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


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

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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