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The Not-So-Great Gerrymander: A Neuroscientist Flunks Statistics

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In a New York Times story, a neuroscientist from Princeton finds an evil Republican plot, but it's all in his head.

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In yesterday's Sunday New York Times, Sam Wang, a neuroscientist from Princeton, charged the Republican party with "the Great Gerrymander of 2012." Gerrymandering is the drawing of political district lines in order to secure favorable election results, usually the protection of incumbents who either are the people drawing the lines, or the people hiring the people to draw the lines. While this is a bipartisan offense, gerrymandering can also be used in a partisan way to create a few districts packed with lots of opposition voters and many districts with moderate majorities of supporters. Historically, this tactic has often been used to reduce the representation of racial minorities.

In the election of 2012, 1.4 million more votes were cast for Democratic candidates for the House of Representatives than for Republican candidates, yet Republican candidates won 33 more seats. The immediate cause is that winning Democratic candidates won their elections by more votes on average than winning Republican candidates. There are several possible explanations for this; Democratic districts could be larger on average, or have higher voter turnout, or be less politically balanced than Republican districts. These factors, in turn, could be the natural outcome of honest procedures for drawing electoral boundaries, or they could be the deliberate result of partisan gerrymandering.

Professor Wang claims to "have developed approaches to detect such shenanigans" and "found strong evidence" that Republicans have engaged in "partisan disenfranchisement" while Democrats are innocent of such tactics. What he has actually done is commit an elementary statistical fallacy.

Before going further, let me state that I have no strong opinion on the subject; this essay is about statistical malpractice, not partisan politics. My casual impression is that many places try reasonably hard to set districts fairly, while other places do whatever they can get away with, and the parties are about equal in their records. I see more evidence of bipartisan gerrymandering to protect incumbents of both parties than partisan gerrymandering to favor one party over the other. And I'm perfectly willing to believe in evil plots by politicians, I just don't accept this evidence for this evil plot.

Also, the issue of gerrymandering is more complex than Wang's simple vote counting. It is possible to have elections in which the winner of the popular vote always wins. Two common systems with this property are popular vote elections (like state gubernatorial elections) and proportional representation (like many countries have for their parliamentary bodies). Using geographic districts sacrifices this property deliberately for two main reasons.

The first is the degree of respect for minority rights. In winner-take-all popular elections, 51% of the population can ignore the other 49%. In proportional representation, strategic disciplined minorities can exert influence far exceeding their numbers. Single-issue parties in particular have excessive power. Geographic districts produce intermediate outcomes, moderate respect for minority rights, while allowing the majority to get things done. Some of the time anyway.

The second main reason for geographic districts is vote total differentials can be inflated by local partisans, both in illegal ways and ways that are legal but extreme. Awarding seats according to geographic districts eliminates the incentive of local factions to run up the vote differential in their districts.

Aside from the statistical problems that are my main interest, Wang's analysis is really an attack on geographic districts in general, not a measure of how honestly or dishonestly those districts were drawn. There are arguments for and against geographic districts, but Wang doesn't make them, he just misinterprets his statistical results.

It's also not clear that there is an advantage to gerrymandering districts in the way Wang thinks he has proven Republicans do it. The result would indeed be more Republicans in the House of Representatives. But those Representatives would come from more balanced districts than Democrats, forcing them to more moderate positions, and to be more respectful of people who disagree. They would be less certain of their seats, less effective at raising money, less able to act on long-term partisan strategy as opposed to short-term political expediency. The effect on political outcomes would be complex. Only in a simple cynical zero-sum party vote-counting game is gerrymandering a clearly positive strategy.

What is Wang's evidence for Republican chicanery? The first thing he does is announce there are five states in which one party got more votes in Congressional elections, but got fewer than half the contested seats (it's not clear if he's counting Senatorial elections in this tabulation, and I can't reproduce his results exactly under either assumption, but the differences are minor). This is not surprising news, since it's also true for the country as a whole. In four of these five states the advantage in representation went to Republicans.

One obvious problem is four out of five is weak evidence on which to accuse one party of being worse than the other. If you flip a fair coin five times, you'll get four or more of either heads or tails three times out of eight, so it's perfectly plausible that the parties are equally guilty but Republicans happened to win in four of the five cases.

Then he gets "more subtle" (I'm not sure what would be less subtle than his initial analysis) and assigns nationwide congressional districts to states randomly and measures how extreme the actual number of Congressional seats is compared to results from random resamplings.

He does not explain this very clearly, but here's what I think he did. In North Carolina, his example, Democrats got 51% of the Congressional vote, but won only four of the 13 seats. Pick 13 congressional districts at random throughout the country, and check if they add up to 51% of the total vote for Democrats. If so, count how many of the districts elected Democrats to Congress. Record that number and repeat a few thousand times. He found less than one simulation in 100 did Democrats win only four seats (I assume he means four or fewer, which is the right way to do this, but I'm not sure).
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