## “Worst of the worst maps”: a factual mistake in Gill v. Whitford

The oral arguments in Gill v. Whitford, the Wisconsin gerrymandering case, are now a month behind us.  But there’s a factual error in the state’s case, and I don’t want to let it be forgotten.  Thanks to Mira Bernstein for pointing this issue out to me.

Misha Tseytlin, Wisconsin’s solicitor general, was one of two lawyers arguing that the state’s Republican-drawn legislative boundaries should be allowed to stand.  Tseytlin argued that the metrics that flagged Wisconsin’s maps as drastically skewed in the GOP’s favor were unreliable:

And I think the easiest way to see this is to take a look at a chart that plaintiff’s own expert created, and that’s available on Supplemental Appendix 235. This is plain — plaintiff’s expert studied maps from 30 years, and he identified the 17 worst of the worst maps. What is so striking about that list of 17 is that 10 were neutral draws.  There were court-drawn maps, commission-drawn maps, bipartisan drawn maps, including the immediately prior Wisconsin drawn map.

That’s a strong claim, which jumped out at me when I read the transcripts–10 of the 17 very worst maps, according to the metrics, were drawn by neutral parties!  That really makes it sound like whatever those metrics are measuring, it’s not partisan gerrymandering.

But the claim isn’t true.

(To be clear, I believe Tseytlin made a mistake here, not a deliberate misrepresentation.)

The table he’s referring to is on p.55 of this paper by Simon Jackman, described as follows:

Of these, 17 plans are utterly unambiguous with respect to the sign of the efficiency gap estimates recorded over the life of the plan:

Let me unpack what Jackman’s saying here.  These are the 17 maps where we can be sure the efficiency gap favored the same party, three elections in a row.  You might ask: why wouldn’t we be sure about which side the map favors?  Isn’t the efficiency gap something we can compute precisely?  Not exactly.  The basic efficiency gap formula assumes both parties are running candidates in every district.  If there’s an uncontested race, you have to make your best estimate for what the candidate’s vote shares would have been if there had been candidates of both parties.  So you have an estimate for the efficiency gap, but also some uncertainty.  The more uncontested races, the more uncertain you are about the efficiency gap.

So the maps on this list aren’t the 17 “worst of the worst maps.”  They’re not the ones with the highest efficiency gaps, not the ones most badly gerrymandered by any measure.  They’re the ones in states with so few uncontested races that we can be essentially certain the efficiency gap favored the same party three years running.

Tseytlin’s argument is supposed to make you think that big efficiency gaps are as likely to come from neutral maps as partisan ones.  But that’s not true.  Maps drawn by Democratic legislatures have average efficiency gap favoring Democrats; those by GOP on average favor the GOP; neutral maps are in between, and have smaller efficiency gaps overall.

That’s from p.35 of another Jackman paper.  Note the big change after 2010.  It wasn’t always the case that partisan legislators automatically thumbed the scales strongly in their favor when drawing the maps.  But these days, it kind of is.  Is that because partisanship is worse now?  Or because cheaper, faster computation makes it easier for one-party legislatures to do what they always would have done, if they could?  I can’t say for sure.

Efficiency gap isn’t a perfect measure, and neither side in this case is arguing it should be the single or final arbiter of unconstitutional gerrymandering.  But the idea that efficiency gap flags neutral maps as often as partisan maps is just wrong, and it shouldn’t have been part of the state’s argument before the court.

## The greatest Astro/Dodger

The World Series is here and so it’s time again to figure out which player in the history of baseball has had the most distinguished joint record of contributions to both teams in contention for the title.  (Last year:  Riggs Stephenson was the greatest Cub/Indian.)  Astros history just isn’t that long, so it’s a little surprising to find we come up with a really solid winner this year:  Jimmy Wynn, “The Toy Cannon,” a longtime Astro who moved to LA in 1974 and had arguably his best season, finishing 5th in MVP voting and leading the Dodgers to a pennant.  Real three-true-outcomes guy:  led the league in walks twice and strikeouts once, and was top-10 in the National League in home runs four times in the AstrodomeCareer total of 41.4 WAR for the Astros, and 12.3 for the Dodgers in just two years there.

As always, thanks to the indispensable Baseball Reference Play Index for making this search possible.

Other contenders:  Don Sutton is clearly tops among pitchers.  Sutton was the flip side of Wynn; he had just two seasons for Houston but they were pretty good.  Beyond that it’s slim pickings.  Jeff Kent put in some years for both teams.  So did Joe Ferguson.

Who are we rooting for?  On the “ex-Orioles on the WS Roster” I guess the Dodgers have the advantage, with Rich Hill and Justin Turner (I have to admit I have no memory of Turner playing for the Orioles at all, even though it wasn’t that long ago!  It was in 2009, a season I have few occasions to recall.)  But both these teams are stocked with players I just plain like:  Kershaw, Puig, Altuve, the great Carlos Beltran…

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## Trace test

Jose Rodriguez gave a great seminar here yesterday about his work on the trace test, a numerical way of identifying irreducible components of varieties.  In Jose’s world, you do a lot of work with homotopy; if a variety X intersects a linear subspace V in points p1, p2, .. pk, you can move V a little bit and numerically follow those k points around.  If you move V more than a little bit — say in a nice long path in the Grassmannian that loops around and returns to its starting point — you’ll come back to p1, p2, .. pk, but maybe in a different order.  In this way you can compute the monodromy of those points; if it’s transitive, and if you’re careful about avoiding some kind of discriminant locus, you’ve proven that p1,p2…pk are all on the same component of V.

But the trace test is another thing; it’s about short paths, not long paths.  For somebody like me, who never thinks about numerical methods, this means “oh we should work in the local ring.”  And then it says something interesting!  It comes down to this.  Suppose F(x,y) is a form (not necessarily homogenous) of degree at most d over a field k.  Hitting it with a linear transformation if need be, we can assume the x^d term is nonzero.  Now think of F as an element of k((y))[x]:  namely

$F = x^d + a_1(y) x^{d-1} + \ldots + a_d(y).$

Letting K be the algebraic closure of k((y)), we can then factor F as (x-r_1) … (x-r_d).  Each of these roots can be computed as explicitly to any desired precision by Hensel’s lemma.  While the r_i may be power series in k((y)) (or in some algebraic extension), the sum of the r_i is -a_1(y), which is a linear function A+by.

Suppose you are wondering whether F factors in k[x,y], and whether, for instance, r_1 and r_2 are the roots of an irreducible factor of F.  For that to be true, r_1 + r_2 must be a linear function of y!  (In Jose’s world, you grab a set of points, you homotopy them around, and observe that if they lie on an irreducible component, their centroid moves linearly as you translate the plane V.)

Anyway, you can falsify this easily; it’s enough for e.g. the quadratic term of r_1 + r_2 to be nonzero.  If you want to prove F is irreducible, you just check that every proper subset of the r_i sums to something nonlinear.

1.  Is this something I already know in another guise?
2.  Is there a nice way to express the condition (which implies irreducibility) that no proper subset of the r_i sums to something with zero quadratic term?

## Game report: Cubs 5, Brewers 0

• I guess the most dominant pitching performance I’ve seen in person?  Quintana never seemed dominant.  The Brewers hit a lot of balls hard.  But a 3-hit complete game shutout is a 3-hit complete game shutout.
• A lot of Cubs fans. A lot a lot.  My kids both agreed there were more Cubs than Brewers fans there, in a game that probably mattered more to Milwaukee.
• For Cubs fans to boo Ryan Braun in Wrigley Field is OK, I guess.  To come to Miller Park and boo Ryan Braun is classless.  Some of those people were wearing Sammy Sosa jerseys!
• This is the first time I’ve sat high up in the outfield.  And the view was great, as it’s been from every other seat I’ve ever occupied there.  A really nice design.  If only the food were better.
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## Road trip to totality

My kids both wanted to see the eclipse and I said “that sounds fun but it’s too far” and I kept thinking about it and thinking about it and finally, Saturday night, I looked inward and asked myself is there really a reason we can’t do this? And the answer was no.  Or rather the answer was “it might be the case that it’s totally impossible to find a place to sleep in the totality zone within 24 hours for a non-insane amount of money, and that would be a reason” so I said, if I can get a room, we’re going.  Hotel Tonight did the rest.  (Not the first time this last-minute hotel app has saved my bacon, by the way.  I don’t use it a lot, but when I need it, it gets the job done.)

Notes on the trip:

• We got to St. Louis Sunday night; the only sight still open was my favorite one, the Gateway Arch.  The arch is one of those things whose size and physical strangeness a photo really doesn’t capture, like Mt. Rushmore.  It works for me in the same way a Richard Serra sculpture works; it cuts the sky up in a way that doesn’t quite make sense.
• I thought I was doing this to be a good dad, but in fact the total eclipse was more spectacular than I’d imagined, worth it in its own right.  From the photos I imagined the whole sky going nighttime dark.  But no, it’s more like twilight. That makes it better.  A dark blue sky with a flaming hole in it.
• Underrated aspect:  the communality of it all.  An experience now rare in everyday life.  You’re in a field with thousands of other people there for the same reason as you, watching the same thing you’re watching.  Like a baseball game!  No radio call can compare with the feeling of jumping up with the crowd for a home run.  You’re just one in an array of sensors, all focused on a sphere briefly suspended in the sky.
• People thought it was going to be cloudy.  I never read so many weather blogs as I did Monday morning.  Our Hotel Tonight room was in O’Fallon, MO, right at the edge of the totality.  Our original plan was to meet Patrick LaVictoire in Hermann, west of where we were.  But the weather blogs said south, go south, as far as you can.  That was a problem, because at the end of the day we had to drive back north.  We got as far as Festus.  There were still three hours to totality and we thought it might be smart to drive further, maybe even all the way to southern Illinois.  But a guy outside the Comfort Inn with a telescope, who seemed to know what he was doing, told us not to bother, it was a crapshoot either way and we weren’t any better off there than here.  I always trust a man with a telescope.
• Google Maps (or the Waze buried within Google Maps) not really adequate to handle the surge of traffic after a one-time event.  Its estimates for how long it would take us to traverse I-55 through southern Illinois were … unduly optimistic.  Google sent us off the highway onto back roads, but here’s the thing — it sent the same suggestion to everyone else, which meant that instead of being in a traffic jam on the interstate we were in a traffic jam on a gravel road in the middle of a cornfield.  When Google says “switch to this road, it’ll save you ten minutes,” does it take into account the effect of its own suggestion, broadcast to thousands of cars in the same jam?  My optimization friends tell me this kind of secondary prediction is really hard.  It would have been much better, in retrospect, for us to have chosen a back road at random; if everybody injected stochasticity that way, the traffic would have been better-distributed, you have to figure.  Should Google build that stochasticity into its route suggestions?
• It became clear around Springfield we weren’t going to get home until well after midnight, so we stopped for the night in David Foster Wallace’s hometown, Normal, IL, fitting, considering we did a supposedly fun thing that turned out to be an actual fun thing which we will hardly ever have the chance to, and thus may never, do again.

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## Not to exceed 25%

Supreme Court will hear a math case!

At issue in Murphy v. Smith:  the amount of a judgment that a court can apply to covering attorney’s fees.  Here’s the relevant statute:

Whenever a monetary judgment is awarded in an action described in paragraph (1), a portion of the judgment (not to exceed 25 percent) shall be applied to satisfy the amount of attorney’s fees awarded against the defendant.

To be clear: there are two amounts of money here.  The first is the amount of attorney’s fees awarded against the defendant; the second is the portion of the judgment which the court applies towards that first amount.  This case concerns the discretion of the court to decide on the second number.

In Murphy’s case, the court decided to apply just 10% of the judgment to attorney’s fees.  Other circuit courts have licensed this practice, interpreting the law to allow the court discretion to apply any portion between 0 and 25% of the judgement to attorney’s fees.  The 7th circuit disagreed, saying that, given that the amount of attorney’s fees awarded exceeded 25% of the judgment, the court was obligated to apply the full 25% maximum.

The cert petition to the Supreme Court hammers this view, which it calls “non-literal”:

The Seventh Circuit is simply wrong in interpreting this language to mean “exactly 25 percent.” “Statutory interpretation, as we always say, begins with the text.” Ross v. Blake, 136 S. Ct. 1850, 1856 (2016). Here, the text is so clear that interpretation should end with the text as well. “Not to exceed” does not mean “exactly.”

This seems pretty clearly correct:  “not to exceed 25%” means what it means, not “exactly 25%.”  So the 7th circuit just blew it, right?

Nope!  The 7th circuit is right, the other circuits and the cert are wrong, and the Supreme Court should affirm.  At least that’s what I say.  Here’s why.

I can imagine at least three interpretations of the statuye.

1.  The court has to apply exactly 25% of the judgment to attorney’s fees.
2.  The court has to apply the smaller of the following numbers:  the total amount awarded in attorney’s fees, or 25% of the judgment.
3.  The court has full discretion to apply any nonnegative amount of the judgment to attorney’s fees.

Cert holds that 3 is correct, that the 7th circuit applied 1, and that 1 is absurdly wrong.  In fact, the 7th circuit applied 2, which is correct, and 1 and 3 are both wrong.

1 is wrong:  1 is wrong for two reasons.  One is pointed out by the cert petition:  “Not to exceed 25%” doesn’t mean “Exactly 25%.”  Another reason is that “Exactly 25%” might be more than the amount awarded in attorney’s fees, in which case it would be ridiculous to apply more money than was actually owed.

7th circuit applied 2, not 1:  The opinion reads:

In Johnson v. Daley, 339 F.3d 582, 585 (7th Cir. 2003) (en banc), we explained that § 1997e(d)(2) required that “attorneys’ compensation come[] first from the damages.” “[O]nly  if 25% of the award is inadequate to compensate counsel fully” does the defendant contribute more to the fees. Id. We continue to believe that is the most natural reading of the statutory text. We do not think the statute contemplated a discretionary decision by the district court. The statute neither uses discretionary language nor provides any guidance for such discretion.

The attorney’s compensation comes first out of the damages, but if that compensation is less than 25% of the damages, then less than 25% of the damages will be applied.  This is interpretation 2.  In the case at hand, 25% of the damages was \$76,933.46 , while the attorney’s fees awarded were \$108,446.54.   So, in this case, the results of applying 1 and 2 are the same; but the court’s interpretation is clearly 2, not the absurd 1.

3 is wrong:  Interpretation 3 is on first glance appealing.  Why shouldn’t “a portion of the judgment (not to exceed 25%)” mean any portion satisfying that inequality?  The reason comes later in the statute; that portion is required to “satisfy the amount of attorney’s fees awarded against the defendant.”  To “satisfy” a claim is to pay it in full, not in part.  Circuits that have adopted interpretation 3, as the 8th did in Boesing v. Spiess, are adopting a reading at least as non-literal as the one cert accuses the 7th of.

Of course, in cases like Murphy v. Smith, the two clauses are in conflict:  25% of the judgment is insufficient to satisfy the amount awarded.  In this case, one requirement must bend.  Under interpretation 2, when the two clauses are in conflict, “satisfy” is the one to give way.  The 7th circuit recognizes this, correctly describing the 25% awarded as ” toward satisfying the attorney fee the court awarded,” not “satisfying” it.

Under interpretation 3, on the other hand, the requirement to “satisfy” has no force even when it is not in conflict with the first clause.  In other words, they interpret the law as if the word “satisfy” were absent, and the clause read “shall be applied to the amount of attorney’s fees.”

Suppose the attorney’s fees awarded in Murphy had been \$60,000.  Under interpretation 3, the court would be free to ignore the requirement to satisfy entirely, and apply only 10% of the judgment to the attorneys, despite the fact that satisfaction was achievable within the statutory 25% limit.

Even worse:  imagine that the statute didn’t have the parenthetical, and said just

Whenever a monetary judgment is awarded in an action described in paragraph (1), a portion of the judgment shall be applied to satisfy the amount of attorney’s fees awarded against the defendant.

It would be crystal clear that the court was required to apply \$60,000, the amount necessary to satisfy the award.  On interpretation 3, the further constraint imposed by the statute gives the court more discretion rather than less in a case like this one!  This can’t be right.

You could imagine switching to an interpretation 3′, in which the court is required to satisfy the amount awarded if it can do so without breaking the 25% limit, but is otherwise totally unconstrained.  Under this theory, an increase in award from \$60,000 to \$100,000 lessens the amount the court is required to contribute — indeed, lessens it to essentially zero.  This also can’t be right.

2 is right:  When two clauses of a statute can’t simultaneously be satisfied, the court’s job is to find some balance which satisfies each requirement to the greatest extent possible in a range of possible cases.  Interpretation 2 seems the most reasonable choice.  The Supreme Court should recognize that, contra the cert petition, this is the interpretation actually adopted by the 7th Circuit, and should go along with it.

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## Maryland flag, my Maryland flag

The Maryland flag is, in my opinion as a Marylander, the greatest state flag.

Ungepotch?  Yes.  But it has that ineffable “it shouldn’t work but it does” that marks really great art.

But here’s something I didn’t know about my home state’s flag:

Despite the antiquity of its design, the Maryland flag is of post-Civil War origin. Throughout the colonial period, only the yellow-and-black Calvert family colors are mentioned in descriptions of the Maryland flag. After independence, the use of the Calvert family colors was discontinued. Various banners were used to represent the state, although none was adopted officially as a state flag. By the Civil War, the most common Maryland flag design probably consisted of the great seal of the state on a blue background. These blue banners were flown at least until the late 1890s….

Reintroduction of the Calvert coat of arms on the great seal of the state [in 1854] was followed by a reappearance at public events of banners in the yellow-and-black Calvert family colors. Called the “Maryland colors” or “Baltimore colors,” these yellow-and-black banners lacked official sanction of the General Assembly, but appear to have quickly become popular with the public as a unique and readily identifiable symbol of Maryland and its long history.

The red-and-white Crossland arms gained popularity in quite a different way. Probably because the yellow-and-black “Maryland colors” were popularly identified with a state which, reluctantly or not, remained in the Union, Marylanders who sympathized with the South adopted the red-and-white of the Crossland arms as their colors. Following Lincoln’s election in 1861, red and white “secession colors” appeared on everything from yarn stockings and cravats to children’s clothing. People displaying these red-and-white symbols of resistance to the Union and to Lincoln’s policies were vigorously prosecuted by Federal authorities.

During the war, Maryland-born Confederate soldiers used both the red-and-white colors and the cross bottony design from the Crossland quadrants of the Calvert coat of arms as a unique way of identifying their place of birth. Pins in the cross bottony shape were worn on uniforms, and the headquarters flag of the Maryland-born Confederate general Bradley T. Johnson was a red cross bottony on a white field.

By the end of the Civil War, therefore, both the yellow-and-black Calvert arms and the red-and-white colors and bottony cross design of the Crossland arms were clearly identified with Maryland, although they represented opposing sides in the conflict.

In 4th grade, in Maryland history, right after having to memorize the names of the counties, we learned about the flag’s origin in the Calvert coat of arms

but not about the symbolic meaning of the flag’s adoption, as an explicit gesture of reconciliation between Confederate sympathizers and Union loyalists sharing power in a post-war border state.

The Howard County flag is based on the Crossland arms.  (There’s also a sheaf of wheat and a silhouette of Howard County nosing its way through a golden triangle.)  The city of Baltimore, on the other hand, uses the Calvert yellow-and-black only.

Oh, and there’s one more flag:

That’s the flag of the Republic of Maryland, an independent country in West Africa settled mostly by free black Marylanders.  It existed only from 1854 to 1857, when it was absorbed into Liberia, of which it’s still a part, called Maryland County.  The county flag still has Lord Baltimore’s yellow, but not the black.

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## Good math days

I have good math days and bad math days; we all do.  An outsider might think the good math days are the days when you have good ideas.  That’s not how it works, at least for me.  You have good ideas on the bad math days, too; but one at a time.  You have an idea, you try it, you make some progress, it doesn’t work, your mind says “too bad.”

On the good math days, you have an idea, you try it, it doesn’t work, you click over to the next idea, you get over the obstacle that was blocking you, then you’re stuck again, you ask your mind “What’s the next thing to do?” you get the next idea, you take another step, and you just keep going.

You don’t feel smarter on the good math days.  It’s not even momentum, exactly, because it’s not a feeling of speed.  More like:  the feeling of being a big, heavy, not very fast vehicle, with very large tires, that’s just going to keep on traveling, over a bump, across a ditch, through a river, continually and inexorably moving in a roughly fixed direction.

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## Show report: Camp Friends and Omni at the Terrace

Beautiful weather last night so I decided, why not, go to the Terrace for the free show WUD put on:  Camp Friends (Madison) and Omni (Atlanta).

Missed most of Camp Friends, who were billed as experimental but in fact played genial, not-real-tight college indie.  Singer took his shirt off.

Omni, though — this is the real thing.  Everyone says it sounds like 1981 (specifically:  1981), and they’re right, but it rather wonderfully doesn’t sound like any particular thing in 1981.  There’s the herky-jerky-shoutiness and clipped chords (but on some songs that sounds like Devo and on others like Joe Jackson) and the jazz chords high on the neck (the Fall?  The Police?) and weird little technical guitar runs that sound like Genesis learning to play new wave guitar on Abacab and arpeggios that sound like Peter Buck learning to play guitar in the first place (these guys are from Georgia, after all.)  What I kind of love about young people is this.  To me, all these sounds are separate styles; to a kid picking up these records now, they’re just 1981, they’re all material to work from, you can put them together and something kind of great comes out of it.

You see a lot of bands with a frontman but not that many which, like Omni, have a frontman and a backman.  Philip Frobos sings and plays bass and mugs and talks to the audience.  Frankie Broyles, the guitar player, is a slight guy who looks like a librarian and stands still and almost expressionless while he plays his tight little runs.  Then, every once in a while, he unleashes an absolute storm of noise.  But still doesn’t grimace, still doesn’t move!  Amazing.  Penn and Teller is the only analogue I can think of.

Omni plays “Jungle Jenny,” live in Atlanta:

And here’s “Wire,” to give a sense of their more-dance-less-rock side:

Both songs are on Omni’s debut album, Deluxe, listenable at Bandcamp.

Best show I’ve seen at the Terrace in a long time.  Good job, WUD.

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## How many books do I read in a year?

Data:

2006: 27

2007: 19

2008: 22

2009: 30

2010: 23

2011: 19

2012: 27

2013: 35

2014: 31

2015: 38

2016: 29

Don’t quite know what to make of this.  I’m sort of surprised there’s so much variation!  I’d have thought I’d have read less when my kids were infants, or when I was writing my own book, but it seems pretty random.   I do see that I’ve been clearly reading more books the last few years than I did in 2012 and before.

Lists, as always, are here (2011 on) and here (2006-2010.)