Federal court strikes down GOP-drawn maps (Wisconsin legislative map)

[DrScholl]

http://www.jsonline.com/story/news/politics/2016/11/21/federal-court-strikes-down-gop-drawn-maps/94233560/

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[Nyvin]

Perfectly reasonable argument.   By drawing an unfair map the Republicans deny the voters freedom of speech and thus is unconstitutional.

Before anyone refutes that....let's keep in mind how much more absurd the Citizens United decision was with Corporations being people and money being speech.

[KingSweden]

Kennedy has shown openness to restricting gerrymandering. Wonder if this will meet his standard of a test that would work

[publicunofficial]

Discrimination against partisans is a lot weaker argument than against race or ethnicity. We'll see.

[krazen1211]

Yawn. Bill Pryor will smack this down hard.

[DrScholl]

Discrimination against partisans is a lot weaker argument than against race or ethnicity. We'll see.

The freedom of speech argument does make it sort of compelling, but it's hard to say what will happen. The thing is that you have clear extremes where Democratic voters are packed mostly into districts that vote extremely Democratic and it's not an issue of geography.

[jimrtex]

The decision explains that the legislature converted most of the swing districts to Republican swing districts, but left the Democrats with 40 house seats. This last election, the Democrats were reduced to 34 seats, 6 less than they were supposedly packed into.

On the other hand, Democrats had a Republican opponent in only 6 of the 34 districts they did win.

If Dane and Milwaukee counties were eliminated, Trump had a 55-40 statewide margin. If you tried to create competitive districts in either county, it would likely require packing Democrats. Similarly, you might be able to create competitive districts in the Winnebago Valley, but only by packing Republicans.

[Bacon King]

I'm very interested in any detailed commentary any of our top-tier redistricting nerds might have to offer here (jimrtex, Torie, muon, etc.).

a. Is the proposed "wasted votes" test a meaningful/relevant/workable standard?
b. How different is it from previous tests the Supreme Court has rejected?
c. Are there any other, narrower tests the Supreme Court might decide to follow instead?
d. By your reckoning, how likely is Justice Kennedy to affirm this ruling, whether he bases it on "wasted votes" or something else?

[Young Conservative]

Yawn. Bill Pryor will smack this down hard.

I seriously doubt he would be confirmed. The filibuster would be endless. He would be a great justice though. Diane Sykes would also be an astounding justice and is confirmae though.

[jimrtex]

Note: I have edited this message to be more careful with the sign of the efficiency gap. It appears that the plaintiffs may simply observed which party has the greater number of wasted votes and calculates the efficiency gap based on that, so the wasted vote is based on that:

WMax = max(WA,WB)
Wmin = min(WA,WB)
EG = (WMax - WMin) / (WMax + Wmin)

Since WMax - Wmin >= 0, EG will always have a positive value.

But a more consistent approach for analytical purposes is to choose a party to be Party 1, and the other as Party 2.

EG = (W1 - W2) / (W1 + W2)

if W1 > W2, then EG > 0; If W1 < W2, then EG < 0

The plaintiffs argument would then be that |EG| > 0.07 is significant.

We should probably avoid using W1 = WD and W2 = WR, or vice versa, because that will produce different signs for an unfair plan for each party.  That is EG > 0 would imply the Democrats were cheated, and EG < 0 would imply the Republicans were cheated. It is possible that since the plaintiffs were Democrats, they chose Party 1 to be the Democrats since they expected to always have more wasted votes.

We could also use

EG1 = (W1 - W2) / (W1 + W2)
EG2 = (W2 - W1) / (W1 + W2)

Then EG1 = -EG2

If EG_i > 0, the ith party will be the injured party.

In the examples below, Party 1 will be Party B, because that was what was used in the plaintiffs example, where Party B with 56% of the vote, only elected 40% of the vote.

End of Note.

I'm very interested in any detailed commentary any of our top-tier redistricting nerds might have to offer here (jimrtex, Torie, muon, etc.).

a. Is the proposed "wasted votes" test a meaningful/relevant/workable standard?
b. How different is it from previous tests the Supreme Court has rejected?
c. Are there any other, narrower tests the Supreme Court might decide to follow instead?
d. By your reckoning, how likely is Justice Kennedy to affirm this ruling, whether he bases it on "wasted votes" or something else?

Consider a single district:

If it is

100D:0R there are 50 wasted D votes, and 0 wasted R votes, 50 net D.
90D:10R Wasted 40D:10R; 30 net D.
80D:20R Wasted 30D:20R; 10 net D.
75D:25R Wasted 25D:25R; 0 net D.
70D:30R Wasted 20D:30R; 10 net R.
60D:40R Wasted 10D:40R; 30 net R.
51D:49R Wasted 1D:49R; 49 net R.
49D:51R Wasted 49D:1R; 49 net D
...
25D:75R Wasted 25D:25R; 0 net R.
0D:100R Wasted 0D:50R; 50 net R

Thus the fairest districts are 75:25, because equal numbers are wasted on both sides. 50% of votes are always wasted, and 99:1 and 51:49 districts are equally unfair. There is also a discontinuity at the presumably swingiest of districts.

The plaintiffs provide the following example:

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This is the text presented in tabular form:

Votes        Wasted
A 60 B 40    A 10 B 40
A 60 B 40    A 10 B 40
A 60 B 40    A 10 B 40
A 20 B 80    A 20 B 30
A 20 B 80    A 20 B 30
  220 280      70  180

Efficiency Gap = (Wasted B - Wasted A) / (Votes A + Votes B) = (180-70)/(220 + 280) = 22%

B with overall majority support is cracked among the first three districts, and packed into the final two.

Now imagine that all the districts were equally partisan.

Votes        Wasted
A 44 B 56    A 44 B  6
A 44 B 56    A 44 B  6
A 44 B 56    A 44 B  6
A 44 B 56    A 44 B  6
A 44 B 56    A 44 B  6
  220 280     220   30

Sign changed, since I had flipped Wasted A and Wasted V when I substituted the values into the formula.

Efficiency Gap = (Wasted B - Wasted A) / (Votes A + Votes B) = (30-220)/(220 + 280) = -38%

The efficiency gap is now 38%, with B favored over A.

Let's do a bit of gerrymandering with the original example, moving 3% B from four districts to flip one of the districts.

Votes        Wasted
A 63 B 37    A 13 B 37
A 63 B 37    A 13 B 37
A 48 B 52    A 48 B  2
A 23 B 77    A 23 B 27
A 23 B 77    A 23 B 27
  220 280     120  130

Efficiency Gap = (Wasted B - Wasted A) / (Votes A + Votes B) = (130-120)/(220 + 280) = 2%

Surprisingly, Party B has more wasted votes, even though they were able to elect 60% of the representatives with 56% of the vote.

But this is a bit iffy for B in the 3rd district. Let's prop it up a bit.

Votes        Wasted
A 65 B 35    A 15 B 35
A 65 B 35    A 15 B 35
A 40 B 60    A 40 B 10
A 25 B 75    A 25 B 25
A 25 B 75    A 25 B 25
  220 280     120  130

Efficiency Gap = (Wasted B - Wasted A) / (Votes A + Votes B) = (130-120)/(220 + 280) = 2%

There is no change in efficiency.

If we shift voters from Party A from a Win A(1) district to a Win A(2) district, and conversely voters from Party B from a Lose B(2) district to a Lose B(1) district, there is no change in efficiency.

If we shift voters from Party A from a Win A(1) district to a Lose A(2) district, they continue to be wasted, and conversely voters from Party B from a Win B(2) district to a Lose B(1) district, they continue to be wasted.

We always have to balance a shift of A voters from one district to another, with a shift of B voters in the other direction. It is only when the district flips that there is a change in efficiency.

The efficiency gap is thus a proportionality measure.

Once we realize this, we go even further to make the 3rd district secure, even in a wave election.

Votes        Wasted
A 65 B 35    A 15 B 35
A 65 B 35    A 15 B 35
A 30 B 70    A 30 B 20
A 30 B 70    A 30 B 20
A 30 B 70    A 30 B 70
  220 280     120  130

Efficiency Gap = (Wasted B - Wasted A) / (Votes A + Votes B) = (130-120)/(220 + 280) = 2%

So how about:

Votes        Wasted
A 80 B 20    A 30 B 20
A 80 B 20    A 30 B 20
A 20 B 80    A 20 B 30
A 20 B 80    A 20 B 30
A 20 B 80    A 20 B 30
  220 280     120  130

Efficiency Gap = (Wasted B - Wasted A) / (Votes A + Votes B) = (130-120)/(220 + 280) = 2%

This is actually more efficient in that we don't even have to bother with elections.

Exercise for the student gerrymanderer: Make a 4th district winnable for B in a wave election without changing the efficiency gap.

[muon2]

jimrtex gives a number of good examples. I would summarize the wasted-vote measure as one that favors a plan with all districts that are fairly safe and distributed proportionally between the parties. Competitive districts are disfavored, since there is more potential for wasted votes when the electorate shifts its preferences a few points either way and causes a district to flip. If this were the standard for testing gerrymanders then bipartisan incumbent-protection plans would be the norm.

In reality partisan fairness and competitiveness are independent measures, though most attempts at redistricting reform only consider one or the other. Partisan fairness considers the overall distribution of the districts in the plan. Competitiveness considers how well a plan will respond to the changing mood of the voters. When I judge plans I use both measures described as the variables SKEW and POLARIZATION below.

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[Virginiá]

Would it be possible for the plaintiffs to, if it reaches the Supreme Court, modify the test a bit so that it helps mitigate the incumbent protection scheme tactic you guys outlined?

I hadn't considered that aspect before, but perhaps it could still serve as a useful part of a multi-part test? With all this in mind, I don't understand how the people behind this test missed this, or perhaps they didn't think it was an issue?

[Kevinstat]

Exercise for the student gerrymanderer: Make a 4th district winnable for B in a wave election without changing the efficiency gap.

Votes        Wasted
A 70 B 30    A 20 B 30
A 54 B 46    A  4 B 46
A 32 B 68    A 32 B 18
A 32 B 68    A 32 B 18
A 32 B 68    A 32 B 18
 220  280     120  130

Efficiency Gap = (Wasted B - Wasted A) / (Votes A + Votes B) = (130-120)/(220 + 280) = 2%

Moving each of the B districts a percentage point less B (still over 2-1 B), I can make the fourth district (or the second on this table) practically a tossup without packing the other A district over 70% A (so the B party's attorneys could say it isn't a vote sink since the Bs will still have 50% more wasted votes in that district in a typical election).

Votes        Wasted
A 70 B 30    A 20 B 30
A 51 B 49    A  1 B 49
A 33 B 67    A 33 B 17
A 33 B 67    A 33 B 17
A 33 B 67    A 33 B 17
 220  280     120  130

Efficiency Gap = (Wasted B - Wasted A) / (Votes A + Votes B) = (130-120)/(220 + 280) = 2%

[jimrtex]

Please check my algebra:

Assumption: There are an equal number of votes cast in each district.

Assertion: We can shift votes around, as long as we don't flip districts, and the Efficiency Gap will be unchanged. See demonstration in previous message.

We can therefore equalize the votes for Party A and Party B, among the districts won by Party A, and also among the districts won by Party B.

Let VA be the percentage of total votes for Party A.
Let VB be the percentage of total votes for Party B

We will assign A and B such that VA > 0.5 > VB. That is Party A is the overall popular vote winner.

Let SA be the districts won by Party A.
Let SB be the districts won by Party B
Let ST be the total number of districts.

Thus SA + SB = ST

Let VAW be the percentage of votes in districts won by Party A in districts won by Party A, and VAL be percentage of votes won by Party A in districts won by Party B. The votes won by Party B in the two types of districts are (1 - VAW) and (1- VAL)

Assuming no ties, then

0 <= VAL < 0.5 < VAW <= 1

For a given value of VA and NT, this may constrain the number of seats SA and SB. For example, Party A must always win at least one seat, since they have a majority of the popular vote.

The votes won Party A in the two types of district equals the overall total votes for Party A. The same is also true for Party B, we will use the complement of the Party A vote, for the Party B vote.

VAW * SA + VAL * SB = VA * ST
(1 - VAW) * SA + (1- VAL) * SB = (1 - VA) * ST

The wasted votes for Party A and Party B are:

WA = (VAW - 0.5) * SA + VAL * SB
WB = (1 - VAW) * SA + (1 - VAL - 0.5) * SB

We have normalized the total number of votes in each district is 1, and the total number of votes = ST.

The Efficiency Gap,  EG = (WA - WB) / ST

Note, that if WA > WB the EG will be positive, and A will be the "cheated" party. If WA < WB the EG will be negative and B will be the "cheated" party. If WA = WB, the two parties will waste equal number of votes.

(WA - WB) = (2 * VAW - 1.5) * SA + (2 * VAL - 0.5) * SB

(WA - WB) = (2 * VAW * SA) + (2 * VAL * SB) - (1.5 * SA + 0.5 * SB)

But VAW * SA + VAL * SB = VA * ST,
And SB = ST - SA

so

(WA - WB) = 2 * VA * ST - (1.5 * SA + 0.5 * (ST - SA))

(WA - WB) = 2 * VA * ST - (SA + 0.5 * ST)

EG = (WA - WB) / ST

EG = 2 * VA - SA/ST - 0.5

If we let ShA = SA/ST, the share of seats won by Party A

EG = 2 * VA - ShA - 0.5

For the conditions of our example, VA = 0.56 and ShA = 2/5 = 0.40 (note we have switched the two parties)

EG = 0.56 * 2 - 0.4 - 0.5 = 0.22, which is what we calculated empirically.

For our example where Party A carried all 5 districts, ShA = 1

EG = 0.56 * 2 - 1.0 - 0.5 = -0.38, which is what we calculated empirically.

And for our example where Party A carried 3 districts, ShA = 0.6

EG = 0.56 * 2 - 0.6 - 0.5 = 0.02, which is what we calculated empirically.

If we set EG = 0, then we can solve for ShA.

VA * 2 - ShA - 0.5 = 0

ShA = VA * 2 - 0.5

The plurality for Party A is: PlA = VA - VB = VA - (1 - VA) = VA * 2 - 1

ShA = VA  * 2 - 1.0 + 0.5

ShA = PlA + 0.5

That is, the fairest distribution is when ShA = Plurality + 0.5.

In our example, PlA = 0.56 - 0.44 = 0.12

So with 56% of the vote, Party A should have 62% of the seats. That is why the 3B:2A distribution is slightly unfair to Party B.

The plaintiffs argue the threshold for an unfair plan is an EG = 0.07 (or -0.07 for the cheated party).

EG = 2 * VA - ShA - 0.5 = -0.07

ShA = 2 * VA - 0.5 + 0.07

PlA = 2 * VA - 1

ShA = 2 * VA - 1 + 0.5 + 0.07

ShA = PlA + 0.57

So with VA = 0.56, ShA = 0.69 would be lawful.

With VA = 0.50, ShA = 0.57 would be lawful.

[muon2]

Would it be possible for the plaintiffs to, if it reaches the Supreme Court, modify the test a bit so that it helps mitigate the incumbent protection scheme tactic you guys outlined?

I hadn't considered that aspect before, but perhaps it could still serve as a useful part of a multi-part test? With all this in mind, I don't understand how the people behind this test missed this, or perhaps they didn't think it was an issue?

I had some conversations this summer with those involved in the suit. The plaintiff's attorneys are not interested in avoiding incumbent protection. They are interested in insuring Dem representation in the face of growing Pub majorities in state legislatures. The Dem fear is that things are grim enough at the state level going into 2020 they can't regain enough seats in 2018 and 2020 to give them the tools at the state level. So they are pinning hopes on a two-prong legal strategy. One prong is to establish proportional partisan representation above other criteria through the maps, and the other prong is to weaken VRA section 2 to support white Dems representing minority areas allowing the minorities to be cracked to create more Dem districts.

[jimrtex]

The original example presented by the plaintiffs, assumed districts with equal numbers of voters.

Votes        Wasted
A 60 B 40    A 10 B 40
A 60 B 40    A 10 B 40
A 60 B 40    A 10 B 40
A 20 B 80    A 20 B 30
A 20 B 80    A 20 B 30
  220 280      70  180

Efficiency Gap = (Wasted B - Wasted A) / (Votes A + Votes B) = (180-70)/(220 + 280) = 22%

But what if there was a difference? In this example, the votes cast in the first three districts is reduced by 10% from 100 to 90, with the residual distributed to the other two districts.

Votes        Wasted
A 54 B 36    A  9 B 36
A 54 B 36    A  9 B 36
A 54 B 36    A  9 B 36
A 29 B 86    A 29 B 28.5
A 29 B 86    A 29 B 28.5
  220 280      85  165

Efficiency Gap = (Wasted B - Wasted A) / (Votes A + Votes B) = (165-85)/(220 + 280) = 16%

So this plan is supposedly fairer to Party B, in party because it makes the two districts won by B more competitive.

[Nyvin]

The original example presented by the plaintiffs, assumed districts with equal numbers of voters.

Votes        Wasted
A 60 B 40    A 10 B 40
A 60 B 40    A 10 B 40
A 60 B 40    A 10 B 40
A 20 B 80    A 20 B 30
A 20 B 80    A 20 B 30
  220 280      70  180

Efficiency Gap = (Wasted B - Wasted A) / (Votes A + Votes B) = (180-70)/(220 + 280) = 22%

But what if there was a difference? In this example, the votes cast in the first three districts is reduced by 10% from 100 to 90, with the residual distributed to the other two districts.

Votes        Wasted
A 54 B 36    A  9 B 36
A 54 B 36    A  9 B 36
A 54 B 36    A  9 B 36
A 29 B 86    A 29 B 28.5
A 29 B 86    A 29 B 28.5
  220 280      85  165

Efficiency Gap = (Wasted B - Wasted A) / (Votes A + Votes B) = (165-85)/(220 + 280) = 16%

So this plan is supposedly fairer to Party B, in party because it makes the two districts won by B more competitive.

The plaintiff's model doesn't rely on equal number of votes in each district?

[KingSweden]

Would it be possible for the plaintiffs to, if it reaches the Supreme Court, modify the test a bit so that it helps mitigate the incumbent protection scheme tactic you guys outlined?

I hadn't considered that aspect before, but perhaps it could still serve as a useful part of a multi-part test? With all this in mind, I don't understand how the people behind this test missed this, or perhaps they didn't think it was an issue?

I had some conversations this summer with those involved in the suit. The plaintiff's attorneys are not interested in avoiding incumbent protection. They are interested in insuring Dem representation in the face of growing Pub majorities in state legislatures. The Dem fear is that things are grim enough at the state level going into 2020 they can't regain enough seats in 2018 and 2020 to give them the tools at the state level. So they are pinning hopes on a two-prong legal strategy. One prong is to establish proportional partisan representation above other criteria through the maps, and the other prong is to weaken VRA section 2 to support white Dems representing minority areas allowing the minorities to be cracked to create more Dem districts.

Interesting they've finally realized section 2 hurts Democrats more than it helps

[jimrtex]

The original example presented by the plaintiffs, assumed districts with equal numbers of voters.

Votes        Wasted
A 60 B 40    A 10 B 40
A 60 B 40    A 10 B 40
A 60 B 40    A 10 B 40
A 20 B 80    A 20 B 30
A 20 B 80    A 20 B 30
  220 280      70  180

Efficiency Gap = (Wasted B - Wasted A) / (Votes A + Votes B) = (180-70)/(220 + 280) = 22%

But what if there was a difference? In this example, the votes cast in the first three districts is reduced by 10% from 100 to 90, with the residual distributed to the other two districts.

Votes        Wasted
A 54 B 36    A  9 B 36
A 54 B 36    A  9 B 36
A 54 B 36    A  9 B 36
A 29 B 86    A 29 B 28.5
A 29 B 86    A 29 B 28.5
  220 280      85  165

Efficiency Gap = (Wasted B - Wasted A) / (Votes A + Votes B) = (165-85)/(220 + 280) = 16%

So this plan is supposedly fairer to Party B, in party because it makes the two districts won by B more competitive.

The plaintiff's model doesn't rely on equal number of votes in each district?

I don't know. I haven't got that far in the decision. I may have to read through the briefs.

I also don't know whether they are using exogenous or endogenous elections. Endogenous elections would use the votes for the legislative elections. In 2016, in the 34 Assembly districts won by the Democrats, 28 had no Republican opponent. Half of all votes cast would be wasted for the Democrats, and no Republican votes would be wasted since none were cast.

The legislature (Republican majority) devised a partisan index for small areas (eg wards) based on a set of statewide elections, which their consultant told them would be representative of an open seat legislative election. One prong of the proposed test for political gerrymandering is intent. The Republicans left plenty of evidence that they were drawing districts to produce more Republican winners, including spreadsheets showing how many seats would be won under different scenarios.

They also identified "donor" districts where Republican legislators could give up Republican votes and still win. Generally swing districts were shifted to become more Republican. In the predicted results, it appeared that half of swing districts were assigned to each party.

In a state like Illinois, you would get the actual map drawers testifying that they just followed the instructions from the Speaker. It might be difficult to prove partisan intent (that Madigan is both House Speaker and head of the Illinois Democratic Party doesn't prove his motives are impure).

In a state like West Virginia, statewide races for President, Governor, Senate, might not be representative of legislative races, which will tend to be more Democratic. Even though the West Virginia legislature flipped in 2016, they weren't running up 42% pluralities, like Trump did.

The hypothetical model that was used to explain the Efficiency Gap used 100 votes per district, which could reasonably be understood as being a percentage as well.

When I started looking at the example closely, I realized it was "unfair" since Party B had 56% of the total vote, and only elected 40% of the legislators. It was after I started playing around that I realized that the only thing that mattered was the distribution of seats.

An analytical model is dependent on there being equal numbers of voters in each district, since it assumes that a plan that produces SA seats won by Party A will have the same vote share for Party A in each district, and also that a plan that produces SB seats won by Party B will have the same vote share for Party A in each district.

It does not matter that this distribution is unrealistic, since we have already demonstrated that the Efficiency Gap metric is not dependent on the distribution among districts, but simply the overall distribution of the population.

[jimrtex]

I was interested in whether the geographic distribution of votes could be accounted for with the Efficiency Gap.

Returning to our hypothetical state, with 56% of the vote for Party B, imagine two areas, Point A and Point B, with the wide Noway River separating the two (this is where the expression that there is "Noway to get from Point A to Point B" came from. It originally meant that the Noway Ferry was the only way to get from Point A and Point B. Point A has 44% of the population and is thoroughly dominated by Party A. Point B has 56% of the population and is as thoroughly dominated by Party B.

There is no way to avoid a 56:44 distribution in districts. Even if there were substantial dispersion across the river, it would likely have the same result.

Point A: Party A 26, Party B 18.
Point B: Party B 38, Party A 18.

Perhaps with a careful drawing of districts, Party B could gain a few more districts, if its supporters who crossed the river were concentrated.

But what if the state were thoroughly homogenized? Every county, town, ward, and even census block was divided 54:46? There would be no way to avoid creating every district as a 56:44 win for B.

While Party A might have a chance to sweep to power in a wave year, the more likely result would be that the party would atrophy. The more able school board and city council members would be recruited by Party B to run for the legislature.

The Efficiency Gap will be zero when, the Share of the Districts won by A, ShA, is equal to twice the Vote Share, VA minus one half.

ShA = 2 * VA - 0.5

In Wisconsin, Trump won 50.4% of the two-way vote, and based on the formula, Republicans should elect 50.9% of the Assembly members, or 50.354 members.

But what if we apportioned assembly members to each county, based on population, and then calculated the efficient representation for each county.

For example, Waukesha County would have 6.787 Assembly members. Trump had 64.3% of the two-way vote, and if there were an efficiency gap of zero, the Republicans would control 78.6% of the districts or 5.332 districts. The Democrats would win the remaining 1.455 districts.

We can calculate the results for the remaining counties, with one minor adjustment. The formula would indicate that a party that received 76% of the vote would control 102% of the districts. So each party was limited to 100% of the districts in county (Clinton had 75.3% of the two-way vote in Dane, and 78.9% in Menominee).

Using this county-based method, Republicans would control 50.354 districts, almost the same as for the statewide result (they vary in the 4th decimal place, 50.3539 vs. 50.3545).

It appears that turnout (votes cast/census population) is somewhat balanced in Wisconsin, with high turnout in Dane (Madison), the three WOW counties around Milwaukee, and six counties in the extreme North (Bayfield, Door, Florence, Iron, Oneida, and Vilas). These may represent persons with second homes, who are seasonal residents, who might not be present on April 1 when the census is taken. There may also be a larger share of retirees or empty nesters.

The low turnout counties are Milwaukee, Kenosha, and Menominee, and a odd grouping in western Wisconsin - start with a stack from Taylor to Monroe, add Juneau, and then skip down to Richland, Lafayette, and Crawford.

If Dane and Milwaukee are treated separately, then Trump had 58% of the two-way vote in the remainder of the state. Republicans would be expected to control 66% (49 of 74 districts). But with only 42% of the two-way vote, is there enough heterogeneity to carve out 25 Democratic seats?

[jimrtex]

I was interested in whether the geographic distribution of votes could be accounted for with the Efficiency Gap.

Returning to our hypothetical state, with 56% of the vote for Party B, imagine two areas, Point A and Point B, with the wide Noway River separating the two (this is where the expression that there is "Noway to get from Point A to Point B" came from. It originally meant that the Noway Ferry was the only way to get from Point A and Point B. Point A has 44% of the population and is thoroughly dominated by Party A. Point B has 56% of the population and is as thoroughly dominated by Party B.

There is no way to avoid a 56:44 distribution in districts. Even if there were substantial dispersion across the river, it would likely have the same result.

Point A: Party A 26, Party B 18.
Point B: Party B 38, Party A 18.

Perhaps with a careful drawing of districts, Party B could gain a few more districts, if its supporters who crossed the river were concentrated.

But what if the state were thoroughly homogenized? Every county, town, ward, and even census block was divided 54:46? There would be no way to avoid creating every district as a 56:44 win for B.

While Party A might have a chance to sweep to power in a wave year, the more likely result would be that the party would atrophy. The more able school board and city council members would be recruited by Party B to run for the legislature.

The Efficiency Gap will be zero when, the Share of the Districts won by A, ShA, is equal to twice the Vote Share, VA minus one half.

ShA = 2 * VA - 0.5

In Wisconsin, Trump won 50.4% of the two-way vote, and based on the formula, Republicans should elect 50.9% of the Assembly members, or 50.354 members.

But what if we apportioned assembly members to each county, based on population, and then calculated the efficient representation for each county.

For example, Waukesha County would have 6.787 Assembly members. Trump had 64.3% of the two-way vote, and if there were an efficiency gap of zero, the Republicans would control 78.6% of the districts or 5.332 districts. The Democrats would win the remaining 1.455 districts.

We can calculate the results for the remaining counties, with one minor adjustment. The formula would indicate that a party that received 76% of the vote would control 102% of the districts. So each party was limited to 100% of the districts in county (Clinton had 75.3% of the two-way vote in Dane, and 78.9% in Menominee).

Using this county-based method, Republicans would control 50.354 districts, almost the same as for the statewide result (they vary in the 4th decimal place, 50.3539 vs. 50.3545).

It appears that turnout (votes cast/census population) is somewhat balanced in Wisconsin, with high turnout in Dane (Madison), the three WOW counties around Milwaukee, and six counties in the extreme North (Bayfield, Door, Florence, Iron, Oneida, and Vilas). These may represent persons with second homes, who are seasonal residents, who might not be present on April 1 when the census is taken. There may also be a larger share of retirees or empty nesters.

The low turnout counties are Milwaukee, Kenosha, and Menominee, and a odd grouping in western Wisconsin - start with a stack from Taylor to Monroe, add Juneau, and then skip down to Richland, Lafayette, and Crawford.

If Dane and Milwaukee are treated separately, then Trump had 58% of the two-way vote in the remainder of the state. Republicans would be expected to control 66% (49 of 74 districts). But with only 42% of the two-way vote, is there enough heterogeneity to carve out 25 Democratic seats?