Montana Rising

A Quick Look at How the 2020 Census May Impact Apportionment

Every 10 years, we hold a Census, and within 1–3 years after that, we reallocate representatives to different states based on population figures derived from that Census. The result is a shift in the distribution of Federal political power among the states. Today, I want to take a look at three questions:

1. Under current rules, what states are likely to gain/lose House seats?
2. How would these gains/losses change under different apportionment rules, given a fixed size of the House?
3. How would these gains/losses change under the same apportionment rules, given the admission of DC and Puerto Rico as states?
4. How would these gains/losses change under substantially different apportionment rules, including some allowing for different house sizes?
5. How would these gains/losses change under substantially different apportionment rules and the admission of DC and Puerto Rico as states?

As you can see, this post is gonna be lit.

Baseline Projections: GET IT MONTANA!

I’ll start off with baseline projections. For these, I use a similar method as that adopted by other electoral forecasting groups. I get a tiny bit more detailed because I do individual component-level forecasts of births, deaths, international, and domestic migration, while many people just forecast growth, but the basic method is the same: extrapolate out current trends in growth, see where we land in 2020. Then, like anybody else who apportions electors, I use the formula that Census has used ever since 1940 to apportion House seats.

Normally I wouldn’t bore you with the details, but in this case I will, because I’m going to have some fun with this later on in the post. The formula is:

Where P equals 2020 population, and n equals a state’s representatives before that round of allocations. Every state is guaranteed 1 representative initially, so we run this formula 385 times in 385 iterated rounds. We can also specify it recursively, but for a simple Excel function like I’m running, doing it this way is straightforward enough. Basically, in each round, a House seat is assigned to whichever state will get an assignment that most equilibrates the ratio of population to House seats. It’s a fair-enough way to do it.

The result of my population forecasts and this rule is as follows:

I really like this map, because it shows some neat stuff. First of all, it kind of tosses a wrench into the “Sunbelt” story. Alabama loses an elector, and many Sunbelts from California to New Mexico to Georgia do not add any electors. Meanwhile, we see electoral gains in Montana and Oregon: not exactly your classic Sunbelt states.

Yes, it’s true, many northerly states lose electors: though notably, not all of them! New England actually does fine! And yes, many southerly states gain electors, like Arizona, Texas, and Florida. But this map is not your classic “Sunbelt/Frostbelt” story. Forget that story; complicate your population forecasts. As Rainer Maria Rilke would say, “Live the difficulty.”

I highlighted Montana because I think it’s nifty that Montana will get its 2nd representative back after losing it in 1990.

Alternate Rules Give Different Outcomes

What if, instead of this calculation, we said we didn’t want any states to have more than 800,000 people per representative? Well, it turns out there’s no way to do this without giving some states zero reps, but we can certainly get closer than under the baseline method Census uses.

This may seem like an obviously better method to some readers, but there are trade-offs. The result is some states have really low ratios of people to reps; i.e. Delaware, South Dakota, and Rhode Island. So the question is what you think is more worrisome: states where the congressional districts are too big, or states where the congressional districts are too small. The baseline method Census uses tries to shoot the gap in a mathematically transparent way, but it does create some very, very big congressional districts in small states.

As you can see, this method is rougher on the big states, while being much more favorable to small states.

Many different apportionment methods have been used in US history; the trouble is that most of them assume that the House of Representatives would grow with each Census. One method that was used for a while, called the Webster Rule, produces very similar results as our baseline:

The only difference here is that the Webster Rule only takes away one of Illinois’ seats, and it doesn’t give Montana a seat. Montana’s gain, then, is a fairly direct product of the rules we use for apportionment.

What If We Added New States?

A fun counterfactual is to look what would happen if we kept our 435 representatives, but added DC and Puerto Rico. Let’s look and see.

Adding DC and Puerto Rico results in bigger losses of House seats in New York and Pennsylvania, a loss in California, less gain in Texas, and no gain in Montana. DC would get 1 House seat, and Puerto Rico would get 4.

Let’s assume that of these 5 new seats, Democrats would win 4. Let’s assume that lost seats in other states would reflect the existing partisan mix of House delegations. The result is that Democrats would gain a net of 2 House seats, Republicans would lose a net of 2 House seats vs. 2010. Without PR and DC added, the 2020 changes have a 1–2 seat GOP bias, so this is a significant loss for the GOP.

The notable thing here, however, is that lots of more Democrat-heavy states are on the chopping block to lose representatives if new states were added. I assumed Democrats got 4/5 new House seats from adding DC and PR… and yet they gained just 2 seats, because the effect of adding DC/PR is to spread the remaining 430 representatives more thinly, and the luck of the draw is such that Democratic states are the ones on the margins of losing House seats. Note that even California faces a potential loss!

What If We Allowed a Bigger House?

Regular readers know that I am fascinated by the question of how we scale and structure legislatures. I am very much on board with expanding the size of the legislature.

To see the scale of expanding the size of the legislature, we need to have some new metrics. I’ll use two metrics: the standard deviation of state population/representatives ratio, the total population/representatives ratio. the first metric shows about how equitable representation is across the states, the second shows roughly how big districts would be.

Let’s start with a simple rule: what if we kept the apportionment rules the same, but expanded the house until we reached a point where no state had a decline in its number of representatives? This is basically what we did for most of the 19th century, and the idea is that apportionment won’t unseat any House member, and won’t lead to any state feeling like they have a diminishing voice in Congress. If we do this, then our benchmark state is Illinois, as it had the worst population performance. We end up with 463 members of the house, up from 435 today.

And, as you can see, the map looks different. California, Texas, North Carolina, and Florida all make substantial gains. The whole Sunbelt actually looks pretty good here.

The problem with this method, however, is that it means that the entire nation’s apportionment is beholden to one state’s population trends. Illinois has had some modest population underperformance. Imagine if we’d had Puerto Rico in the mix: you’d have to add a very large number of seats elsewhere for Puerto Rico to maintain its House seats despite rapidly declining population.

This method yields 722,000 people per House seat nationally, versus 770,000 if we keep the numbers locked at 435. Expanding the House yields a standard deviation of 73,000 across each state, versus 85,000 for a fixed 435. The coefficients of variation are 11% for the 435 baseline vs. 10% for the 464 no-lost-seats method. In other words, adopting a “no lost seats” model reduces the degree of variation in how “representative” a representative is, and does so not just by reducing the national average district size, but by actually allocating those House seats more efficiently, i.e. in a way that yields less lopsided districts in relation to one another.

In fact, it’s basically a fundamental law of the Huntington-Hill apportionment method that as population increases, borders remain fixed, total legislative size remains fixed, and the minimum-seats threshold is fixed, that the degree of lopsidedness in representation must increase. We cannot easily change state borders or remove the 1-seat-minimum, and population increase will continue for at least 2 or 3 more Census rounds… which means we can either increase the size of the legislature, or accept increasingly more and more lopsided an unequal districts.

Another popular way to augment apportionment is the so-called “Wyoming Rule,” i.e. the least populous state gets 1 House seat, and every other state just gets its population divided by the least populous state. The Wyoming Rule would, in 2020, yield 577 seats. People per House seat falls to 703,000, suggesting better national representation, and the standard deviation falls to 58,000, suggesting more equality of representation… but the coefficient of variation, at 10.4%, is actually slightly higher than for the simple no-lost-seats method. In other words, the Wyoming rule manages to increase representation, and by increasing representation it equilibrates representation, but it actually equilibrates less compared to the increase in representation than a simple no-lost-seats rule. Here’s a map of the Wyoming Rule effects:

As you can see, thee gains here are a totally different pattern. Any populous state makes substantial gains, regardless of its growth.

But here we have an optical illusion. When we increase the size of the House, some of these gains are illusory; that is, they are new seats, but they don’t increase a state’s share of the House. Here is what the Wyoming Rule looks like, represented as the change in their share of House seats each state would experience.

The Wyoming Rule ends up having a pretty interesting impact on share of the House. Overall, it’s not big: the biggest change, in Texas, is just a 0.6 percentage point increase in their share of the House. Most of the northeastern states are worse off, the south is a mixed bag as are the great plains, the mountain west and PNW make gains, while California, Alaska, and Hawaii lose out.

Assuming state-level party shares are stable under the Wyoming rule, which might not necessarily be the case, this implementation would result in a very small decrease in the GOP share of the House, from 55.4% to 54.3%.

But hold on. This incorporates both the Wyoming Rule and the 2010–2020 changes in population. What we really want is to isolate the Wyoming Rule vs. normal Huntington-Hill for 2020.

Here, we see the raw effects of the Wyoming Rule. And those effects are… very weird. The Wyoming rule helps a fairly hodge-podge set of states. Mostly, these effects are driven by the exigencies of Huntington-Hill-style rounding being different from Wyoming-rounding. The larger the size of the legislature, the smaller these effects would be. But, on net, a shift from Huntington-Hill to Wyoming Rule would reduce Republican control from 54.7% under Huntington-Hill in 2020 to 54.3% under the Wyoming Rule.

The point of this is to note that it doesn’t matter very much for partisan control how to apportion House seats. As long as it’s any one of the many above-board, mathematically transparent, population-based methods, you will get very similar results, with differences largely accounted for by rounding errors.

This continues to the electoral college as well. If the 2016 election had been conducted with the 2020 Wyoming Rule House as its House base, plus 100 Senators, the outcome would have been the exact same. President Trump clocks in 388 electoral college votes in that scenario, versus 292 for Clinton. In fact, under the Wyoming Rule, the margin of victory is even more extreme: Trump nets 33% more Electors, rather than 31% as actually occurred (I count based on state committed electors, not the actual votes those electors cast).

This is your regular reminder that what creates electoral college weirdness isn’t misallocation of House seats, nor the presence of Senatorial electors, nor the weird shapes of states, but WINNER TAKE ALL. The only thing you need to change if you want to create radically different electoral outcomes and incentives is widely-adopted winner-take-all.

What If We Add States And Adopt New Rules?

Let’s get crazy now.

Let’s add DC and Puerto Rico into the mix, and adopt the Wyoming rule.

Uhhh… nothing changes.

See, here’s the trick with the Wyoming Rule: it doesn’t matter what states you add, or how population changes in any other state other than the least populous state. All that matters is the state in question’s population, and the population of the smallest state. So Puerto Rico would get 5 House seats (7 electors). And it wouldn’t substantially alter any electoral outcomes except a few close house votes, and of course it would significantly impact the Senate to add 4 new senators for DC and PR.

Including Puerto Rico in the long run could have a big impact under the “no seats lost” rule. Had Puerto Rico been included in 2010, it would have had 5 House seats. In the interim, it has lost 600,000 people. As that trend continues, it could become difficult to maintain Puerto Rico at even just 4 seats. Puerto Rico is near the high-ish side at 790,000 people per representative, which means it isn’t in immediate danger of being cut… but a decline to 3 representatives by 2030 is plausible.

What’s Best?

The optimal size and structure of the legislature is a theoretically fraught problem, and one our Founders debated in some length. They were of the view that either a very small or a very large legislature was bad. They also used apportionment methods that required them to explicitly have in view a certain population-to-representatives ratio, and, as long as that method was maintained (until 1842), they kept that ratio below 60,000. By 2020, we will be at nearly 800,000.

Of course, one person can effectively represent more people than in the past. We provide legislators with larger staffs, they have been telecommunications, more supporting civil institutions, faster transportation, etc. It is not as imperative that we have one House member per 60,000 people as in the past.

On the other hand, government has become more complex. We expect government to do more things, carry out more invasive tasks, and address far more technically burdensome issues. Likewise, we have centralized a substantial amount of power in the Federal government.

So there are some arguments for allowing the population-to-representatives ratio to rise, and there are some arguments for not letting it rise too much.

My hope is that when the reapportionment bill is being debated. members of Congress will thoughtfully consider how the nation is best represented, and not merely take the choices of 1912 as some kind of de facto constitution. They aren’t. The rules about how many people we elect, how we elect them, and even where, when, and how they meet are not set in stone or even in the constitution, but rather are a question of changeable law and practice, and thus worthy of revisiting and questioning at regular intervals, such as the decennial census.

Check out my Podcast about the history of American migration.

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I’m a native of Wilmore, Kentucky, a graduate of Transylvania University, and also the George Washington University’s Elliott School. My real job is as an economist at USDA’s Foreign Agricultural Service, where I analyze and forecast cotton market conditions. I’m married to a kickass Kentucky woman named Ruth.

My posts are not endorsed by and do not in any way represent the opinions of the United States government or any branch, department, agency, or division of it. My writing represents exclusively my own opinions. I did not receive any financial support or remuneration from any party for this research.