What Congress would look like with 100 additional seats

In the formula, which you can see at right, P is a state’s population and n is the number of seats it currently has. The state that has n seats and produces the largest A value at any point in the process is next in line to gain its next seat. The formula ensures at each point that the next seat added goes to the state that (1) is farthest from the average per district population AND (2) does not become farther from the average if it is given an additional seat.

Anyway, that’s the boring math part. Here’s the more interesting democracy part: It’s probably a really good idea to add more seats, given that each member of a 435-man Congress is representing, on average, more than 700,000 constituents, whereas originally, the target was about 30,000 constituents per member. In Federalist Number 55, James Madison discussed the dangers of both a too-large Congress and a too-small one:

One interesting idea, mentioned in a Wikipedia stub but barely anywhere else, is the so-called “Wyoming Rule,” which proposes to add districts until the smallest single-district state (population 568,000) is not so badly over-represented. As it happens, you can get pretty close to that number (average 579,000) by adding exactly 100 districts.

I think this would be great, just because it would improve most people’s representation qualitatively. Quantitatively, though, the benefits are not so evident. I think the folks who have discussed this idea are confused on a number of levels. For one thing, Wyoming is not the most overrepresented state — by a long way, that distinction goes to Rhode Island, with its two districts, average population 528,000. (As we’ll see in a moment, you could add 100 seats to the Congress and Rhode Island, with two seats, would still be overrepresented.)

Second, their discussion seems to suggest that an enlargement of the House would benefit Democrats because it would add clout to larger states like California. This is incorrect. In fact, it would probably make little difference for either party. And large states like California and Texas are the least likely to benefit (or suffer) greatly from a change in the House’s size. Their large numbers of districts guarantee that they are always close to mean representation, no matter how large the House gets, because they can add them at smaller increments without upsetting the average too badly.

To give you some idea of how this all works out, I’ve calculated what Congress would look like if you added 100 seats. Here is the table:

The most underrepresented state in the House right now is Montana, where 994,000 people share a single congressman. If you added 100 seats to the Congress, Montanans would gain one seat and 63% percent more representation in Congress. Californians would lose a small amount of congressional clout.

Other small states like Alaska and South Dakota would suffer in a 535-member House. By the very nature of the process, small states are the most likely to win or lose big in reapportionment. The question of who wins or loses (Delaware, say, or South Dakota?) is really a random one, depending less on the mean population of the districts than on the exact point at which you stop awarding new seats. In this case, South Dakota would get the 536th seat, and ends up being the big loser. No matter how many seats you add, Someone is always going to be on the cusp of getting a new one, and they’re the ones most likely to lose or gain.

The only solution to representational inequity is to abolish statehood — something that cannot be done under the Constitution without the assent of all 50 state legislatures. Another would be to make Congress unreasonably large.