Gerrymandering Means the End of Democracy

Readers of this blog and my public writing will know that I am not a fan of democracy without qualifications. There are many ways in which it is not ideal; by giving everyone the same voting power, we are unable to capture how some people will feel much more strongly about issues than others, and we are unable to incentivize people to overcome their atavistic prejudices. We cannot guarantee that it will have an outcome which is not perverse, or any outcome at all.

But do not be mistaken. Democracy may not be perfect. But it’s the best we’ve got, and the best we will have. If it errs, it errs in us being governed by too few, rather than by too many. However venal the many may be, it is better to maximize the welfare of a majority of society, rather than just a few.

I am therefore extremely concerned about gerrymandering. Gerrymandering is the practice of drawing districts so that your party has an electoral advantage. It’s like if someone could spread their points scored in a game over the whole season. It does you no good to run up the score in one game, if you could instead spread your points just enough to win all of the games. Politicians can therefore either pack their opponents into a few safe districts, where they are free to run up the score while they take most of the seats, or if they have a majority, arrange districts such that a large minority of voters have no representation at all.

Things used to be worse. Before Baker v Carr, there was no requirement that districts had to be of equal population, allowing counties of a thousand to count the same as districts a hundred times larger. On the other hand, things used to be better. In the last few months, there has been an alarming breakdown in the peace. Spurred by the current President, the Republican controlled states are moving to eliminate the last redoubts of Democratic voters in the House. In retaliation, the voters of California have given the state government the authority to gerrymander the maps. The Supreme Court will be considering, in Callais vs. Landry, whether governments in the Southern states are required to give any representation to Black voters.

I do not wish to mince words. This means the end of democracy. If it advances to such a point that the country is governed by a thin minority, only civil war or authoritarianism is left. I do not venture which will happen, nor which will be better. I say only that it differs from annulling an election in degree, not in kind. These would be the circumstances under which the most extreme solutions are justified.

Gerrymandering can be properly thought of as a subset of Bayesian persuasion problems. In Kamenica-Gentzkow (2011), we have a Sender and a Receiver, who can be thought of as a Principal and an Agent. Both Sender and Receiver start with a shared belief about the state of the world, and the Sender can send information to the Receiver in order to induce an action. The Sender is restricted to only true information, and cannot “fool” the receiver. In other words, the average posterior belief must necessarily equal the average prior belief. What Kamenica and Gentzkow are able to show is that if the Receiver takes any non-linear action as a result of the Sender’s signals, then it is possible for the Sender to profitably manipulate the Receiver. The Sender’s signal induces some distribution of posterior beliefs, which are on average the prior, but heap as much as possible just beyond the threshold to cause the action the Sender wants more of. (More formally, they can commit to any Blackwell experiment and any garbling of the signal, such that the Sender can induce any distribution over posteriors.)

To put this concretely, suppose that there is a judge and a prosecutor. The judge wishes to convict the guilty, and acquit the innocent; the prosecutor wants only to convict as many people as possible. Both judge and prosecutor start with the (true) belief that 30% of people brought before the docket will be guilty, and the judge will convict only if the prosecutor adduces sufficient evidence to raise the posterior probability of guilt above 50%. If the prosecutor is bound only to tell the truth, and nothing but the truth, then it would seem that they could only convict 30% of people, but that is not so. Suppose, for instance, they test the blood at the crime scene, which is Type A blood. This occurs in 42% of people – thus, plugging that into Bayes’ formula will just barely push it above the threshold for guilt. The prosecutor is able to convict 42% of people, despite everyone knowing only 30% are guilty.

The people to point out this concordance, and analyze gerrymandering with the same mathematical tools, are Kolotilin and Wolitzky (2025). With gerrymandering, we have to keep the number of voters in each district the same, akin to keeping the mean of posteriors the same in the Bayesian Persuasion problem, but we otherwise have the same solutions. If you could perfectly anticipate who people would vote for, then the solution is simple. Given your minority of voters m, where m is below 1 half, you spread 2m voters amongst as many districts as you can win with exactly 50% of the vote, and receive 0 votes in all of the other districts. This is the traditional cracking-and-packing.

We do not, of course, know precisely who people are going to vote for. What makes it interesting is that there are two sources of uncertainty. One is aggregate uncertainty, where the country as a whole might swing. The other is idiosyncratic uncertainty, where the gerrymanderer is uncertain about what sorts of voters will vote their way.

With aggregate uncertainty, cracking and packing is still optimal. Define “voting types” as a continuous line, and the parties taking either side of that line as voters. An aggregate swing is the position dividing the two being moved. It’s optimal to place your very strongest voters into districts where they hold narrow majorities, and match them against the strongest voters for the other party. The waverers can be placed in their own district. If there is only idiosyncratic uncertainty, then they assign the types of voters that vote above median such that they win (in expectation) as many districts as possible. They should pack opponents, but not moderates, who are matched against the strongest voters. When we have both, the larger one determines the optimal plan. Given their estimates, they believe that traditional pack and crack is approximately optimal.

Democrats, the party whom I consider to be the party of good, decent, and moral people in America today, are sharply disadvantaged by the electoral maps as drawn; and if the states are able to gerrymander without fetter they will be yet more disadvantaged. Republicans, being always the victims of Democratic perfidy, alternately deny this, or claim the Democrats did it first. At present, though, they can point to only one genuinely gerrymandered state – Illinois. Maryland used to be gerrymandered, to the tune of two lost House seats, but is no longer.

The map favors Republicans. That much is indisputable. The absolute best work on this topic is Berry, Cox, and Haile (2025), who take the tools developed to estimate demand and apply them to the demand for policy. I covered this in more detail in my article arguing for the first author (among others) to receive the Nobel Prize in economics, though I warn you that it is a difficult and knotty topic to get into. For estimating demand, we estimate models where people make a discrete choice between different products, and then we estimate the elasticity

As an exercise, they show what would happen if the relative appeal of candidates of the two parties were adjusted such that they would capture 50% of the statewide vote. Were this to be done, Republicans would win 55% of seats with 50% of the votes.

It is not sufficient to simply compare vote share and proportion of seats, because this is simultaneously determined by people’s beliefs about the efficacy of voting. Candidates might run in uncontested races, which will depress observed vote share for the disadvantaged part. You need to properly estimate demand.

If both parties go as hard as they can to redistrict, the results would sharply favor Republicans. Finding the optimal districts is difficult, as it is an NP-hard problem, but we can get pretty close. Goedert, Hildenbrand, Travis, and Pierson (2024) calculate what is possible if both parties could gerrymander optimally, and show that control is enough to swing over 100 seats. Both because Republicans control more states, and in comparing cases where either party controls all states, things are much more biased in favor of Republicans. One of the big areas where Republicans can improve upon is in the South, where there are many majority-minority districts. Black people are a strongly Democratic demographic, so requiring them to get representation has the effect of preserving democratic districts. If the Supreme Court rules that drawing them out is permissible, the 35% of the South which consistently votes Democratic goes to 0. (Especially since elections in the South have so little uncertainty over how people will vote, being along racial lines,

Interestingly, requirements that districts be compact have almost no effect on the ability of partisans to gerrymander. They measure compactness with the Polsby-Popper measure, which is the area of the district times 4pi, divided by the perimeter squared. This is essentially comparing it to a circle of the same area. I’m covering this just cause I think it’s neat.

We can easily solve gerrymandering by having proportional reputation. While there is still scope for the voting system to be manipulated – if you knew precisely how many people were to vote for each party, you could manipulate the size of the legislative body to your advantage – this is obviously an incredibly limited scope. Before we do this, though, we should ask: what might the cost of this be? I see several reasonable objections.

The first is that we might want to represent the interests of distinct communities or places in the legislature. Much of a legislator’s work is in constituency services, goading bureaucrats into action. Local representatives means that one representative has a considerable stake in a small set of issues, rather than the party as a whole having a small interest in all issues.

Having regional districts, and therefore having only one representative, may decrease corruption through several channels. First, if someone engages in corruption, they cannot be buried in a party’s list. By requiring people to reject the entire party, instead of just a person, proportional representation makes it easier to fight corruption. Having independent legislators who represent definite districts makes it possible for legislators to gain a reputation for incorruptibility. This argument was originally made by Roger Myerson in the context of arguing for federalism, but it works at least a little in the House.

I am not convinced that these overwhelm the case for proportional representation. Having regional representation is hardly an unalloyed good; I see no reason to think that trading favors, infrastructure projects for this district in exchange for a military base in another, is best. Gerrymandering will tend to undermine the efficacy of constituent services, as representatives get in safer districts and no longer have to fight as hard. At best, they can hold only when there are parties of honor in power, and those we have not.

It is unfortunate, but goodness itself is endangered by district maps. Smart, capable, intelligent, and ambitious people move to the cities, where their votes are easily packed. Rural districts are places where failures, people of no ambition or talent, people whose past indiscretions hang as rolls of fat around them, the sickly, the parasites on the productive, the leeches, the ticks who are bleeding us dry, hold sway, and elect representatives to govern over us. This will only get worse.

So what can we do? I think the courts need to step in to prevent gerrymandering, and it must be the case that maps can be rejected even when compact. If the courts abandon their duty, then we shall see us move toward unrepresentative government, and one party autocracies in every state. This is a crisis, and we must steer ourselves away from calamity. I wish only that we took this more seriously.