Grading Wisconsin's potential new legislative maps

Wright petitioners, Governor Evers, and Clarke petitioners rise to the top of the class.

The Wisconsin legislature and governor failed to agree on Assembly and Senate maps in the state Supreme Court’s current redistricting case. So the Court invited parties to provide potential maps. Last Friday afternoon, seven sets of maps were submitted for consideration.

Here I report on a deep dive by the team here at the Princeton Gerrymandering Project/Electoral Innovation Lab into these seven sets of maps. We applied a modified version of our grading system to assess the plans according to the Court’s own criteria.

PGP analytics have previously identified the Court-overturned maps as the most extreme legislative gerrymander in the nation. The maps allow fewer than 50% of voters, if they vote Republican, to nonetheless elect a majority and even a supermajority in the Assembly and the Senate.

The Wisconsin Supreme Court, led by a new liberal majority, struck down both the Assembly and Senate maps, noting that they violate a constitutional requirement that districts be contiguous. Judging the maps based on contiguity had two advantages. First, the offense could be judged unambiguously with ease. Second, citing the state constitution potentially avoids review in federal court. Whatever the reason given, the maps must now be redrawn.

The Court rejected plans submitted by amicus District Solutions/Petering/FastMap, stating that it will only consider maps drawn by parties to the lawsuit. That limits the Court’s choices to the remaining six plans: Governor Evers, the Wright petitioners, Assembly Republicans, Senate Democrats, Clarke petitioners (LawForward), and Johnson intervenors (Wisconsin Institute for Law and Liberty).

Three of these choices appear to meet the Court’s criteria, with various strengths and weaknesses.

Criteria for new maps: splits and partisan symmetry

The Court listed criteria (link to opinion) that it would use to evaluate remedial maps:

1. Federal requirements for equal population as well as compliance with the Equal Protection Clause and the Voting Rights Act.

2. The Wisconsin constitution’s requirements for contiguity and compactness.

3. Minimizing the degree to which counties, municipalities, towns, and wards are split.

4. Absence of bias toward either political party.

In addition, the court stated that it would consider preservation of communities of interest.

Regarding partisanship, the Court noted that as a judicial body it cannot favor one political party over another. Therefore a remedial map should show as little favor to either Democrats or Republicans as possible. This is highly significant: meeting this criterion opens the way to Wisconsin’s first representative legislature in decades.

All seven plans meet requirements #1 and #2 above. They repair the original problem of noncontiguous districts. All Assembly and Senate plans have similar compactness scores (average Reock score between 0.41 and 0.44, with the exceptions of the Petering/FastMap Assembly plan at 0.49, and the Legislative Republicans’ Assembly plan, which scores most poorly at 0.38). And all seven plans, both Assembly and Senate, have district populations that stay within 2% of the average, within the range cited in examples by the Court as acceptable.

The key criteria: geographic splits and partisan balance

This leaves two criteria where the plans differ meaningfully: geographic splits (#3), and partisan bias (#4). Here is how we quantified them.

Geographic splits. The same part of the state constitution used to strike down noncontiguous districts also specifies not splitting governmental jurisdictions:

The Court said it would allow some splitting, but that it prefers fewer splits.

Partisan symmetry. The court did not specify particular criteria for how it would evaluate partisanship. Here I will use a simple measure, the difference in partisanship between the median district and the statewide average (the “mean-median difference”).

The mean-median difference is an effective way to measure partisan bias in a 50-50 state like Wisconsin. It is simple to calculate and has a clear interpretation: If the mean-median difference is zero, then whoever gets more than 50% of the votes likely also gets 50% of the seats. Conversely, as the mean-median difference starts to get larger, one party develops a substantial advantage.

The mean-median difference is closely related to the expected number of seats:

One simple concept underlying the concept of partisan symmetry is the following: if one party gets a majority of the vote, in a partisan-symmetric plan it will also win a majority of the legislature.

To help interpret the mean-median difference, I will give an estimate of the probability that a party who wins a majority of the statewide vote will also win a legislative majority, assuming that each party’s statewide vote share will vary somewhere within the range of 46% to 54%.

The Princeton Gerrymandering Project’s grading system for a districting plan usually relies on both computer simulations and a measurement of partisan symmetry. Because the Court mentioned only avoiding partisan advantage, PGP’s grades for the seven sets of remedial Wisconsin plans will be determined using only partisan symmetry. (We still used the computer simulations to evaluate other grades on the report card such as compactness and competition.)

Two easy graphs

Senate plans

To visualize differences among the plans, here is a scatter plot of mean-median difference vs. splits for the Senate plans. If one separates the plans by the Democratic/progressive side (blue x's) vs. the Republican/conservative side (red x's), a pattern emerges.

Of these Senate plans, those with a mean-median difference closest to zero came from Senate Democrats, the Wright Petitioners, and Governor Evers.

For the five petitioner/Democratic plans in the lower left (blue x’s) and the Petering/FastMap plan (empty circle), there’s a pretty clear tradeoff between splits and partisan symmetry. Basically, more splits move the advantage closer to zero - and even build a slight Democratic advantage.

Note the the red x’s, which indicate Republican/conservative plans. One has lots of splits and one has very few splits. But in both cases, the partisan asymmetry is quite large. These plans appear not to be engaging in a tradeoff.

Assembly plans

Here is the corresponding graph for Assembly plans.

Of the admissible plans, the Wright Petitioners have a mean-median difference that is closest to zero.

Now let’s grade the plans.

Grading The Plans

Assembly Republicans: Addressing contiguity issues only

Assembly Republicans took the stance that they should make the fewest changes necessary to make districts contiguous. They did this - but along the way, they split dozens of governmental units. In the Marquette analysis, the overturned plan has 50 municipal splits and no ward splits, whereas the Assembly Republicans’ plan has 114 municipal splits and 117 ward splits. This is more than three times as many splits as the least-split plans. Indeed, the Assembly Republican plan has more splits than any two other plans combined. Their plans are also the least compact of all seven offerings.

Unsurprisingly, these plans retain the partisan advantage in the overturned maps: in the Assembly, favoring Republicans by 6.7% (overturned map was 6.3%), and in the Senate, 6.2% (was 5.6%).

Probability of a majoritarian Assembly or Senate: 100% if Republicans get more votes, 0% if Democrats get more votes.

Princeton Gerrymandering Project grades: Assembly, F. Senate, F. (click links for report cards)

If Republicans had chosen, they could have followed the lead of the Johnson intervenors, who were helped by the Wisconsin Institute on Law and Liberty, a conservative think tank. Law & Liberty’s plans have very few splits, yet retain nearly the same partisan advantage as the Assembly Republicans: a mean-median difference of 4.7% in the Assembly and 5.5% in the Senate. They also have twice as many competitive seats as the Assembly Republicans’ plan. Because PGP’s grading rubric gives a bonus for competition, the Law & Liberty Assembly and Senate maps get a grade of “C.”

A partisan-fair map that divides communities: District Solutions

One disallowed outside contribution came from District Solutions, a private company. They offered plans drawn by an algorithm called FastMap. Their plans achieve partisan balance (mean-median differences of 0.0% in the Assembly and 0.7% favoring Democrats in the Senate) and are geographically more compact than any other plan.

However, FastMap seems not to put much value in preserving government boundaries. The District Solutions maps divide communities almost as much as the legislative Republicans’ maps, with 157 splits in the Assembly map and 107 splits in the Senate map. Among other things, this cuts up the Madison area into pie slices:

Probability of a majoritarian Assembly: >90% if Republicans get more votes, >90% if Democrats get more votes. Grade: A for partisan fairness, F for splits.

Probability of a majoritarian Senate : 80% if Republicans get more votes, >95% if Democrats get more votes. Grade: A for partisan fairness, C for splits.

But is such a community-blind approach really necessary to achieve partisan symmetry? As it turns out, no.

Partial credit: Senate Democrats take care of their own chamber

The plan offered by Senate Democrats gets partway to partisan symmetry. It gets rid of a bit more than half the partisan bias in the Assembly (mean-median difference of 2.8%) and all of the bias in the Senate (mean-median difference of 0.1%). It appears that Senate Democrats were particularly attentive to their own chamber.

The plans have quite a few splits, though. The only plans with more splits are the Legislative Republicans’ and the District Solutions maps. Also, the Assembly plan has very few competitive districts. Overall, these plans have some significant weaknesses.

Probability of a majoritarian Assembly: >95% if Republicans get more votes, 30% if Democrats get more votes. Grade: B. Competitiveness grade: F.

Probability of a majoritarian Senate: >90% if Republicans get more votes, >90% if Democrats get more votes. Grade: A. Competitiveness grade: A.

Finally, we get to two plans that appear to meet all the Court’s criteria.

Wright Petitioners & Governor Evers: Having their cake and eating it too?

In Wisconsin, because of the clustering of Democratic and Republican voters in different regions of the state, one might expect it to be difficult to simultaneously maximize partisan symmetry and minimize geographic splits. That may be true, but the Wright Petitioners (Assembly, Senate plans on PGP) and Governor Evers (Assembly, Senate) come closest.

Both of these parties offered maps that had quite small mean-median differences: 0.9% (Assembly) and 0.8% (Senate) in the Wright petitioners’ plans, and 1.7% and 1.0% in Governor Evers’s plans. The Wright petitioners got their better mean-median differences with slightly more splits (115 and 71) than Governor Evers (104 and 68).

In the Wright map, unlike the FastMap plan, Madison is now maintained whole:

and the same is true for Governor Evers’s map:

Wright plan probability of a majoritarian Assembly: >90% if Republicans get more votes, 80% if Democrats get more votes. Grade: A.

Wright plan probability of a majoritarian Senate: >90% if Republicans get more votes, 80% if Democrats get more votes. Grade: A.

Evers plan probability of a majoritarian Assembly: >95% if Republicans get more votes, 60% if Democrats get more votes. Grade: A.

Evers plan probability of a majoritarian Senate: >90% if Republicans get more votes, 75% if Democrats get more votes. Grade: A.

The Clarke petitioners strike a different balance

If the Court wants to give more weight to splits instead of partisan fairness, another option is the Clarke petitioners’ map, prepared with LawForward. This plan has an exceptionally small number of splits for both the Assembly and Senate plans, on a par with the Johnson/Law & Liberty maps.

The Clarke plan does not go as far as the Wright or Evers plans in addressing partisan symmetry, with mean-median differences of 1.2% in the Assembly and 2.4% in the Senate. These values open a greater possibility of a countermajoritarian outcome, in both cases favoring Republicans.

Clarke plan probability of a majoritarian Assembly: >90% if Republicans get more votes, 70% if Democrats get more votes. Grade: A.

Clarke plan probability of a majoritarian Senate: >95% if Republicans get more votes, 40% if Democrats get more votes. Grade: A.

Conclusion

Finally, a summary of how the various plans rank. The Wright petitioners score very well on partisan symmetry. Factoring in splits, the plans from Governor Evers and the Clarke petitioners also rank highly.

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Many thanks to Ethan Arsht (Electoral Innovation Lab) and Setu Loomba (Princeton Gerrymandering Project) for calculations, graphics, and report cards, and to John D. Johnson (Marquette Law) for the calculation of municipality and ward splits. An earlier version of this post was posted on Twitter.com. This post was edited on January 19 to correct the list of plans that will be considered by the court.