At oral arguments in yesterday’s partisan gerrymandering cases, several Justices raised questions about whether partisan-gerrymandering challenges implicitly appeal in one way or another to a baseline of proportional representation (PR).  This is an idea introduced by Justice O’Connor in her concurrence in Davis v. Bandemer, 478 U.S. 109 (1986).  A lot of media commentary relies on a similar idea, when journalists simplistically compare a party’s statewide vote share to the statewide number of seats it gets.

But whether Justice O’Connor was right about that at the time she wrote more than thirty years ago, it is not true that social-science experts today or modern litigation challenges rest on any implicit or explicit baseline of PR.  Indeed, political scientists have long understood that a system of single-member districting, such as we use for Congress, should not be expected to produce PR.  The basic reason is that in such a system, a candidate who wins 51% of the vote gets 100% of the seat at issue.  You can have a statewide system of neutrally drawn, competitive districts in which one party wins 51% of the vote in each district and thus ends up with all the seats – and the other party would end up with all the seats if it won 51% of the vote in each district.  There are benefits to single-member districts, but sometimes, those benefits come at a cost to PR.

Precisely because experts have long understood that single-member districts will not necessarily produce PR, their tests for identifying partisan gerrymanders or for defining a fair districting plan have self-consciously rejected any idea that PR provides an appropriate baseline.  One way of defining such a baseline, which has become feasible only in recent years, is to generate tens of thousands of maps based on traditional districting criteria that assign people to districts based on neutral principles, rather than their partisan affiliation.  We can then see the range of partisan outcomes those thousands of plans produce.  This range of partisan outcomes from these thousands of neutral maps – not PR – becomes the baseline against which an actual enacted plan can be judged.

The baseline generated by these maps will often not be PR because the way voters are geographically distributed determines how a neutrally drawn plan will perform.  For example, an amicus brief filed in the case on behalf of mathematicians and law professors shows the insight these techniques provide in a state like Massachusetts.  In the 2000-2010 election cycle, Republicans received about 30-37% of the vote statewide for Congress.  But Massachusetts had a 10-0 Democratic delegation in Congress.  If PR were the baseline, Republicans would be “entitled” to at least three of those seats. 

But when a vast array of neutral drawn maps was put together, it turns out that not a single plan based on traditional districting criteria would produce a single Republican-majority district.  That’s because Republican voters in Massachusetts are spread out so evenly across the State, there is nowhere a concentrated enough number of Republicans to form the majority in a district drawn to comply with traditional, neutral districting criteria.  In other words, the correct baseline for Massachusetts, at least in the 2000 round of redistricting, is actually 10-0 Democratic.  That is striking and might sound odd to lay ears, but it demonstrates quite clearly that when thousands of neutrally-drawn maps reflecting a state’s political geography are used, they provide a baseline for a neutral plan that can be quite different from PR (there might be Republican-dominated states that generate equally dramatic results, but not all states have been studied yet). 

Indeed, as another amicus brief, on behalf of political geographers, points out, these alternative maps show that in several states, a neutrally drawn map will tend to give Republicans somewhat more seats than they would have if PR were the baseline – because Democrats are highly clustered in urban areas.  That’s another demonstration that using these tools has nothing to do with PR.  The baseline is defined by what thousands of neutral plans would produce, and that can be a Democratic advantage in MA, but a Republican advantage in other states (as compared to what a PR requirement would entail).

When thousands of neutral maps were drawn for North Carolina, they showed that about 46% of the maps would produce a 7-6 Democratic delegation for Congress and 32% would produce a 7-6 Republican delegation.  In other words, the vast majority of time, the baseline in NC for a neutrally-drawn plan would produce either a 7-6 or 6-7 delegation.  One expert who drew 3,000 neutral maps found that not a single one of those maps would produce a 10-3 Republican delegation, as the enacted plan was expressly designed to do and did in fact do.  Another expert who drew more than 24,000 neutral plans found that 99.3% of those maps did not produce a 10-3 Republican map. 

These thousands of maps can play two roles.  When no direct evidence exists about whether a legislature intended to create a partisan gerrymander, this analysis can provide significant probative circumstantial evidence.  If there is close to no possibility that a neutrally-drawn plan would produce a 10-3 delegation, then partisan manipulation can be presumed to explain why the map looks the way it does.  But these maps can also demonstrate how extreme the partisan gerrymander is (whether intent is admitted or not).  If virtually none of the time would a neutral map produce a 10-3 delegation, than such a map is not just a partisan gerrymander, but an extreme statistical outlier.  By contrast, let’s say we have a state with 15 districts, and when thousands of alternative maps are drawn, 33% produce an 8-7 split for one party, 33% produce a 9-6 split for that party, and 33% produce a 10-5 split for that party.  We could not say that any of those maps would be an extreme statistical outlier.  Extreme outliers are also easy to define statistically; they simply require deciding how far from the center (the mean) of the distribution a plan has to be in order to be considered an extreme outlier. 

This discussion also relates to an interesting question Justice Alito began to ask.  Played out more fully, he asked didn’t Democrats in the 2018 elections get a roughly proportional percentage of seats in the House to their nationwide vote share?  Democrats did receive about 55% of the vote and got 54% of the seats, according to this report.   But notice that this question itself assumes PR is the right baseline for judging what non-partisan districting nationwide would produce.  And for the reasons just discussed, it’s not.  Maybe Democrats would have won significantly fewer seats if neutrally-drawn districts had been used nationwide.  Maybe they would have won more seats.  We can’t know without exploring alternative maps for all the States (with more than one district) or applying other metrics.

[Disclosure:  I am part of the legal team representing the Common Cause group of appellees in this case]