Free Republic
Browse · Search
General/Chat
Topics · Post Article

Skip to comments.

The Cube Root Rule (Expand The House)
LinkedIn ^ | 6/19/2026 | Scott Whipkey

Posted on 06/26/2026 11:04:35 AM PDT by CathyWhite

In Part 1 (link below), I argued that the House of Representatives was designed to grow.

For most of American history, it did.

Then, in 1929, Congress froze the House at 435 seats.

It has remained there ever since.

Part 2 asks a different question: If the House is supposed to grow, how large should it be?

At first, I thought the answer might have something to do with human nature. Maybe there was something buried deep in our DNA — some limit on how many people we can know, trust, manage, or represent.

I was wrong.

The deeper I dug, the more one name kept appearing.

Rein Taagepera.

Taagepera trained as a physicist before turning to political science. He approached representative government the way physicists approach any complex system: by looking for patterns that emerge as it grows.

He discovered a surprisingly simple relationship: representative assemblies tend to approximate the cube root of the population they represent.

I understood the pattern. But I still didn't understand why.

So I emailed him, and to my surprise, the 93-year-old Taagepera wrote back.

"At first, I took this approach to be so evident that I did not bother explaining it," he wrote. "But when I did, I found that the concept still did not enter the heads of all too many political scientists."

Imagine a cube. Double the length of its sides and its volume increases eightfold. Triple it and the volume increases twenty-sevenfold. Growth is not linear — as systems become larger, the relationships between their parts change.

The cube root rule is about scale. Taagepera explained it this way:

"The gist is that we aim at minimizing the number of communication channels for one representative. Too few representatives, and the communication load shoots up in the constituency. Too many representatives, and the communication load shoots up in the assembly."

Representative democracies face two competing pressures: communication between citizens and representatives, and communication within the legislature itself. If a legislature is too large, the institution becomes difficult to coordinate; if it's too small, districts become enormous and representation grows distant. The United States — 435 representatives for 340 million people — sits firmly in the second category, and the cube root relationship appears to describe where the real balance point lies.

The Framers of the Constitution didn't know the cube root rule, but they understood the underlying problem. Article I, Section 2 caps representation at one member for every 30,000 people — a ceiling, not a mandate. The Framers weren't insisting the House maintain that exact ratio forever; they were expressing a broader principle: representation should expand as the population does.

Taagepera's research suggests that large democracies tend to settle into roughly the same balance point as they grow. For the United States today, the cube root of roughly 340 million Americans is about 700.

Not 435.

Not 11,000.

About 700.

For many people, the immediate reaction is understandable: "The last thing we need is more members of Congress."

But expanding the House does not increase the power of politicians. It dilutes it. Power becomes less concentrated.

A larger House reduces the ability of small groups and individual members to hold the system hostage simply because margins are razor thin. Political influence becomes distributed across more representatives and more communities. Smaller districts also lower the barrier to entry for new political movements. Independent candidates and third parties gain a more realistic path to winning seats. The power of the duoparty diminishes.

Engineers run into a version of this same scaling problem. As a bridge or a building grows larger, its weight increases by the cube of its size — but the strength of its supporting beams only increases by the square. Scale it up far enough while keeping the old proportions, and the structure fails under its own weight. The fix isn't to shrink the building back down. It's to redesign it — thicker columns, redistributed load, a structural logic built for the new scale.

The U.S. House of Representatives suffers the same problem. It's still shaped for a country of a few million. It was never resized for a country of 340 million.

Today, the average House member represents roughly 780,000 Americans, with some districts over a million. A 700-member House would reduce the average to roughly 500,000. Representatives would serve smaller communities, spend less time and money across enormous districts, and be more accessible and accountable to the voters who elect them.

When I started down this rabbit hole, I was looking for a number. What I found was an explanation.

The Constitution supplied the principle.

Rein Taagepera supplied the math.

A century ago, Congress stopped growing the House.

Maybe it's time to start again.

-----

Part 1 (https://thehill.com/opinion/congress-blog/5796470-the-us-house-was-designed-to-grow-lets-expand-it/)


TOPICS: History; Science
KEYWORDS: congress; constitution; house; supremecourt

Click here: to donate by Credit Card

Or here: to donate by PayPal

Or by mail to: Free Republic, LLC - PO Box 9771 - Fresno, CA 93794

Thank you very much and God bless you.


Navigation: use the links below to view more comments.
first 1-2021-4041-54 next last

1 posted on 06/26/2026 11:04:35 AM PDT by CathyWhite
[ Post Reply | Private Reply | View Replies]

To: CathyWhite

If you want to use the cube root approach, it should be done on a state-by-state level, not a total US population. This would effectively prevent larger states from dominating smaller states.

So a state with 1,000,000 people would get 100 representatives, whereas a state with 27,000,000 would get 300 reps.

Otherwise, leave it as is, asany increase in reps would tilt the balance to large states, which would be the end of the republic.


2 posted on 06/26/2026 11:15:00 AM PDT by kosciusko51
[ Post Reply | Private Reply | To 1 | View Replies]

To: CathyWhite

Now THAT makes sense - - would love to see it.


3 posted on 06/26/2026 11:16:47 AM PDT by impactplayer
[ Post Reply | Private Reply | To 1 | View Replies]

To: CathyWhite

While we are at it, let’s have a bunch of states implement an idea I’ve suggested for some time: eliminate House districts. Go back to the way many states operated in the early years of this country, and elect all the House member through a single at-large election in the state. At a bare minimum, it would eliminate all the idiocy surrounding these endless gerrymandering conflicts.


4 posted on 06/26/2026 11:21:15 AM PDT by Alberta's Child (If I leave here, it’s because I’m tired of arguing with geriatric parrots wearing MAGA hats.)
[ Post Reply | Private Reply | To 1 | View Replies]

To: CathyWhite

But expanding the House does not increase the power of politicians. It dilutes it. Power becomes less concentrated.


that is an interesting thought......................


5 posted on 06/26/2026 11:24:01 AM PDT by PeterPrinciple ((Thinking Caps are no longer being issued, but there must be a warehouse full of them somewhere))
[ Post Reply | Private Reply | To 1 | View Replies]

To: kosciusko51

I don’t think it would tilt the balance any more than the current apportionment. But it would dilute the power of Congress, and be consistent with Article 1, Section 2.


6 posted on 06/26/2026 11:29:00 AM PDT by CathyWhite (Texans for Trump.)
[ Post Reply | Private Reply | To 2 | View Replies]

To: kosciusko51

I think that’s what the Senate is for, and why there are two houses of Congress.


7 posted on 06/26/2026 11:31:01 AM PDT by CathyWhite (Texans for Trump.)
[ Post Reply | Private Reply | To 2 | View Replies]

To: Alberta's Child

Then conservatives from big states would have zero voice. I’d rather we eliminate winner-take-all states for national elections.


8 posted on 06/26/2026 11:34:16 AM PDT by CathyWhite (Texans for Trump.)
[ Post Reply | Private Reply | To 4 | View Replies]

To: CathyWhite

I have been arguing for this for awhile.

If you expanded it to 1 rep per 100,000, there would be 3600 reps. Make them stay at home in their home districts and vote electronically for 90% of the year and allow them to go to Washington to have meetings and hob knob 1 week every quarter.

100,000 people is how many people live in my county. I personally know A LOT of people in my county. I can guarantee I am 3 degrees of separation from eating a meal at the same room in the past 4 years with almost everyone in the county.

If my Rep knew he was going to have to sit in the same rooms, breathe the same air, sit in the same pews and cheer at the same kid’s baseball games as the people who would be voting for him, do you think he would be more likely to represent their best interests?

This proposal combined with congressional districts drawn by algorithm rather than politics would completely fix our problems.

Our main problem is that they people who rule over us, hate us. They have no connection to us. They are the globalist oligarchs. They are the multinational corporations. They are international interests.

They are not US.


9 posted on 06/26/2026 11:40:55 AM PDT by nitzy
[ Post Reply | Private Reply | To 1 | View Replies]

To: CathyWhite

I would propose that the ratio of Senators to representatives remain around the ratio of the early Republic to balance states versus population. Otherwise, increasing the number of reps reduces the state influence, tilting towards larger states.


10 posted on 06/26/2026 11:41:59 AM PDT by kosciusko51
[ Post Reply | Private Reply | To 7 | View Replies]

To: PeterPrinciple

Exactly, which would make gerrymandering, gridlock, last-minute-500-page-last-minute-omnibus-bills, 90/10 approval bills that don’t get passed ALL less likely.

And things like Term Limits and Election Reform much More likely.


11 posted on 06/26/2026 11:43:01 AM PDT by CathyWhite (Texans for Trump.)
[ Post Reply | Private Reply | To 5 | View Replies]

To: nitzy

Yes!!

I had AI do the districts for 700 seats. I don’t know how to post the image.


12 posted on 06/26/2026 11:45:00 AM PDT by CathyWhite (Texans for Trump.)
[ Post Reply | Private Reply | To 9 | View Replies]

To: CathyWhite

The Maine/Nebraska model for selection of electors is not bad. Two electors chosen via statewide vote total and one elector chosen by the vote in each congressional district. The current system likely over-rewards candidates winning close elections in a state (as an extreme example, Bush getting 27 EVs in 2000 for winning FL by about 500 votes) and gives at least some voters in less competitive states a meaningful reason to vote (Why would a Republican in CA even bother to vote in a Presidential election, for instance).

The problem is analogous to nuclear disarmament negotiations - who’s going to go first? In the old Cold War days, both we and the Russians would hesitate to give up our arsenals because if we did and the other guys didn’t we would be at their mercy. In like manner, a state that gives up a winner take all approach loses most of its influence in the election if other states don’t also go along. That’s probably why this will never actually happen.


13 posted on 06/26/2026 11:46:47 AM PDT by stremba
[ Post Reply | Private Reply | To 8 | View Replies]

To: kosciusko51
This would effectively prevent larger states from dominating smaller states.

The Senate, with two Senators no matter how small or large the state, is supposed to address that very problem.

14 posted on 06/26/2026 11:47:52 AM PDT by pierrem15 ("Massacrez-les, car le seigneur connait les siens" )
[ Post Reply | Private Reply | To 2 | View Replies]

To: CathyWhite

It would also likely lead to fewer “safe” districts and more where there are actual elections where a member of the House might actually get voted out when they don’t do their job. What a concept!!


15 posted on 06/26/2026 11:48:36 AM PDT by stremba
[ Post Reply | Private Reply | To 11 | View Replies]

To: CathyWhite
The winner-take-all system gives individual states greater clout. The big states get a lot of attention and the smaller states get some whereas they might be ignored entirely otherwise. In 2000 George W. Bush carried New Hampshire by a little more than 7,000 votes. If Gore had won New Hampshire's 4 electoral votes, he would have become President.

Of course it does cause many people to decide it is not worth the trouble of voting if they know that their state goes reliably for one party or the other.

16 posted on 06/26/2026 11:48:46 AM PDT by Verginius Rufus
[ Post Reply | Private Reply | To 8 | View Replies]

To: kosciusko51

Yes but we need to stay within the structure that the Founders intended regarding Congress. We got away from it a hundred years ago when Congress (unconstitutionally?) froze the House at 445.


17 posted on 06/26/2026 11:50:30 AM PDT by CathyWhite (Texans for Trump.)
[ Post Reply | Private Reply | To 10 | View Replies]

To: CathyWhite

But expanding the House does not increase the power of politicians. It dilutes it. Power becomes less concentrated.


Another solutions might be to provide paid vacation for them 360 days per year so they had few days to cause trouble.


18 posted on 06/26/2026 11:50:36 AM PDT by PeterPrinciple ((Thinking Caps are no longer being issued, but there must be a warehouse full of them somewhere))
[ Post Reply | Private Reply | To 1 | View Replies]

To: stremba

And the reps wouldn’t be so beholden to big national sponsors.


19 posted on 06/26/2026 11:52:15 AM PDT by CathyWhite (Texans for Trump.)
[ Post Reply | Private Reply | To 15 | View Replies]

To: CathyWhite

Why would that be true? As a proportion of the whole House, the big states would not have any more representation than they do now. Suppose we doubled the size from 435 to 870. The size of each state’s delegation would simply double as well, and each state would be represented by the same percentage of House members as they are currently.


20 posted on 06/26/2026 11:52:29 AM PDT by stremba
[ Post Reply | Private Reply | To 8 | View Replies]


Navigation: use the links below to view more comments.
first 1-2021-4041-54 next last

Disclaimer: Opinions posted on Free Republic are those of the individual posters and do not necessarily represent the opinion of Free Republic or its management. All materials posted herein are protected by copyright law and the exemption for fair use of copyrighted works.

Free Republic
Browse · Search
General/Chat
Topics · Post Article

FreeRepublic, LLC, PO BOX 9771, FRESNO, CA 93794
FreeRepublic.com is powered by software copyright 2000-2008 John Robinson