# Senate Elections: An Explainer

After yesterday’s elections, I’ve started to see commentary like “the Democrats got most of the votes but they LOST ground in the Senate; American institutions are anti-democratic and broken!” While there are a lot of issues with American political institutions, many of these takes rely on bad math and confuse different levels of the problem. This essay hopes to clarify four distinct layers at which US Senate elections might produce counterintuitive results, so that our commentary can be better informed.

I. The Existence of Districts

Suppose that we have a country, Polistan, with two political parties, the Greens and the Yellows, and a two-seat legislature.

Polistan is a democracy. How should they choose their legislators?

One method would be to hold an at-large, party-list election. All of the Polistan voters (which is every adult citizen, Polistan is a civilized country) write down “Green” or “Yellow”, and then the votes are counted. If 100% of the votes are Green, the Greens get both seats, and vice versa if 100% of the votes are Yellow. If the votes are split exactly 50–50, then each party gets 1 seat.

Even this system has some problems! Suppose the election is unequal; how should the seats be distributed? We might say: have the balance of seats most closely approximate the distribution of ballots—so if the Greens get 60% and the Yellows 40%, each should get one seat, and the cutoff for the second seat would be a 75% victory for one party. We can see how this could be pretty frustrating—imagine if the Greens win 74% of the vote but can’t pass a single law because of the minority Yellow legislator—but every other cutoff will cause its own problems. Imagine if the Yellows win, say, 48% of the vote but have no representation in the legislature!

Increasing the number of seats will simply shift the problem from one type to another. If you have 100 at-large seats (and the Greens and Yellows have high party discipline), then a 52% victory by the Greens will lead to a 4-seat majority, and in turn unilateral control over government. Legislative outcomes would be substantially the same as saying “whichever party wins more than half gets both legislative seats” in the two-seat scenario, and it’s easy to see how this can be enormously unpopular.

Another method for choosing legislators is to divide Polistan into districts. Commonly these districts are geographic, for practical reasons, but they need not be. All we need to do is put half of the voters in District 1, the other half in District 2 and have them vote “Green” or “Yellow”. Whichever color wins in a district chooses that representative.

Now, this seems simple enough. But here we have a problem! Suppose the Greens win 60% of the overall vote. If the two Districts are pretty much the same—say, we randomly mailed each Polistani a “1” or a “2” and had them vote accordingly—then the Greens will win the elections in both districts, and they’ll pick both legislators and have unanimous control over the government. That won’t sit well with the Yellows.

On the other hand, we might sort the parties out by district—maybe Yellows live in the West and Greens in the East and we divided the country geographically. Imagine that the district sort perfectly by party—that is, everyone in District 1 is More Green (whatever that means) than anyone in District 2. Then, if the Greens win 60% of the overall vote, they’ll get to 100% in District 1 and only 20% in District 2. (Ten percent of the national voting population is District 2 Green voters, which is twenty percent of District 2’s voting population.)

That brings us back to the at-large problem we had above: the Greens command a substantial national majority but face only deadlock in the legislature. The Greens would need to win 75% of the overall vote—every single District 1 voter, plus half of the District 2 voters—in order to capture the legislature.

Okay. Enough with Polistan; what overall observations can we derive here?

In “at large” voting, we had to choose how a popular vote margin could convert into a legislative margin. Our dials and levers here were the numbers of seats and the mechanism of victory. No matter what we chose, someone was likely to be unhappy—either a slim minority with no meaningful representation, or a substantial majority facing a minority blockade.

In district-based voting, we faced the SAME question: what should a popular vote majority mean in the legislature? But we had a DIFFERENT mechanism of control: the composition of districts! When the districts were politically similar, a small popular vote margin translated into a substantial legislative margin. But when the districts were politically dissimilar, a substantial popular vote margin translated into a limited legislative margin.

The similarity between different electoral districts was the input that converted a national popular vote victory into different levels of strength in the legislature. In general, many similar districts is a huge force multiplier for slim national majorities—in theory a tiny majority can capture every district by the same tiny margin. On the other hand, dissimilar districts blunt the impact of a national majority, and lead to a legislature with a composition closer to the breakdown in votes.

Now, as long as there’s a large number of districts and no jiggery-pokery in district composition (both of which are sort of ANGRY SHRUG EMOJI levels of true for the US Senate), the legislative majority shouldn’t be much smaller than the electoral majority. That is, if you win e.g. 60% of the votes you should get at least 60% of the seats, if not more.(Your limit case is where you win every vote in the first 6 districts out of ten, and zero votes elsewhere.)

Okay.

II. The Existence of Classes

Not in the Marxist sense.

US Senators serve six-year terms. However, we hold elections for the senate every two years. How?

Each Senate seat belongs to one of three “Classes”, imaginatively named Class 1, Class 2, and Class 3. (If you want to be classier, you can use Roman numerals. I won’t.)

Every two years, the Senate seats in the next class come up for election. So in 2018 we had a Class 1 election; in 2020 we’ll have a Class 2 election; in 2016 we had a Class 3 election, etc.

Each state has two senators, and both of those senators belong to different classes. So each state belongs to 2 of 3 classes. California, for example, has a Class 1 Senator (Diane Feinstein) and a Class 3 Senator (Kamala Harris).

That means that in each Senate election, a different subset of the country is on the ballot.

Because what matters is majority (and/or supermajority) control of the chamber, reporting doesn’t tend to focus on this. Instead, it focuses on whether the parties make gains or losses in the Senate, and where they end up.

But that can substantially distort our perspective on the events of the election. In the 2018 election, there were 35 Senate seats up for grabs. (33 seats in Class 1, plus 2 special elections.) The Democrats won 57% of the vote, according to the NYT. They also won 21/35 seats, or 60% of available seats. We could drop the special elections, which didn’t change anything in the other classes, and re-describe this as a 20/33 victory in Class 1, or 61%.

(All numbers as of this writing; depending on how AZ and FL go, Democrats may pick up two more seats but I wouldn’t count on it.)

In other words, Democrats outperformed their popular victory in the legislature.

Let me say that again: Democrats won more seats in the Senate than their popular vote margin would suggest.

And yet the Democrats lost ground in the Senate. Why?

Well, in 2012, the last time that Class 1 was up for election, the Democrats won 54.7% of the Senate vote, and 25 of the 33 races—76%!

Now, on the one hand that sounds kind of nuts—a 10 point popular vote margin converted into a 50 point margin in the legislature. (Wrt Class 1.) But that’s the natural outcome of having many similar districts. What happened this year was that the force multiplier of a wave election declined.

And, since the Democrats lost ground in Class 1, they lost ground in the Senate overall. Class 2 and Class 3 are both substantially more Republican than Class 1, which translates to an overall Republican majority in the Senate.

But if the Democrats can win nationally in the upcoming Class 2 and 3 elections, they can (in theory) convert that national win into a larger Senate majority. The numbers as yet don’t imply an a priori antidemocratic (or anti-Democratic) outcome. They just suggest that the Senate is moving away from “all the states vote similarly” towards “many states vote differently.”

That said, there ARE two major countervailing forces in the Senate which have to be acknowledged, and which probably exerted their own influence on the outcome, and which are likely to worsen over time.

III. The Inequality of State Populations

This is the big (heh), obvious one. Every state gets two Senators, regardless of size. That means that parties with proportionally greater support in smaller states can dominate the Senate despite losing the overall national popular vote. This inequality is bad today, and it’ll only grow worse as states continue to drift apart in overall population.

IV. The Accidental Gerrymander

In our two-district toy model above, it was always the case that the party with more votes did not have less representation in the legislature. That’s a limited condition and it allowed a bunch of stuff we don’t like, but it was a condition we met.

Unfortunately, once you introduce just 1 more district you create the possibility of gerrymandering. Imagine a three-district election, where all the districts are equal size. And imagine the Greens get 100% of the vote in District 1, and 49% of the vote in Districts 2 and 3. Then we have a Yellow-Majority legislature (66% Yellow), even though the Greens won ~66% of the overall vote.

That’s bad, and we can agree that it’s bad. It’s tricks like this that left the House uncompetitive from 2010 to today.

It’s not AS bad at the state level, because state borders can’t be moved around and so you get what you get. But it is of course possible to have an accidental gerrymander, and in fact it often occurs; the map of states happens to favor this party over that. Such favoritism has been historically transient and quickly-shifting, though if the party lines begin to map more clearly to state attributes the accidental gerrymander of history might settle more firmly into one camp rather than the other.

V. Synthesis

The thing is, state inequality and gerrymandering are real and scary. But they didn’t win last night. The Democrats won the majority of votes. And they won a greater majority of seats. That’s traditional and appropriate in a district-based legislative election. To the winner go the spoils.

Another and more concrete way to put it is: if every single Senate seat had been on the ballot yesterday, and the if Democrats converted the national mood (6.9+ Dem) into Senate seats as effectively as they did overall—both big Ifs, but not absurd ones—then there would be about 57 Democratic Senators overall.

Maybe in a future election things will be different, and state inequality and gerrymandering will overwhelm voting power. Maybe the Democrats will get 60% of the vote and 55% of the seats, which might be spun as a victory or a loss, depending; maybe they’ll get 55% of the vote and 45% of the seats, which would be a catastrophe.

It’s also possible that these two factors will represent a persistent headwind, and if the Republicans get increasing winner’s bonuses while Democrat winner bonuses decrease, the inter-annual effect can be the gerrymandering away of political power in the Senate. If the Dems win Class 1 with 60% of the vote and get 60% of the seats, and the Reps win Class 3 with 51% of the vote and get 70% of the seats, there’s a net gerrymander even if every individual election obeys the rule that the winning party gets at least the percentage of seats they get of votes.

And, lest we forget, the Republican platform is Actively Very Bad, and deserves morally to lose regardless of whether electorally it deserves to lose. And vote suppression, which helps Republicans, is a moral travesty and deserves to die in a only-just-barely-metaphorical fire.

BUT. We shouldn’t be confused about which factors are at play and which ones are not. I hope this very lengthy explanation has been of help.