Countering gerrymandering in Pennsylvania with numerical models

Wired highlights a few academics who argued against gerrymandered political districts in Pennsylvania with models showing the low probability that the map is nonpartisan:

Then, Pegden analyzed the partisan slant of each new map compared to the original, using a well-known metric called the median versus mean test. In this case, Pegden compared the Republican vote share in each of Pennsylvania’s 18 districts. For each map, he calculated the difference between the median vote share across all the districts and the mean vote share across all of the districts. The bigger the difference, the more of an advantage the Republicans had in that map.

After conducting his trillion simulations, Pegden found that the 2011 Pennsylvania map exhibited more partisan bias than 99.999999 percent of maps he tested. In other words, making even the tiniest changes in almost any direction to the existing map chiseled away at the Republican advantage…

Like Pegden, Chen uses computer programs to simulate alternative maps. But instead of starting with the original map and making small changes, Chen’s program develops entirely new maps, based on a series of geographic constraints. The maps should be compact in shape, preserve county and municipal boundaries, and have equal populations. They’re drawn, in other words, in some magical world where partisanship doesn’t exist. The only goal, says Chen, is that these maps be “geographically normal.”

Chen generated 500 such maps for Pennsylvania, and analyzed each of them based on how many Republican seats they would yield. He also looked at how many counties and municipalities were split across districts, a practice the Pennsylvania constitution forbids “unless absolutely necessary.” Keeping counties and municipalities together, the thinking goes, keeps communities together. He compared those figures to the disputed map, and presented the results to the court…

Most of the maps gave Republicans nine seats. Just two percent gave them 10 seats. None even came close to the disputed map, which gives Republicans a whopping 13 seats.

It takes a lot of work to develop these models and they are based on particular assumptions as well as methods for calculations. Still, could a political side present a reasonable statistical counterargument?

Given both the innumeracy of the American population and some resistance to experts, I wonder how the public would view such models. On one hand, gerrymandering can be countered by simple arguments: the shapes drawn on the map are pretty strange and can’t truly represent any meaningful community. On the other hand, the models reinforce how unlikely these particular maps are. It isn’t just that the shapes are unusual; they are highly unlikely given various inputs that go into creating meaningful districts. Perhaps any of these argument are meaningless if your side is winning through the maps.

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