Could Someone, Anyone, Please Get the Unfairness of Gerrymandering Right?

FINE. It'll have to be me.

Among the big winners of election day 2025 was democracy—or rather, Democrats. In California, voters approved Proposition 50, a rational response to Texas’s aggressive redistricting as if they were saying, “If you’re going to draw lines to favor your side, we’ll draw ours too.” The result is a redistricting arms race, and Republicans currently hold more arms, since they control more states where maps can be redrawn, current Texas legal decisions notwithstanding. Missouri, for instance, could soon erase one of its two Democratic congressional districts. North Carolina and perhaps Ohio gerrymanders could also net out in Republicans’ favor.

This leads to the perennial argument over what a “fair” map should yield. The prevailing but misguided consensus holds that a state’s congressional delegation should mirror its presidential vote: if 38% voted for the Democrat, roughly 38% of its representatives “should” be Democrats. Both parties embrace this logic—not because they’re lying, but because it flatters their interests and fundamentally misunderstands how elections work.

Let me explain why this reasoning is mathematically wrong.

Everyone’s Getting the Math Wrong

On the conservative side, Victor Davis Hanson makes the case about California’s 52 congressional seats while discussing redistricting and what Gavin Newsom doesn’t want you to know:

“Here in California, to take the most relevant example that involves Prop 50, we have 52 congressional districts—52. Currently, there are only nine Republicans out of that 52. That represents about 17% of the congressional districts. However, in most statewide and national elections, Republicans usually poll about 40%.”

Newsom loves the gerrymandering issue. He’s taking victory laps in Texas over it. And you know what? Gerrymandering is fire, and Newsom is right that you have to fight fire with fire. But let us not be ignorant or deceived about what the ideal number of representatives would be without the distortions created by gerrymandering..

I am constitutionally—lower-case “c”—ill-disposed to calling everything a crisis. This development is troubling, but not apocalyptic. True constitutional crises occur when branches of government collide with no remedy in the Constitution. We’re not there yet. We’re just in a messy situation that could, like almost anything, escalate.

The Proportionality Trap

Even responsible, non-partisan sources use this weird rule-of-thumb “fairness” metric. The New York Times article “Gerrymandering War Spreading Across U.S. Is a Crisis, Experts Say” notes that Louisiana, Mississippi, Alabama, and Tennessee could soon send no Democrats to Congress, despite 34 to 38% of their voters choosing Kamala Harris in 2024. The implicit argument is clear: these numbers should match.

The American Constitution Society makes the same case with more examples: “In Texas, where Kamala Harris won 42% of the vote in the 2024 presidential election, Democrats hold only 34% of the congressional seats (13 of 38 seats). In Indiana, Democrats hold two of seven seats, which is 22% despite Harris’ 40% share of the 2024 vote. In Missouri: Democrats hold two of eight seats, which is 25% despite Harris’ 40% share of the 2024 vote. In Mississippi: Democrats hold one of four seats, which is 25% despite Harris’ 38% share of the 2024 vote.”

The Brookings Institution piles on with empirical data: “In red states … Republicans garnered 56% of the vote but 74.6% of representation.” The Associated Press reports the same pattern: “Fifty-eight percent of Missouri voted for Trump, but they want to send an 87% representation to Congress.” The Center for American Progress argues for districts where “the views of elected representatives … better reflect those of the people who elect them.”

Critics see all of this as proof of injustice.

Yet Massachusetts, where 36% voted for Donald Trump, already sends zero Republicans to Washington. Is that a crisis? There’s decent evidence that it’s all but impossible to draw a fair map that actually includes any Republicans in Massachusetts, even if more than a third of the state is of a rightward ilk. And if it were, there’s no better place to implement the principles pioneered in the land of Elbridge Gerry.

A couple of notes: There’s no racial disenfranchisement at play in Massachusetts, and the preclearance considerations of Section 5 of the Voting Rights Act wouldn’t apply, as it targets former Confederate states with histories of suppressing Black voters. The cases now before the Supreme Court also don’t factor into a map like Massachusetts’. My point isn’t that one situation is fair and the other isn’t; it’s to define what constitutes “fair.”

Fair is NOT for three Massachusetts seats to go to Republicans or four Missouri seats to go to Democrats just because 40% of that state voted for Harris.

The Math That Everyone Ignores

The common argument—that fairness means seats proportional to votes—doesn’t meet the standards of basic probability.

Even academics fall into this trap. A 2021 paper by John F. Nagle and Alec Ramsay considers “deviations from the proportionality ideal” as part of their fairness metrics for districting. But what they call “deviations from perfect proportionality” are statistical necessities. Even a purely neutral, random map would produce a delegation skewed toward the majority party, because representation is a discrete, winner-take-all process—exactly what the hypergeometric distribution shows.

Think about it: In a state that is 60–40 in favor of one party, if every congressional district were drawn in perfect accordance with the overall political makeup of the state, you’d have zero representatives from the minority party. If state congressional districts were drawn “proportionally” to reflect the state overall, every congressional district would have the overall skew of the state, which in over 40 states practically means clean-sweeps of congressional races.

But that’s not how districts are drawn or should be drawn. But how they SHOULD be drawn isn’t to get congressional districts in line with overall state voter registration.

I give you hypergeometric distribution.

God, Guns and Gum

Imagine the state as a gumball machine containing 99 gumballs total: 59 red and 40 blue. That’s a 60-40 split, matching our hypothetical state’s partisan breakdown.