But as Duchin and other mathematicians have shown in a flurry of recent papers, the efficiency gap is deeply flawed.

In some cases, it leads to unintuitive conclusions. For example, you’d think that a state where one party wins 60 percent of the vote and 60 percent of the seats did things right. Not so, according to the efficiency gap. If you do the math, that state would get flagged for extreme partisan gerrymandering—in favor of the losing party. Perversely, then, the easiest remedy might to be rig things so that the minority party gets even fewer seats.

Another problem is that the efficiency gap takes no account of political geography. In Wisconsin, most Democrats are concentrated in cities like Milwaukee, producing lopsided races there. To the efficiency gap, that could look like nefarious packing, when in reality it’s simple demographics. Similarly, if several nearby districts all swung toward one party in a close election year, that completely natural outcome could get flagged as cracking.

Other critiques of the efficiency gap get more technical. (Many were first posted on ArXiv.org, a preprint server where mathematicians and physicists share new work.) But they all boil down to the same thing: Elections are complicated and volatile, and no one number can capture all that. As Duchin writes, “gerrymandering is a fundamentally multidimensional problem, so it is manifestly impossible to convert that into a single number without a loss of information that is bound to produce many false positives or false negatives for gerrymandering.”

Duchin and other critics don’t dismiss the efficiency gap as worthless, just point out that it’s too simplistic to use by itself. And to be fair, when Stephanopoulos and other lawyers argued against the Wisconsin gerrymander, they laid out a far more nuanced case. Among other things, they addressed the political-geography objections. They also employed computer simulations that produced 200 random but realistic statewide maps, then determined how an election would play out in each case. According to this analysis, the current Wisconsin map favored Republicans far more heavily than any random map did, providing strong evidence of manipulation. (In response to a request for comment, Stephanopoulos pointed to a paper he and McGhee wrote that addresses criticism like Duchin’s.)

Overall, then, the people who study the efficiency gap know its limitations. The real question is whether the courts will also recognize those limits. The efficiency gap is a nice, novel tool. The danger isn’t the efficiency gap itself, but rather the temptation to look only at the efficiency gap, and make it the effective definition of partisan gerrymandering in the future. As Duchin and her colleague Mira Bernstein recently wrote, “a famous formula can take on a life of its own and this one will need to be watched closely.”

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