How Many Votes Are We Looking For?
Brat won by a margin of about 7,000 votes. We're looking for evidence of 7,000 Democratic voters crossing over to vote for Brat. That's about 5 percent of the total number of votes Obama received in this district. So those are our magic numbers, 7,000 and 5 percent.
How Will We Know When We See Them?
Before we go looking for extra votes from Democrats, we need to know what we're looking for. What would it look like if Obama voters did cross over to vote for Brat?
Let's assume that the chances of a Republican voting for Cantor are independent of the precinct they vote in; that is, a uniform level of support for Cantor across each county. In addition, we need to assume uniform crossover voting behavior. Then, as the concentration of Democratic voters in a precinct increases, Cantor's vote share should decrease. As the number of Obama voters crossing over increases, the effect should grow more pronounced. We end up with a family of curves. Below, the results calculated using the numbers for all of VA-07:
You can see that at 5 percent crossover voters or less, the effects are pretty subtle in precincts with less than 60 percent of the vote for Obama in 2012.
The other effect we would have to see is on turnout. Again, this effect is only obvious at pretty high levels of Obama support:
So do these graphs match the data? Read on.
Where Are We Looking For Crossover Dems?
In order to be able to see anything like in the graphs above, we need to have three things:
1. A reasonable approximation of our main assumptions.
2. Political diversity, with precincts evenly spread over the range of 10-90 percent Obama.
3. Lots of data.
There's only one county that fits the last two criteria reasonably well: Henrico. Chesterfield and Richmond City also fit OK, but could use more data. Families of curves were built matching the turnout and results from each of these counties.
What Do We See?
Henrico County first:
The first thing you should notice is that the data fit the general sweep of the models. That means, yes, we indeed had crossover voting. I assume that this would have occurred in all counties to some extent, not just this one. With that assumption, we can say with certainty that there were indeed thousands of crossover voters.
Second, look at the amount of scatter. That's our assumptions being violated. There's simply a varying amount of baseline support for Cantor among Republicans between precincts, which is understandable. Indeed, from the turnout plot, it looks like turnout increases slightly in more conservative precincts.
Finally, how many crossover voters did we have? Because of the scatter, we're not going to be able to pinpoint a number with any certainty. We can't even tell with much confidence if the 5 percent line or the 10 percent line would be a better fit. But we can feel confident about stating a range, about 5-10 percent.
You can see the relationships on the graphs above on the maps here as well. Henrico County is the crooked n-shaped one half-surrounding Richmond. The bright purple precincts where Cantor did worst are mostly the same as the blue ones where Obama did best, and the dark orange ones where turnout was highest.
Next, Chesterfield County:
Here, the range of crossover voters would be 2-5 percent, but we have only four data points to go by above the 60 percent threshold. The Turnout graph, notably, is essentially flat.
Finally, Richmond City:
Even fewer data here. But, they do show the expected pattern. The range is, again, 5-10 percent.
Looking Back to 2012
Cantor also was on the primary ballot in 2012. If we look back we see similar patterns, albeit with lower estimated crossover. Here's graphs comparing 2014 and 2012 voting patterns in Chesterfield, Hannover, Henrico, and Richmond City. Note that because Hannover is no longer the home base of Cantor's opponent, it "behaves" much better.
So, voters crossing over is not unique to this year. What changed is that this year, many Republicans wouldn't vote for Cantor.
We can also estimate from comparing 2012 and 2014 turnout that Romney voters increased their turnout by about 30 percent, while Obama voters increased their turnout by about 75 percent. These are rough estimates; what is clear is that the increase among Obama voters was greater.
What's That Mean?
Based on the ranges of crossover voting seen above, we can extrapolate to the whole district from the three counties with sufficient data, assuming crossover voting behavior is relatively similar across the district. This range is 4 percent to 8 percent of Obama voters crossing over to vote for Brat, or about 6,000 to 12,000 voters.
If we estimate the number of Obama voters who voted for against Cantor in the Republican primary in 2012 instead of 2014, and increase their number by 75 percent we get ... 6,000 to 11,000 voters.
Remember, the margin of victory was about 7,000 votes.
Without these crossover voters, we can calculate that Cantor would have had 48 percent-54 percent of the vote.
Conclusion: Thousands of Democratic voters crossed over to vote against Cantor, many of whom also did so in 2012. They added substantially to Cantor's humiliation on election night, subtracting at least 4 points from his vote share, and quite possibly sealing his fate.
Hey, Wait! I Want To See More Data!
Sounds good to me. Here's all the precinct data. I've highlighted Brat's home region, where turnout was high, and support for Cantor was very low. You can see that when the Home Court Advantage effect is removed, there's a weak relationship between % Obama and % Cantor. Otherwise, it's just a scatterplot with no relationship whatsoever that would fool you into thinking Obama voters didn't come out to vote against Cantor.
The other five counties don't have precincts where Obama received more than 60 percent, so there's really not much to see. But here they are anyway
Compare the above graph to the one below for 2012 primary results, when Republican support for Cantor was much more uniform across the district, in accordance with the assumptions necessary to identify crossover voting across a region. (Support was still lower in Hanover and New Kent though.) The trend of decreasing support for Cantor in more democratic precincts is clear for the 2012 data.
OK, Interesting But ...
... what about all those other precinct-level analyses that David Jarman talked about in his excellent summary?
Good question. Let's see what happens. We'll use 6 percent crossover Obama voters and 27 percent of the Romney voters, then run some calculations based on precinct data, and compare to the real numbers.
A. Michael McDonald's scatterplot showing lower vote totals in most Democratic precincts. Plotting model results in the same way shows the same shape graph with or without Obama voters crossing over. In other words, it's a Republican primary; the vast majority of voters are Republicans, hence they are more likely to be voting in Republican precincts, which therefore have more voters.
B. Four graphs in the NYT piece here.
Graph 1 - There is evidence of crossover voting. No argument here.
Graph 2 - Turnout was higher in Republican precincts, and Democratic precincts didn't contribute many votes. True, but meaningless. 68 percent of Obama voters live in Republican precincts; their votes will show up on the Republican side of this graph. Anyways, calculations show much higher turnout in Republican precincts with 6 percent crossover Dems, just as with no crossover voting.
Graph 3 - Brat's margin of victory didn't come from Democratic areas. No, it didn't. It doesn't have to. Again, 68 percent of Obama voters are in Romney precincts; if they vote for Brat, their votes will show up in Romney precincts.
Graph 4 - Biggest numerical increases in turnout compared to 2012 primary in Henrico County came in Republican districts. Yes, that's what we would see with 6 percent crossover voting. Why? Because the precincts with the largest number of Republicans are also the precincts where Democrats do the worst. Increase turnout in each precinct by 35 percent, and those with the most Republicans will show the most increase.
One last thing.
So I just showed you that there possibly—maybe even probably—were more than enough votes from Obama supporters to account for Brat's margin of victory. So why do I insist they're not responsible for said victory?
I'm trying to make a distinction between how he won—the exact makeup of his coalition—and why he won. Crossover voters contributed to the win, and were an important part, but the major reason behind it is that Republicans just didn't like Cantor.
Update: For some reason my updates are not working. I'll try again: jpmassar points out in the comments that not all crossover voters would have voted for Brat, which is true. I assumed all of them voted for Brat. If this assumption were severely violated, say only 50% voted for Brat, we would see much of the data for turnout above the 15% curve, which we don't.
Update 2: New post-election polling by Cantor's pollster confirms the numbers in this post. From the new poll I calculated that 5-7% of Obama voters crossed over to vote for Brat, right in the middle of my 4-8% estimate. In reference to Update 1 above, the poll also tells us that about 85% of Obama crossover voters voted for Brat; in other words, in addition to the 5-7% who voted for Brat. My calculations are based on defining 'Obama voters' as all those who say they 'Always' or 'Usually' vote Democratic.
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