what normal districting looks like. And what the math folks have brought to the table is better and better methods for sampling from that huge, unthinkable wilderness of plans." - Duchin
"Blind isn't always fair." - Duchin
"A drunken monkey can eventually type Hamlet... but why should we outsource our redistricting to a drunken monkey?" - Duchin, quoting an attorney in the Pennsylvania redistricting case
"The redistricting wars have notched up to nuclear this year." - Duchin
"So there's this real genius economist at Harvard... he's figured out that when you lock up more criminals in prison, crime actually goes down. Now imagine that... So I've heard he's working on a new research paper now, and the working title is, 'Nighttime Causes Darkness.'" - Levitt, recounting Rush Limbaugh's on-air mockery of his prison research