On May 8, the Wisconsin voters who had sued to overturn Wisconsin’s Assembly redistricting on the grounds that it was a partisan gerrymander filed this brief in the U.S. Supreme Court, asking the Court not to disturb the ruling of the 3-judge U.S. District Court that overturned the gerrymander. The case is Gill v Whitford, 16-1161. Thanks to Rick Hasen for the link.
The brief claims:
“the efficiency gap is about comparing the wasted votes of each party, not determining whether the party’s percentage of the statewide vote share is reflected in the number of representatives that party elects.”
This is false. The efficiency gap mathematically is a measure of the percentage of seats won vs. the percentage of statewide votes.
Imagine that you calculate the number of wasted votes for Plan 1. You then shift voters around in a way that does not flip any seats for Plan 2. Then the number of wasted votes will remain unchanged.
For example, if you have three seats that are 60:40, 60:40, 60:40, and one that is 20:80, the number of wasted votes for Party A is 10, 10, 10, 20 = 50; and for Party B is 40, 40, 40, 30 = 150. The efficiency gap for Party B is (150-50)/200 or 50%.
If we move voters around among the first three districts without flipping them, the efficiency gap does not change. A wasted vote for Party A remains wasted as it is moved to another district, as does a vote for Party B. For example if we move a voter from Party A from District 1 to District 3, and a voter from Party B the opposite direction, so that the districts are 59:41, 60:40, 61:39, and 20:80, the number of wasted votes remains the same: 9, 10, 11, 20 = 50 and 41, 40, 39, 80 = 150.
We can continue to shift voters so that the districts become 51:49, 51:49, 78:22, and 20:80 such that Districts 1 and 2 become quite competitive, and District 3 is not even close. But the wasted votes are 1, 1, 28, 20 = 50, and 49, 49, 22, and 30 = 150.
We can move voters from where they are an excessive (wasted) vote for the winner and become a wasted vote for the loser and still no change. 51:49, 51:49, 51:49, and 47:53, and the wasted votes remain the same:
1, 1, 1, 47 = 50 and 49, 49, 49, 3 = 150. No change.
Only if we actually flip a seat is there a change: 65:35, 65:35, 49:51, 21:79 where wasted votes for Party A are 15, 15, 49, 21 = 100 and Party B is 35, 35, 1, 29 = 100 wasted votes, and the efficiency gap is 0%.
But we could also use: 85:15, 85:15, 15:85, 15:85, and the wasted votes are 35, 35, 15, 15 = 100 and 15, 15, 35, 35 = 100, and the efficiency gap remains 0%.
If a measure does not change UNLESS we change the PROPORTION of seats won, then it is a measure of (dis)proportionality.
There is an exception to the above. Going back to our first example:
60:40, 60:40, 60:40 and 20:80; and wasted votes of 10, 10, 10, 20 = 50; and 40, 40, 40, 30 = 150.
Now lets move some voters to District 4 without any compensating changes:
60:30, 60:30, 60:30 and 20:110; and wasted votes of 15, 15, 15, 20 = 65; and 30, 30, 30, 45 = 135.
The efficiency gap is reduced from 50% to 35%. We can allegedly make a plan “fairer” by using districts of varying sizes. In effect, the premise behind ‘Reynolds v Sims’ of “One Man, One Vote” is erroneous.
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A plan that had districts of 60:40, 60:40, 60:40, and 60:40 and an efficiency gap of (160-40)/(40+160) = 60% could be changed to:
81:40, 81:40, 39:40, 39:40 and the efficiency gap reduced to 19%.
But let’s go a bit further:
90.5:49.5, 90.5:49.5, 29.5:30.5, 29.5:30.5 and the wasted votes for Party A are 20.5, 20.5, 29.5, and 29.5 for a total of 100 wasted votes. For Party B, 49.5, 49.5, 0.5, and 0.5 for a total of 100 wasted votes. Since the wasted votes are equal, the efficiency gap is zero-point-zero-zero percent.
What if voters statewide were randomly assigned ballots for the districts with the number of ballots for each district equal? How would that violate Reynolds v Sims?
If Trump and Clinton voters were assigned randomly to 99 House districts with 28,160 voters each, Trump would be expected to carry 90.6 districts.
Trump had 50.4% of the two-way vote. If Trump had received 51% of the two-way vote, he would have carried 98.96 districts (a 99:0 sweep in 24 out of 25 elections).
This assumes that there would be no systematic effects (e.g. voters assigned to districts D, J, and T being more likely to vote for Trump; and those assigned to districts H, R, and C being more like to vote for Clinton)
The efficiency gap would be huge in this case, because almost all Clinton votes would be wasted, and extremely few of Trump voters.
Let’s assume it was a 91 to 8 district win for Trump, and he had 50.4% of the vote. We then hack the random number generator, such that persons with names like Johnson, Washington, and Jones were assigned to the 8 districts carried by Clinton, and to keep the districts equal in population we would transfer voters with German names to the other 91 districts. This would tend to move Black voters to the 8 Clinton districts, because a larger share of Johnson’s, Washington’s, and Jones’s are Black, than are persons with other names. And let’s imagine that our hack made the 8 Clinton districts 60%C:40%T, and the 91 Trumps districts 51.3%T:48.7%C. Just increasing the margin from 50.4% to 51.3% would make those 91 districts certain wins for Trump.
But the efficiency gap would be identical.
Imagine you had been pulled over for speeding. When your case went to trial, rather than showing radar results, they brought in an expert who testified that you were 6’1. You might have been speeding and you might be 6’1, but they don’t correlate, let alone have causal relationship.