The mathematics of the 23rd Amendment

This quetsion is a spin-off from the DC statehood Great Debate, but I suppose it better fits in the Election board.

As is well known, the number of electors each state gets in the Electoral College is equal to the sum of its senators and representatives. In other words, it is the number of its representatives plus 2.

DC is not a state, but under the 23rd Amendment it gets a number of electors that is equal to the sum of the senators and representatives that it would have if it were a state (though subject to a cap that it cannot have more electors than the least populous state). This gives DC three electors, as it would have one representative if it were a state.

What I’m wondering is how this can be squared with the fact that the total size of the House is fixed at 435. This total number is reallocated after each census to take population shifts into account, but an increase in the overall population does not increase the total number of representatives; it simply shuffles those 435 representatives around among the states. That means that if DC were a state, it would get one representative, but that would mean that some other state somewhere would get one less representative than it has in the DC-not-a-state scenario.

In other words, doesn’t the 23rd Amendment mean that the allocation of electors to the states should be based not on the actual number of senators and representatives that the fifty states have, but on a hypothetical House of Representatives as it would look like if DC were a state, with one state somewhere having one fewer representative, and hence elector, than it really does to make way for DC? To my knowledge, this is not done; the three DC electors come on top of the 535 electors for the fifty states, for an overall total of 538.

There is no partisan motivation in the question, I’m just wondering what the mathematics behind the “whole number of Senators and Representatives in Congress to which the District would be entitled if it were a State” clause are.

I think that, strictly speaking, you would need to do the full calculation as is DC were a state, under which some other state would lose one (or more) representatives, in order to determine DC’s electoral votes. But then, once you found that number for DC, you would then throw out everything else about that calculation, and calculate again without DC to determine the sizes of House delegations. Because even though it gets electors, DC does not have representatives.

Doing it the way you suggest would result in 434 representatives, because someone would lose one but DC wouldn’t actually gain one to make up for it.

Of course, it’s all moot anyway, because so long as we have even one state small enough to have only a single rep, DC’s number is always 3.

The language doesn’t say anything about the total number of electors, but it does indicate the number of DC electors is based on the apportionment as if it were a 51st state as you indicated. But it is not creating an actual state representative, affecting the total number of representatives, affecting the actual apportionment, or considering a limit on the number of electors. It clearly means that when the number of representatives is set by law at 435 that there will be a total of 538 electors, 435 representatives+100 senators+3 DC electors (assuming no others).

This could get a little tricky if every state had more than one representative and DC population reached the point where it could warrant two representatives. The apportionment when DC is considered a for this purpose state could require a slightly larger population than an actual state with 2 representatives.

Speaking just to this snip …

The 23rd is an amendment. The 435 number is fixed by ordinary congressional legislation and could be altered at any time for any reason, sound or unsound.

But yes you’re right that the mathematical “formula” set out in the amendment is ambiguous as to whether it’s computed on the house as it is, or the house as it would be were DC a state which had reps.

To a certain degree, the latter computation is either circular or moot depending on how you want to interpret it. If DC were a state, then we’d calculate the House in the usual way but with 51 states and DC would have the electors that calculation produces. No different than any other small (or large) state. But if we’re going to use that calc, we wouldn’t need the 23rd amendment.

Therefore by elimination it’s an artificial calc best based on ordinary 50-state reality as it is, not hypothetical 51-state reality.

Though I admit that’s a lot more hand-waving of an argument than I wish it was.

Digging into the legislative history of the 23A would perhaps be definitive.

What is the ambiguity?

As the OP explained:

If the district were a state, then you’d be allocating the 435 across 51 states not 50. And if the size of DC and the other small states were different enough that might produce a different result for DC versus if you did the calculation with 50 states and DC sitting out as we do now.

The plain text does not say which formulation to use. It’s a failure of the author’s imagination not to the see the two very different interpretations.

As a practical matter the difference will be moot until we have a lot larger house than 435. Because we have so many states that are getting the minimum 1 rep. But remember again that the 23A is an amendment. So it has to work even if we expand the HoR to 6000 reps as is often suggested to right the obvious unconstitutional wrong that rural states voters have so much more congressional power than urban area voters.

Imagine in that case that DC would get 2 reps in a 50-state apportionment but just 1 in a 51-state apportionment. That would be a tough problem to sort out.

Right now it’s 1 rep under either calc, so the difference is moot. But it’s there.

So you think the text could reasonably interpreted to mean ‘to which the District would be entitled if it were one of the existing states’? To me that adds unspecified parameters. I suppose it could have been much clear by specifying ‘an additional state’ or ‘an existing state’.

Also, assuming that it means an existing state, then which one? There’s no specification for that, it could mean Delaware or California, or and of the rest.

I’m not advocating for this position. I fact my first post argued back to the OP @Schnitte against that interpretation. I’m simply explaining now what the ambiguity is. I agree with you that it’s a slightly strained reading.

But if the stakes ever become non-zero, I predict there will be a battle over it.

My reading is that you have a way to interpret the language so that it produces a non-ambiguous result, and another way to interpret it that can’t. I go with the former.

Yeah, there would be a battle if this situation ever does occur. It is extremely unlikely to ever happen.

I guess if DC became a state, then the 23rd Amendment would be void.

It doesn’t say that anywhere but I assume getting statehood approved would entail an amendment voiding the 23rd. And maybe altering other parts of the constitution as well.

That’s also my understanding. The constitution says that a district under the control of the federal government exists, so statehood for all of what is now DC would require a constitutional amendment since there would, after this move, be no constitutionally required federal district left. Statehood for most, or almost all, of what is now DC could be achieved by means of ordinary legislation, without a constitutional amendment, by reducing the size of the District of Columbia to possibly a tiny bit, e.g. just the National Mall and surrounding building and monuments, and admitting the rest of what is now DC as a state. Thereby the constitutional requirement that there must be a federal district would be met. But then that remaining small bit would still be entitled to three electors under the 23rd Amendment, chosen in a manner determined by Congress.

Isn’t the amendment only about the number of electors D.C. gets, not about the number of electors any of the states gets? Yes, if D.C. were a state, that could affect the number of representatives, and therefore electors, some other states had; but as I interpret it, the 23rd amendment only cares how many representatives D.C. would have, not how many other states would have.

That is actually what I was getting at. I’m wondering whether the 23rd Amendment has the consequence that the entire calculation of representatives for the purposes of determining the number of electors has to be based on a hypothetical “what if DC were a state” scenario, rather than a “take the number of senators and representatives that each state has in reality, and then add three for DC” scenario. The two calculations would arrive at the same result for every state, except for one, which is the state that would have to give one of its representatives to DC.

Except DC doesn’t actually get a representative. It gets an elector. So there’s no reason why a state has to give up its representative.

Think of it as a two step process.

Step 1: Act as if the District of Columbia is one of fifty-one states and figures out how many representatives it would get. Give it that many electors. All actual states ignore this step.

Step 2: Do the process again. Ignore the District of Columbia this time. Apportion the fifty states their representation based on their populations.

As I interpret it, the amendment is not about the “entire calculation of representatives.” It’s just about how many electors D.C. gets, and has no effect on anything else (like the number of electors any (other) state gets).

Be careful about assuming—when it comes to apportionment of representatives, there are “paradoxes” that can occur when you change one little thing, like the “New States Paradox”: