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The research that convinced SCOTUS to take the Wisconsin gerrymandering case, explained

The Wisconsin statehouse
After 2010, Wisconsin legislators drew districts in a way Democrats argue is deeply rigged against them
UniversalImagesGroup / Getty

In June, the Supreme Court agreed to hear its first partisan gerrymandering case in more than a decade. This case, Gill v. Whitford, involves a challenge to the district plan that Wisconsin passed for its state house after the 2010 Census. The case also involves a quantitative measure of gerrymandering — the efficiency gap — that has created a bit of a buzz. One reporter compares it to a “silver-bullet democracy theorem” and a “gerrymandering miracle drug.” Another speculates that it may be the “holy grail of election law jurisprudence.”

I’m an attorney in Whitford and the co-author of an article advocating the efficiency gap, so I appreciate the attention the metric is getting. But I still think much of this interest is misplaced. The efficiency gap is, in fact, a simple and intuitive measure of gerrymandering, and I’ll explain why in a minute. But the true breakthrough in Whitford isn’t that plaintiffs have finally managed to quantify gerrymandering. Rather, it’s that they’ve used the efficiency gap (and other metrics) to analyze the Wisconsin plan in new and powerful ways. These analyses are the real story of the litigation — not the formulas that enabled them.

For more than three decades, the Supreme Court has recognized that severe partisan gerrymandering can violate the Constitution. But until Whitford, not a single federal court had struck down a map on this basis. Early litigants lost because the standard the courts used prior to 2004 was so demanding it could never be met. Since 2004, the courts haven’t even been able to agree on a test, rendering most lawsuits hopeless. However, in a 2006 case, five justices expressed interest in statistical metrics that show how a plan benefits (or handicaps) a given party. The efficiency gap is such a metric.

To grasp the efficiency gap, you have to realize that partisan gerrymandering is always carried out in one of two ways. Either a party cracks (that is, splits) the other party’s voters among many districts in which their preferred candidates lose by relatively narrow margins. Or a party packs the other side’s voters into a few districts in which their preferred candidates win by overwhelming margins.

Both cracking and packing produce wasted votes that don’t contribute to a candidate’s election. In the case of cracking, these are all of the votes cast for a losing candidate. In the case of packing, they’re all of the votes cast for a winning candidate in excess of the 50 percent (plus one) needed for victory. The efficiency gap is simply one party’s total wasted votes, minus the other party’s total wasted votes, divided by all of the votes cast in the election.

How the “efficiency gap” works

To illustrate, take a state with five districts: two won easily by Democrats, 76 percent to 24 percent, and three won more narrowly by Republicans, 59 percent to 41 percent. Democrats waste 26 percent of the vote in the two districts they win and 41 percent in the three districts they lose. Republicans waste 24 percent of the vote in the two districts they lose and 9 percent in the three districts they win. Over all, Democrats get 55 percent of the statewide vote but just 40 percent of the seats, yielding a pro-Republican efficiency gap of 20 percent.

The Wisconsin map at issue in Whitford is like this example — only with 99 districts instead of five. According to one of the plaintiffs’ experts, University of Wisconsin professor Kenneth Mayer, there are 42 districts in which the Republican candidate typically wins between 50 percent and 60 percent of the vote. In contrast, there are just 17 where the Democrat prevails this narrowly.

There’s also only a single district in which the Republican candidate usually wins more than 75 percent of the vote, compared to 10 where the Democrat triumphs this easily. It is this asymmetric cracking and packing that yields many more Democratic than Republican wasted votes. It’s what’s responsible for the Wisconsin plan’s double-digit pro-Republican efficiency gaps: 13 percent in 2012, 10 percent in 2014, and 11 percent in 2016.

By itself, this is as far as the efficiency gap gets us. And note that it’s not very far. We don’t know, for instance, how biased the Wisconsin plan is compared to maps in other states and at other times. Nor do we know whether the Wisconsin plan’s skew is inconsistent with what we’d expect given the state’s political geography. And nor is it clear if the Wisconsin plan would continue to exhibit a pro-Republican tilt if the state’s electoral conditions changed.

Experts have used the efficiency gap to compare Wisconsin’s plan to other districting maps

Notably, the state raised all of these issues at trial, as it defended its plan. It claimed that the plan resembled many others in use across the country; that the clustering of Democrats in Milwaukee and Madison explained the map’s pro-Republican efficiency gap; and that this bias could disappear if only Democrats ran better campaigns. Issues like these are also why the trial court treated the efficiency gap as “corroborative evidence of an aggressive partisan gerrymander” — not ironclad proof.

What did the trial court need beyond the efficiency gap to strike down the Wisconsin plan? It needed analysis, which the plaintiffs provided in spades.

Start with how the Wisconsin plan fares relative to other maps. Another of the plaintiffs’ experts, Stanford professor Simon Jackman, prepared the below chart. It displays the average efficiency gap produced over its lifetime by almost every state house plan in America from 1972 to 2014. (Negative values are pro-Republican; positive values are pro-Democratic.)

The Wisconsin plan is in red, and lies at the very bottom of the historical distribution, at the extreme pro-Republican edge. In fact, its average efficiency gap is bigger than that of any map used prior to the current cycle. This data is what led the trial court to the conclusion that “the [efficiency gaps] for the 2012 and 2014 races in Wisconsin … were particularly high by historical levels.”

A graph comparing state house plans, 1972-2014
State house plans, 1972-2014. (Wisconsin’s plan is in red.)
Simon Jackman

Next, take the question of what efficiency gap we’d expect given Wisconsin’s spatial patterns — its political geography. To answer it, Michigan professor Jowei Chen used a computer algorithm to create 200 state house maps. All of these maps performed at least as well as the actual plan on every nonpartisan criterion. They complied with the Constitution’s one person, one vote requirement (because each district had about the same population). They complied with the Voting Rights Act (because they ensured black and Latino representation). They split fewer counties and municipalities. And their districts were more compact.

But as the below graph shows, not a single simulated map had an efficiency gap as large as the actual plan. In fact, most of the simulated maps had efficiency gaps within a few percentage points of zero. The simulations therefore refute any claim that the actual plan’s pro-Republican skew is justified by Wisconsin’s geography. If it were, at least some — not none — of the simulations would have been as biased. The trial court agreed: “Wisconsin’s natural political geography ... simply does not explain adequately the sizeable disparate effect seen in 2012 and 2014.”

a graph showing Wisconsin’s partisan redistricting plan compared with other possible plans the state might have drawn. Jowei Chen

Lastly, to assess the durability of the Republican advantage, Jackman used a technique called sensitivity testing. This means that he took the results of Wisconsin’s actual 2012 election, and then shifted them by several percentage points in either party’s direction, thus mimicking a wide range of electoral conditions. (This was a response to the criticism that the efficiency gap in one or two elections might be atypical.) For each shift, he recalculated the plan’s efficiency gap assuming that each district swung by the same margin as the state as a whole.

The below chart displays the results of the sensitivity testing. The zero point in the middle is the Wisconsin plan’s actual efficiency gap in 2012. The points to the left indicate how the plan’s efficiency gap would change in the event of Republican gains of a certain size. The points to the right show what would happen if Democrats gained.

What jumps out from the figure is the impressive persistence of the Republican edge. If Republicans improved substantially on their 2012 performance, the plan’s efficiency gap would remain large and pro-Republican. More importantly, if the statewide vote swung by 5 points in a Democratic direction — representing the largest Democratic wave in more than 40 years — the plan’s efficiency gap would still favor Republicans by double digits. In the trial court’s words, “in any likely electoral scenario, the number of Republican seats would not drop below 50%.”

A chart showing how the Wisconsin plan would perform if voting patterns shifted
How the Wisconsin plan would perform if voting patterns shifted
Simon Jackman

Consider, then, what the efficiency gap alone tells us: just that the Wisconsin plan favored Republicans in 2012, 2014, and 2016. Contrast this with what we learn from the analyses: 1) that the plan’s pro-Republican bias is nearly unprecedented historically; 2) that this skew can’t be attributed to Wisconsin’s political geography; and 3) that the tilt is likely to persist under any electoral environment.

That’s why if the Whitford plaintiffs end up prevailing, it’ll be because of their methods, not their metric. The efficiency gap is an elegant way to quantify the extent of partisan gerrymandering. But more than that is needed to win a case. The challenged plan must also be more biased than other maps, inconsistent with the state’s spatial patterns, and durable in its effects. And these elements can only be established by additional studies.

So to those who are curious how Whitford differs from earlier challenges — and why the Supreme Court has reentered the gerrymandering fray — my advice is to look beyond the efficiency gap. It’s not the metric that’s unique; it’s how it’s being put to use.

Nicholas Stephanopoulos is a professor of law at the University of Chicago Law School. He is also one of the attorneys for the plaintiffs in Whitford.

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