A simple deterministic way to increase the House size that solves a number of issues.
“I am unalterably opposed to limiting the membership of the House to the arbitrary number of 435. Why 435? Why not 400? Why not 300? Why not 250, 450, 535, or 600? Why is this number 435 sacred? What merit is there in having a membership of 435 that we would not have if the membership were 335 or 535? There is no sanctity in the number 435… There is absolutely no reason, philosophy, or common sense in arbitrarily fixing the membership of the House at 435 or at any other number.” (Rep. Ralph Lozier (Missouri), 1928 floor debate)
The wonderful Mr. Beat has recently been using his fame and power for good by essentially single-handedly bringing uncapping the House of Representatives into the public consciousness.
However, uncapping the House cannot be done lightly. There are serious arguments that a major increase could have negative consequences for accountability. And though I think the benefits likely outweigh the drawbacks, I do have some serious concerns about the viability of this proposal. In the petition, I saw a serious flashing warning sign:
“There could be the Wyoming rule that could increase it by around 140 seats. Or do the Constitutional literalist route in that the ratio couldn’t exceed 1 per every 30,000 people, which could extend the House to at least 11,000 people. There’s also the cube root rule that could increase it to 690-700.” (source)
I am admittedly a political pragmatist. I think that the simplest solution is often the best, and that’s why Approval voting is the only voting reform I actively support. So when I imagine people going to members of Congress and showing them this petition, which suggests potentially increasing the House from 435 to 11,000, I worry that the proposition will seem so radical that they simply tune out completely. They can easily point to that one sentence as an excuse to protect taxpayer dollars. In the same way Ranked-Choice Voting is facing backlash (for good reason) by being an expensive logistical nightmare, I think that we should prioritize having answers to the obvious follow-up questions ready.
If we can give a concrete method that is pragmatic and leaves little to be ironed out later, I think that’s the way to go. And I would like to share an incredible suggestion by Michael G. Neubauer
Full disclosure, this topic is not exactly my wheelhouse, but I think getting this method out there is worth doing. All of my claims and quotes are sourced from Neubauer’s paper, which you can read for free here.
Before we get into the math of why his proposal is sound, I think it’s worth stating it up front, and then we can go into why this is an excellent suggestion.
Definition: A House size is agreeable if
- It is not an Alabama Paradox House size
- The apportionment from Webster and Vinton’s method agree.
We will explain what these terms mean shortly. The proposal is as follows:
The Neubauer Proposal: After each census, increase the House size to the first agreeable House size larger than the existing House size.
To put it simply:
Neubauer summarizes the benefits for this method, which we will shortly justify.
For me, item 5 is my favorite. Because the first question I think any lawmaker is going to have is “okay, let’s say we do this. How many seats are we talking about?” Neubauer crunched the numbers and this method would have increased the House size
This is not radical. We are talking 6 seats across two decades. I understand that for many of the people who are clamoring for 11,000 House seats, this might seem like far too few. It would essentially be so small that it could be unnoticeable.
However, given that the people we are asking to make this change have a severe conflict of interest (“If we do this, my power and influence diminishes”), I think that modest proposals are the way to go. Once we uncap the House, there’s far more room to grow it in the future, especially as we accumulate more House members who may be more sympathetic to the idea of increasing the House size by a larger amount. But being able to say that we are only proposing a method that would add just a handful of seats per decade stops a number of objections right in their tracks:
Once we get the boulder moving, it’s much easier to increase its speed. For example, we could later propose finding the first agreeable House size over a certain number (like, say, 500).
Okay, now that we have the solution, let’s discuss the math of why this is so good.
There are essentially three desirable qualities of an apportionment method:
Like everything in the math of politics, you can’t have all of these things at once for a fixed House size $M$. None of the classical methods manage it. Webster and Vinton each come close, but each fail in at least one of these three areas.
Back in the day, there were two competing methods by Adams and Jefferson. Jefferson’s method blatantly favored big states, while Adams’ method favored small states. And these are “beyond repair”, according to Neubauer. Their severe systemic bias makes them nonstarters.
These, along with Webster, belong to the collection of divisor methods with fixed rounding rules. You pick some divisor $D$, starting with the standard divisor $s=P/M$ where $P$ is the total population and $M$ is the number of seats, and then you divide each state’s population $p_j$ by $D$ to get a quotient (ex. $p_j/D=12.4$ means that the state should get seats approximately in that ballpark). Then you round that quotient to get the number of seats for that state. If this doesn’t add up to $M$, then you adjust $D$ (increasing if you have too many seats, and decreasing if you have too few) until you get $M$ seats.
Jefferson says to round down, Adams says to round up, and Webster says to round to the nearest. Neubauer proves that Webster’s method “is expected to be unbiased for all states.” The problem with these methods is that a state might get more than their quota. In 1790, Jefferson’s method with a 30,000-person minimum district would have given Virginia (his home state) 21 seats with a quota of 19.53.
Unfortunately, the method we are using right now, Huntington-Hill, is not unbiased. It favors small states. This is despite mathematician Edward Huntington’s 1928 claim that “(t)he mathematical evidence,…, clearly indicates that the method of equal proportions is the one method which has no bias in favor of either the smaller or the larger states.” This claim turned out to be simply false. Dean’s method is similarly biased for smaller states, even more so than Hill (but not as much as Adams).
In the pursuit of a method that minimizes bias, we are left with Webster. However, any divisor method risks quota violations we can’t rule out.
To be quota-consistent, we need to make sure that no state gets more than 1 seat away from their quota. For example, if a state should get 12.4 seats, it should get either 12 or 13. This leads us to remainder methods, like Vinton.
For these methods, we take their quotient (ex. $p_j/s=12.4$, using that same standard divisor $s$ from before) and round down to get the lower quota (12). Then we take the fractional part of the quotients of each state (ex. 0.4 for our theoretical state) and give the remaining seats one at a time to the states with the largest fractional parts. This will absolutely ensure that every state gets the right number of seats, and Neubauer proves that the average bias of this method is near zero (correlation -0.03).
Unfortunately, this method has the issue of Alabama Paradoxes.
After the 1880 census, C.W. Seaton (an amazing name for the guy who decides how many seats to give each state) calculated apportionments for House sizes from 275 to 350, and found an interesting anomaly.
“While making these calculations I met with the so-called Alabama paradox where Alabama was allotted 8 Representatives out of a total of 299, receiving but 7 when the total became 300.” (source)
The mechanism is loosely this: when you increase the number of seats, the remainders get shuffled around. And larger states usually have their fractional parts “leapfrog” the remainders of smaller states. So increasing the House size might bring your remainder from closer to 1 to closer to 0, and you might lose a seat you previously got for having a large remainder. This is a chaotic effect that is hard to predict, and it is a serious problem for Vinton’s method.
Using the 2020 census populations, 32.35% of all House sizes between 400 and 2000 are Alabama Paradox sizes under Vinton’s method. That is, if you were to use a smaller House size, some state would get more seats. This is very undesirable because then the chosen House size can be weaponized against states.
“In Maine goes, out Maine goes – God help the state of Maine when mathematics reach for her and strike her down.” (Rep. Charles Littlefield, 1901)
Ideally, we do not want a method that gives states reason to hire mathematicians to crunch the numbers and find the House size that most benefits them (or hurts their rivals).
Webster is unbiased but can suffer quota violations. Vinton is quota-consistent but suffers from the Alabama Paradox and minute bias. For a fixed $M$, there’s no method that can prevent all of these issues. Thus, Neubauer suggests changing the problem by simply requiring the things we want, and removing the requirement of a fixed $M$. We let the number of seats float until the two best methods agree (and for which there is no Alabama Paradox). This is the definition of an agreeable House size, and it is a very simple and elegant solution to the problem.
Empirically, agreeable House sizes are not rare, which does mean that the House would grow very slowly. But this can be a feature, not a bug. It can ease the minds of lawmakers who are worried about their power being diluted and who might otherwise reach for plausible-sounding logistical objections to stop the conversation outright.
Further, the Constitution doesn’t settle which fairness principle should govern apportionment, so there is no precedent that would prevent us from using this method.
After the 1990 census, Washington state had a population of 4,887,941 and got 9 seats. Montana had a population of 803,655 and got 1. This meant that Washington’s district sizes were about 543,105 people, while Montana’s would be exactly 803,655. This is a difference of 260,550 people. If we had shifted a seat from WA to MT, the district sizes would be 610,993 and 401,828, which is a smaller absolute gap of 209,165 people. This would make the two states’ representation more equal in absolute terms.
The Hill method looks at things in relative terms. The “relative gap” for the 9-1 apportionment is about 48.0%:
\[\frac{803,655 - 543,105}{543,105} \approx 0.480\]while the 8-2 apportionment has a relative gap of about 52.06%:
\[\frac{610,993 - 401,828}{401,828} \approx 0.5206\]The 8-2 apportionment has a greater relative difference than 9-1–and since the Hill method minimizes relative differences, it picks 9-1.
United States Dep’t of Commerce v. Montana went to the Supreme Court, and Justice Stevens’ opinion stated:
“What is the better measure of inequality–absolute difference in district size, absolute difference in share of a Representative, relative difference in district size or share? Neither mathematical analysis nor constitutional interpretation provides a conclusive answer. In none of these alternative measures of inequality do we find a substantive principle of commanding constitutional significance. The polestar of equal representation does not provide sufficient guidance to allow us to discern a single constitutionally permissible course.” (source)
This does give us a good amount of wiggle-room to justify this method of apportionment. That is, we are not “locked into” using Hill’s method.
I say that we go with the easy sell to get the ball rolling, and we can start making considerations of more radical changes later. How many seats doesn’t matter if we cannot get any change at all.
Let us not allow the perfect to be the enemy of the good. If you are interested in helping to get Congress to uncap the House, consider joining the Project No Cap Discord server!
subscribe to be notified of future articles:
and here are some related posts you might like to read next:
Fisher, Taylor Eigen (Jul 2026). Uncapping the House Doesn’t Have to Be Radical. https://eigentaylor.github.io/blog/uncap/. Accessed Jul 31, 2026.
or as a BibTeX entry:
@article{fisher2026uncapping-the-house-doesn-t-have-to-be-radical,
title = {Uncapping the House Doesn't Have to Be Radical},
author = {Fisher, Taylor Eigen},
howpublished = {https://eigentaylor.github.io},
year = {2026},
month = {Jul},
url = {https://eigentaylor.github.io/blog/uncap/},
urldate = {2026-07-31}
}