The problem for Democrats is that they have overwhelming majorities not only in the dense, poor urban centers, but also in isolated, far-flung college towns, historical mining areas and 19th-century manufacturing towns that are surrounded by and ultimately overwhelmed by rural Republicans.

A motivated Democratic cartographer could produce districts that accurately reflected overall partisanship in states like these by carefully crafting the metropolitan districts and snaking districts along the historical canals and rail lines that once connected the nonmetropolitan Democratic enclaves. But such districts are unlikely to emerge by chance from a nonpartisan process. On the other hand, a Republican cartographer in these and other Midwestern states, along with some Southern states like Georgia and Tennessee, could do little to improve on the advantage bestowed by the existing human geography.

By no means does this imply that critics of gerrymandering are always wrong. In the states most frequently derided as overt Republican gerrymanders, our analysis shows that gerrymandering has indeed given the Republicans additional seats beyond the already pro-Republican average of our simulations. Most notable are North Carolina, Florida, Pennsylvania, Texas and Michigan.

But keep in mind that Democrats play this game as well. For example, by artfully dividing up Chicago into pie-sliced districts extending from Lake Michigan into the suburbs, the Illinois Democrats have done better for themselves than the outcome of our nonpartisan simulations. The Democrats have achieved something similar in Maryland. And in what will come as a surprise to many in the reform community, California’s redistricting commission produced multiple Democratic seats beyond the predictions of our simulations. Evidently the enormous and sophisticated lobbying efforts of California Democrats were successful.