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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).

In this analysis, he turns up five more states in addition to the five above, with extreme discrepancies between statewide Congressional vote totals and actual seats won. It gets confusing here, because his figure also shows 10 total states with issues, but only nine of them are mentioned in the text.

Wisconsin is in the text but not the figure, Indiana the reverse. I'll chalk this up to an editing error and say he finds 11 states with issues. Six of them favored Republicans, three favored Democrats and Indiana and Wisconsin seem to be in between but leaning Republican.

We're still nowhere near conventional levels of statistical significance, even if we call this eight Republican cheats to three Democratic. That is we do not have the claimed "strong evidence" of "partisan disenfranchisement"; the data so far are consistent with equal opportunity gerrymandering. However, there is something more striking about the data. Wang has just listed the large swing states in the election. That's no coincidence. If you look at the map in the article, the states form a fairly tight grouping which should have alerted him that he was looking at something other than election fraud.

Wang's test has nothing to do with gerrymandering. All we're finding is the states in which the geographic districts made the most difference, and there will always be such states. It doesn't matter how we draw the boundaries, some states have to be most extreme. However, those states will not be random states, they will be the large states and the states in which Republicans and Democrats are most closely matched.

It's easiest to see why with Wang's initial criterion; the party that got more total votes in Congressional races got fewer than half the Representatives. This cannot happen in Delaware, Alaska, Montana, Vermont, Wyoming, or either Dakota. Why? Because those states have only one Congressional district each, the winner of the district will have all the seats for the state, thus more than half. It also cannot happen in Hawaii, Rhode Island, Maine, New Hampshire, or Idaho, the states with two districts each. The statewide winning party has to win in at least one of the two districts, thus get at least half the seats.

It is possible in a three-district state; for example, the Democratic candidate could win one district by 100,000 votes, while Republicans could win in the other two by 20,000 and 30,000 votes. Democrats would have taken the state total by 50,000 votes, but won only one-third of the seats.

Although this is possible in the three-district states -- New Mexico, Nevada, Nebraska, West Virginia, and Utah -- it is unlikely. The party that wins two-thirds of the districts in a state is likely to win the total vote. Compare this to California, with its 53 districts. In that state a party that won 27 districts could much more easily do it on fewer votes than the party that won 26. That's why all the states on Wang's list have more than the median number of districts.

The other thing that makes it easy for the party winning the total vote to get fewer than half the seats is if the state is close to evenly split among the parties. If one party gets 90% of the statewide vote, it's hard to lose more than half the districts. But if it has 50% plus one vote, it's quite easy. This is the reason all the states on Wang's list had vote splits closer to 50% than the median.

In fact, if you take the 25 states with more than the median number of districts, and the 25 states with vote totals closer to 50% than the median, you find 14 states on both lists. All 11 of Wang's states are in this group. All he has done is found an expensive way to identify the big swing states, then somehow convince himself the existence of big swing states is a smoking gun for Republican electoral malfeasance.

The big swing states will almost always be the ones in which the statewide total vote goes one way while the state Congressional delegation goes the other. Although the analysis is more complicated, for the same reasons the big swing states will be the ones that come up most extreme in Wang's simulations. When I simulate Montana, I pick one district in the country where the Republican candidate won 55% of the vote that went to the two parties. That district will always have been won by a Republican, which will match Montana's result exactly.

When I simulate Idaho, I have to find two national districts whose combined vote was 67% Republican. Almost all of those pairs will be two districts that went Republican, which matches the Idaho result, so Idaho will not look extreme.

But when I simulate North Carolina, things are different. I have to find 13 districts that combined for a 51% Democratic vote. Most of these sets will have between five and eight districts won by Democrats, so the North Carolina result of four will seem extreme. All that tells me is North Carolina is a big state with districts that are more lopsided than the country as a whole, and that those lopsided districts average out to a state that is split nearly evenly. I knew that before I did the simulation. It's not proof of gerrymandering. If anything it's the opposite. You would expect the most gerrymandering in the states dominated by one party, not the states most evenly split between the two parties.

There is a statistical oddity here, but there's nothing partisan about it. Why do 11 of 14 big swing states have districts that are more lopsided than the national average? As soon as you ask the question, the answer is obvious. Big states are more diverse. They have larger cities and a greater variety of economic activities. This can create more districts in which one party or the other has a strong advantage. In some large states, the one-sidedness is statewide as well. But for a line of big states running roughly from Michigan to Florida, the one-sidedness is split about evenly, with strong Republican and strong Democratic districts mixed together. This is a pattern of political demography, not an evil plot by Republicans.

I do agree in general that it's a bad idea to let elected people control the way elections are run. That applies to district selection, vote tabulation, voter registration and everything else. Unfortunately, it's an equally bad idea to put unaccountable people in charge. I think the best solution is to have clear general principles and a transparent public process. It will not be perfect, but it should be good enough for government work.
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