"The efficiency gap": understanding the math behind a crucial Supreme Court gerrymandering case

Originally published at: https://boingboing.net/2018/01/01/gill-v-whitford.html


Hasn’t the current administration got around to banning “math based” arguments? Surely gut feeling and gumption are the order of the day. If was good enough for the Founding Fathers, it is good enough for… waddaya mean Jefferson, Washington, Franklin and Adams all supported Mathematical Education!? We’ll have none of your fancy, liberal “history based” arguments around here! Goddam “Liberal Arts”!


Math is not the answer.

Why are political parties and race more deserving than sexual orientation, or home vs public schoolers? Most suggestions to “fix” gerrymandering involve some kind of quota system as a test of electoral fairness, but pre-selecting certain groups as “protected” puts the system in a terrible bind. All math methods rely on geographic clustering of like-minded voters, but in today’s world, some voting blocks may be uniformly distributed across a state, and can never elect a sympathetic representative. Or live on-line. This is why the “math tests” of fairness are ultimately pointless.

Only some form or proportional voting ensures our constitution rights are respected, while avoiding equally troublesome preferences- - see
Cumulative voting and gerrymandering

and this illustration of how compact districts are easily foiled:
[district shapes cannot fix gerrymandering]


While the Tufts-based MGGG group is doing lots of great work (particularly at this point, I think, organizing conferences, bringing people together and facilitating discussions), I think it’s important to clarify that the efficiency gap was developed by political scientist Eric McGhee several years ago. (My understanding is that he then joined forces with Nicholas Stephanopoulos to flesh out how it could be used in litigation.) See https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3077766 for a recent article by the two of them.


While I’d like to reduce gerrymandering, the fact is even if we got it fairly fair, we are still hopelessly stuck in a 2 party system.


Sure, criticisms can be made of single-member plurality districts (what we currently have for congressional races) and maybe another method should be advocated for. But math can still help guard against the most egregious abuses of gerrymandering until our overall system changes. There are a number of tests (including the efficiency gap) that don’t depend on the shapes of districts and that don’t depend on “quotas.”


You could have a smaller government if representatives had weighted votes. Then instead of electing 4 people you elect one who gets 4 votes. I’m not saying this is strictly a better form of government, but it does mostly eliminate gerrymandering and it reduces the number of people that have to collect a salary to represent us.

You’ll have the precise same outcome as today, except all the laws would have 4 times as many votes attached.


Fully agreed. We need to get rid of that absurd “one person, one vote” thing and go to a system wherein each voter gets a bag full of votes (same amount for each person, wise guys!) and can assign them in any amount to any candidate. Regional grouping is at least as bad for districts as it is for the way we divide up Senators.

1 Like

But the math is measuring “something”. For example, party affiliation. But why party affiliation? A bit self-serving that politician try to manipulate party affiliation among all possible metrics…

I’m pretty skeptical of cumulative voting for political elections.

Say my district sends two representatives, my ideal outcome is Alice and Bob are elected, with a preference to Alice being chosen. Now how do I allocate my votes? All to Alice to guarantee one slot? Half-and-half, with the risk neither are chosen? Most to Alice in some proportion?

Even when I’ve made a clear decision it’s very unclear how I should vote.

On the other hand, ranked voting does let me express my exact intent, of Alice then Bob. And I don’t have to worry as much about the weird game theory about how other people allocate their votes.


But the math is measuring “something”. For example, party affiliation. But why party affiliation? A bit self-serving that politician try to manipulate party affiliation among all possible metrics…

Is this sarcasm?

Turns out ranked voting is very hard for most people to understand how it works (see some of the references to the voting literature mentioned in my article). Plus humans have trouble making sensible rankings beyond the first three desired candidates. So ranked voting is met with skepticism. Fortunately, cumulative voting is common in much of the world so there is lots of real-world evidence it works as intended.

Fairvote.org lobbys for cumulative voting, in a slightly different way than I propose. See their website for historical examples.


I think you’ve misunderstood something. This article, and the math in question is about how to establish whether and where a particular set of districts have been manipulated to effect electoral outcomes.

So two things

  1. You need some metric by which to model the population in a given area. So that you can compare how votes among that population would turn out given an ideal “fair” playing field with how they turn out given the playing field we actually have. In terms of modeling political outcomes. Party affiliation, race, age, gender etc are all fairly diagnostic. That’s what they guys are doing. Trying to figure out a way to demonstrate the “fairness” of a given set of congressional districts in a way that’s provable in court. Establish the gap between the ideal, and the reality.

  2. Party affiliation, and often race, age, gender, even sexual orientation. Are the metrics used to establish these gerrymandered districts. So this:

Is exactly right. The GOP has been actively manipulating districts according to party affiliation for a decade or more. Because its much, much harder to prove. And provided the results are not “extreme” according to an arbitrary standard. Entirely legal.

Gerrymandering based on race, gender, age, sexual orientation, religion etc. Is explicitly illegal. And finding proof that its happened is as simple as finding the documents or statements where those responsible are all “we’re totally gonna suppress the black vote dudes!”

Party affiliation, aside from being a fairly direct and legal way to disadvantage your opponents, is also a pretty easy analog for things like race, gender, age and so forth. Because simply put all those non-white, gay, female, and young people. They have a disproportion tendency to be not in the GOP.

In order to have a set of districts proven, in court. To have been illegally gerrymandered based on party affiliation. You need some standard to prove it by. And we currently don’t really have one. These guys are trying to create one. And get it accepted by the courts.


This isn’t a general argument for a general audience on gerrymandering. It is an argument directed specifically at one person only, namely Justice Kennedy, since his is the only opinion that matters. It doesn’t matter what you or I think of it, it matters what Justice Kennedy thinks of it. It is carefully crafted to address his expressed concerns and issues. All the other justices are on record (and it is hilarious how each of them appears to be talking to Kennedy and nobody else) when they make their position:

Chief Justice Roberts: “sociological gobbledygook”
Justice Samuel Alito: distasteful, but preventative measures are unmanageable, unreliable, or too confusing
Justice Gorsuch: its imponderable, “A pinch of this, a pinch of that.”
Justice Thomas never says anything, but you can guess.

Justice Ginsburg: “The result is preordained… [what about] the precious right to vote?"
Justice Sotomayor: “It’s O.K. to stack the decks so that… one party—even though it gets a minority of votes—can get the majority of seats?”
Justice Breyer proposed a standard that courts could examine.
Justice Kagan: “This is not kind of hypothetical, airy-fairy. This is pretty scientific by this point.”

So its all up to Justice Kennedy. He has stated he is looking for a “limited and precise rationale…to correct an established violation of the Constitution in some redistricting cases.”

And Patrick Honner, Moon Duchin, et al, are doing their very best to give Justice Kennedy exactly that limited and precise rationale that he has asked for. Lets hope the math isn’t too hard for him


As the Texas Amicus before SCOTUS states, in anticipation of your exact point:

http://www.scotusblog.com/wp-content/uploads/2017/04/16-1161-cert-amicus-texas.pdf page 11:

As the district court put it, the plaintiffs’ proposed test—the efficiency gap—“measures the magnitude of a plan’s deviation from the relationship we would expect to observe between votes and seats.” J.S. App. 169a. But there is no reason to expect proportional representation in a system based on single-member districts. More importantly, there is no constitutional basis to compel the States to achieve proportional partisan representation in their legislatures.

They agree with the math, just don’t think there is a constitutional issue in play. Fortunately, as we saw in Baker v Carr, the law evolves.

1 Like

Proportional voting is also math… Frequently complex in order to get “good” results when the votes themselves are ambiguous.

Also I don’t think proportional voting would get us out of the hole gerrymandering has got us in. It would let you support both a major party candidate and one (or more) minor party ones. I think it would reveal that the minor parties actually have a lot more support then the current votes show. However the major parties probably still have most of the votes, and can still gerrymander their way to substantial advantage.

The biggest effect from proportional voting would be the lack of major party spinoffs “stealing” votes. If Bernie had run as an independent HRC would have lost a ton of votes in the current system. With proportional voting (or at least ranked voting of most sorts) anyone that liked both candidates, even if they had a strong preference for one or the other, could indeed vote for both…

EDIT: I don’t think I made it clear, I’m in favor of both anti-gerrymandering and proportional voting (I favor concordant voting, but would be happy with many forms of proportional voting). I just think they fix different problems, both of which the USA is suffering from.


Stripes-- there is no possibility of gerrymandering, because there would be a single district in a cumulative voting scheme. Eliminating geography as a way to tilt election results. BUT, to your point, any system can be gamed by the people in power. For example, minority voting suppression in the face of tight (but unnecessary) ID requirements. Or, in many states you only require 1000 names on a petition to run for either major party, but 10% of the votes cast in the last election to run as an independent…

Radiolab has a spin-off podcast called More Perfect that ran entire episode focusing not only on the efficiency gap, but the exact point you bring up. Namely, that the Supreme Court ruled a long time ago that gerrymandering is unconstitutional, but that it has yet to accept a legal test that objectively (from a legal perspective) defines gerrymandering. That’s what the math in this article is about, nothing more. Alternative voting schemes may or may not solve the general problem of gerrymandering more effectively, but the case before the Supreme Court last October required a test that applies to our current voting methods.


You are absolutely right. The issue is how to measure gerrymandering (a) - not how to develop an optimal electoral system (b). One might want to do a) but not want to do b). Of course perhaps people should want b) but hey ho.

And in that sense measuring the efficiency of voting is useful. How many Dem votes should it take to elect one congress critter? If it takes a factor of 2 more then you have a pretty good idea that all is not well. A factor of 3? I wonder how many boundary changes move that efficiency variable in a direction which is against the interest of the party in power?