Monday, December 10, 2018

The Popular Vote vs. the Map

In 2012, Democrats were outraged at the gerrymandered congressional map. They won the national popular vote by 2.5 million votes (once you account for uncontested races), but lost the house 234-201.

This time, there hasn’t been as much outrage, because Democrats managed to win despite the map. Some people[LINK] on the right have been saying that the congressional map was in fact fair this election, because Democrats’ share of seats approximately equalled their share of votes. That’s really misleading.

The congressional map remains plenty biased. Democrats won 235 seats and 6.7% of the vote (more on how I arrive at 6.7% later). Republicans could have won 235 seats with only 1.1% of the vote. That 5.6% difference is what Democrats needed to overcome the congressional map. Talk about doing it backwards and in high heels! (I shouldn’t say this).

I modeled how the 2018 election would have gone under different popular vote shares. To get the outcome under a popular vote tie (0% margin), for example, I shifted each district by 6.7%. There were 204 districts that Democrats won by more than 6.7%, that were more liberal than the nation as a whole, and 231 that were more conservative. That means that if the parties had gotten the same number of votes, Democrats would have lost the House. (This isn’t exactly how I did it; I assumed swings were linear in log odds and accounted for how many voters were in each district.)

Majority (218) Proportional Republicans Democrats 235 235 255 255 0 100 200 300 400 Seats -100 -50 0 50 100% Popular Vote Margin

One thing that jumps out at you is the winner-take-all districts. With winner-take-all, when you win, you win big. Under proportional representation, if a party wins 25% of the votes, they get 25% of the seats. In winner take all, they get less than 10%. But winner-take-all doesn’t have to be unfair to one side or the other. The bias is the gaps between the lines.

Democratic voters are packed into heavily Democratic districts, so they’re guaranteed a larger base. If Republicans won overwhelmingly, winning the national popular vote 75%-25%, they’d still lose 34 seats. That’s Democrats’ large base. Those 34 districts are in cities, including 9 in New York City alone, and 31 of the 34 are majority minority (the majority white ones are in Manhattan and Seattle).

On the other hand, if Democrats won 75-25, they’d win all but 12 seats. Democrats would sweep Louisiana, for example, where there are 5 districts that are currently 70% Republican. So Republicans’ base of guaranteed seats is smaller.

But it doesn’t help to have more seats you’re guaranteed to win; the goal is to win a majority. Unless we switched to two-member districts (like we had in the early 1800’s), running up big margins in your strongest districts doesn’t help. And because Democrats are packed in their blue islands, the swing districts are more conservative than the nation as a whole.

Here’s a close up of the plausible vote totals (60-40 or closer).

235 235 255 255 Majority (218) Proportional 200 300 Seats -20 0 +20% Popular Vote Margin
Democrats needed to win the popular vote 51.4-48.6 for a majority. We would have had a repeat of 2012 if Democrats had again won by 2%.

Gerrymandering or Geography



So far, I haven’t said anything about whether this gap is driven by gerrymandering (Republicans drawing districts that pack Democrats together) or geography (Democrats live around other Democrats). Both of those could explain why swing districts lean Republican. To answer this question, we need to know what a non-gerrymandered map would look like. But how do you define that?

Dave Wasserman at FiveThirtyEight drew hypothetical congressional maps by following a few different rules. One rule was to make districts as compact as possible. That results in hilarious-looking circular districts. Another, more plausible, rule was to make districts as compact as possible while trying to follow county borders. Here’s Michigan as an example.


So how fair are these un-gerrymandered, compact districts?

Actual Districts Compact Districts 249 235 235 255 255 100 200 300 Seats -20 0 +20%   Popular Vote Margin

They’re better, but they’re not fair. Democrats need to win by 1.9% for a majority, instead of 2.9%. Getting rid of the gerrymandering is an improvement, but those lines aren’t that much closer together. Much of the gap is geographic reality.

We can measure the extent of gerrymandering by comparing each state’s current map to the compact maps. The compact districts aren’t drawn with partisan intent, but they do advantage Republicans. You could call the bias from So this is a measure of malicious gerrymandering, beyond what you’d get drawing compact districts.


Texas, Ohio, Florida, and North Carolina are known to be the worst offenders, so it’s good to see them at the top of this list. On the other side, California’s districts were drawn by an independent redistricting commission. But the commission drew competitive districts, and in the ensuing wave, Democrats swept them.

Below are the results for six different maps that FiveThirtyEight drew. The competitive map is intended to have the maximum number of swing districts, and the proportional map is intended to make each state’s delegation proportional to its vote.


You can see that the round compact districts and the county-based compact districts produce almost identical results. It’s also interesting that the gap is bigger at higher Democratic vote shares, suggesting that gerrymandering protects Republican incumbents more than it adds new Republican seats.

Getting the Right Total for the Popular Vote



So about that 6.7% figure for the popular vote. Democrats won 53.4% of the vote, while Republicans won 44.8%. That’s an 8.6% margin of victory. But there were 42 uncontested races, and 35 of those were Democrats without a Republican challenger. Instead of giving the winner 100% of the vote in those districts, I filled in the results by assuming they swung the same amount from 2016 as other districts (actually the same amount after a log odds transformation). That yields 6.7%.

Now some people have been comparing the 8.6% figure against Republicans’ 2010 margin of 6.8%, or their 1994 margin of...also 6.8%. Was Democrats’ 2018 wave actually smaller than those Republican waves? No, because in 1994 and 2010, 30 and 24 Republicans ran unopposed (compared to 14 and 5 Democrats—sensing a pattern?) The Economist made an effort to correct for this, and while I don’t know their method, they got adjusted margins of about 5% for each of those Republican wave years. Here’s their graphic with 6.7% for 2018 added.


In the 2016 Presidential and the 2012 House elections, Democrats won the popular vote by 2% and lost the election. Republicans won 7 more seats 2010 than Democrats won this year, despite getting fewer votes. That bias in the system is here to stay. So tune out anyone who says Democrats’ victory wasn’t convincing—no one said that in 2010.

The code and data are available on my Github, and you can find more thoughts on data, politics, and economics from me on Twitter. Credit to Dave Wasserman, whose popular vote tracker and district maps are the basis for the above.