I was reading an article in the NY Times explaining the math behind gerrymandering.

They used the Maryland 6th District as an example, that had 26k wasted votes and all 133k republican wasted votes. Overall, Maryland has a 10.7 % efficiency gap that favors the Democrats.

I understand all of this. What I don't seem to understand is what would've changed if Maryland had a 7% efficiency gap? Would the 7% threshold "make" the state Republican instead of Democrat?

How is all this math related to the Maryland 6th district gerrymandering case that's gone to court twice? Or how would the votes change had the supreme court overruled it?

And how is this packing and cracking of votes related to the redrawing of districts?

  • 2
    There's an implicit assumption here that someone who votes for a Democratic candidate in one district would vote for a Democratic candidate in another district. However, people don't vote strictly partisan. Sometimes it's about the candidate, not the party.
    – user2565
    Commented Jul 1, 2018 at 15:28
  • 1
    My answer politics.stackexchange.com/a/18495/2565 may or may not be helpful. It sort of kind of shows that, without gerrymandering, even a small majority would control 100% of the seats.
    – user2565
    Commented Jul 2, 2018 at 16:49

2 Answers 2


What I don't seem to understand is what would've changed if Maryland had a 7% efficiency gap? Would the 7% threshold "make" the state Republican instead of Democrat?

No, or at least not necessarily.

The efficiency gap is directed. 10.7% or 7% doesn't actually tell you anything about who it favors. Either one can favor the Democrats or the Republicans. However, if it is less than 7%, they say that it is neutral. (They being the people who wrote up the efficiency gap system with a purely arbitrary cutoff.) I.e. less than 7% in either direction is neutral or within normal bounds. However, even 1% could be said to be in the direction of the Democrats or the Republicans.

Also, the 7% threshold is only half of it. They also have a two-seat threshold. So unless the efficiency gap is large enough that it takes at least two seats to bring it back to neutral, it doesn't count. In Maryland, the gap is only one seat.

Efficiency gap by state.

Those two parts of the threshold are basically just saying that they can't gerrymander their way to a 0% efficiency gap. There will almost always be some discrepancy between the total vote and the actual result. For example, if the vote were exactly split, each party getting 50%, there is no way to give each half the seats. Because seats themselves are indivisible. We can't have four and a half seats for each. The closest we can get is five to four, as Maryland has an odd number of seats (nine).

This is problematic from a Republican perspective, because the way that efficiency gap analysis is calculated somehow finds that no Democratic gerrymanders exist (or at least they are not actionable under the arbitrary thresholds chosen). Yet Republicans can see Democratic gerrymanders in Maryland, Illinois, and California. For that matter if there were a proportional standard, Republicans could see improvements in Connecticut and Massachusetts.

Third parties fare even worse. Both the Libertarians and the Greens have enough support in California to get at least one seat under a proportional standard. But efficiency gap analysis doesn't give them any seats because their support is too spread out rather than concentrated in a few areas.

To return to the literal question that you asked, a state with an efficiency gap less than 7% can be considered either neutral or leaning towards one party. We don't know which party from the size of the efficiency gap. But it is not considered to be gerrymandered regardless. It is a neutral (or within normal bounds) partition even if it slightly favors one party.

The threshold to switch from one party to another is an efficiency gap of 0%. 7% is just a proposed threshold to go from "leaning but fair" to partisan gerrymandered.

What changes

So in the comments, you ask how the court would fix a 10.7% efficiency gap. The answer is that they would either send the district map back to the legislature to be redone or redistrict the state themselves.

Of course, a big problem with efficiency gap analysis is that it can only be done after the fact and it can change with each election. So in 2022, some map would be used. In 2023, they would analyze that map and potentially redistrict if the efficiency gap was too high. In 2024, that map would be used. In 2025, they would analyze the map and redistrict if the efficiency gap was too high. So on and so forth.

Efficiency gap analysis essentially chases its own tail. It's always running the next election based on the results of the last election.

By contrast, there are any number of systems that support a proportional test that fix themselves in the same election:

  1. In Germany, they give underrepresented parties extra seats until the results are proportional.

  2. In proportional representation, they simply allocate seats based on their proportion of the vote.

  3. In Single Transferable Vote, they lump seats together and transfer votes from one candidate to another so that proportionally, everyone casts one vote.

By contrast, efficiency gap analysis simply tells them that by its measure, the districting plan is unfair. Fixing that is left up to the people who draw the maps. So the natural result of efficiency gap analysis will be a gerrymander every two years rather than every ten. These gerrymanders will be restricted by the efficiency gap analysis but not prevented by it.

In the next election, the results will be whatever they are. Then they use efficiency gap analysis to challenge the partition for the next election. Where again, the results will be whatever and provide room to challenge for the next election.

One of the advantages of a challenge like this is that the plaintiff has little to lose and potentially a lot to gain. The efficiency gap could go from 10.7% favoring the Democrats to 5% favoring the Republicans in a new map. And in a new election, that 5% might grow to 10.7%. Because the efficiency gap is based on voting rather than on more stable measures.

Regardless, efficiency gap analysis does not fix the results of the election that just took place. It attempts to fix the next election. Of course, its attempt to fix the next election may increase the efficiency gap of that election.

Packing and cracking

Packing and cracking are gerrymander techniques. For example, let's say that there was a demographic group that typically voted for one party. We'll call this group white evangelicals and assume that they vote overwhelmingly for the Republicans. Or we could call the group blacks or African-Americans and assume they vote for the Republicans.

Either way, assume this group is predominantly located in one area of the state. We can either try to pack them entirely into one district or try to crack them across multiple districts. If we pack them into a district (draw the lines such that they are all in the same district), we can make that district vote for their party and every other district safer for the other party.

Or we can crack the group across several districts, diluting their voting strength and allowing the party that they do not prefer to win their district. But wait, we can also use cracking the opposite way. If we have a bunch of districts that lean towards one party and one area that is overwhelmingly for the other party, we can crack that one area into the other districts and make a bunch of districts that lean the other way.

Similarly, we can pack voters of one persuasion with a lump of other voters to change a district from one party to the other. All that this really means is that the lines were drawn such that people living in this place, who happen to vote similarly would be in in the same district as the other voters.

There's an actual recent example of this. The Pennsylvania Supreme Court redrew Pennsylvania's districts. Looking particularly at what was district 8 and is now district 1, most of the district is Bucks county (and the entirety of Bucks is in the one district). Bucks is pretty even between Republicans and Democrats. Prior to the redraw, district 8 also included some of the Republican areas of Philadelphia and Montgomery counties. After the redraw, it includes some Democratic areas of Montgomery county in district 1.

Now, the court claims that it was just reversing the gerrymander by moving some of the wasted Republican votes from district 1 to other districts while moving some wasted Democratic votes from other districts to district 1. But in essence, they are packing Republicans into overwhelmingly Democratic districts while cracking Democratic areas into a Republican district.

Packing: concentrating voters of a particular political persuasion or demographic group into one district either to make the district vote their way or to overwhelm their vote and render it harmless by leaving them in a district that will never vote their way.

Cracking: dividing voters of a particular political persuasion or demographic group across multiple districts, either to dilute their vote by hiding it under an overwhelming advantage for the other party or to expand their influence by adding their vote to a near even split.

Most commonly we talk about packing in the sense of drawing voters out of other districts to form one district such that their preferred party wins in the one district but loses in the other districts. And cracking in terms of diluting the influence of one group of voters so that their preferred party loses in every district. But it's essentially the same action either way.

As a practical matter, Democrats are for packing their voters into urban districts in states like Utah and Nebraska which are overwhelmingly Republican and against it in states like Pennsylvania and Maryland. This is because in states like Utah and Nebraska, it gives them a chance at one seat per state. If instead their voters were cracked over multiple urban/rural districts, they would lose in every one.

Meanwhile, cracking urban districts in states like Pennsylvania and Maryland could lead to an overwhelming Democratic advantage. Because the urban voters are overwhelmingly Democratic while the suburban voters are more even.

Gerrymander explained

This answer posts:

Gerrymandering, explained

(source, adapted from original)

The leftmost image shows no districting and therefore no packing or cracking.

Number one is an example of packing. Both Republicans and Democrats are packed into their own districts. However, its results are perfectly proportional. Twenty of the votes are wasted, twelve for the Democrats and eight for the Republicans. The efficiency gap would favor the Republicans even though it is perfectly representative. So efficiency gap analysis would lead to a plan that swaps two Republicans with two Democrats. So four people would have representation not of their choice, assuming all else were equal.

Number two is an example of cracking. Republicans and Democrats are cracked across all five districts in such a way as to give the Democrats all the seats. This is a type of gerrymander, giving Democrats two more seats than their proportion of the vote would suggest.

Number three exhibits both cracking and packing. Democrats are packed into two districts and cracked across the other three. Republicans are packed into the three districts where the Democrats are cracked. Republicans win three districts, one more than they do in perfect representation.

We say that the Republicans are packed because they have more votes in three of the districts than their overall split. The Democrats are cracked in the same three districts because they are underrepresented in those districts. In the remaining two districts, Democrats are packed.

This is slightly incorrect in that it acts as if we knew how people voted. In reality, we don't know that. We know how regions (called precincts) voted in aggregate. So real districting plans don't involve people but regions. And regions don't vote monolithically. Instead, each district has its own separate vote. This makes the math more difficult but doesn't really change the concept. It mainly means that the perfectly representative districting plan is purely theoretical and doesn't appear in practice.

In practice, if we want something approaching perfect representation, we change the voting method from single districts to multiple districts.

  • I wouldn't say that the analysis shows that "no Democratic gerrymanders exist" - rather, I would say that "no Democratic gerrymanders are actionable under their system." It's clear from the slides in the analysis you linked that Connecticut and Nevada (just to name two) are heavily gapped towards Democrats - but because their delegations are small, there's not enough seats to even make it possible to have a two seat swing. States with larger delegations (such as NC and Ohio) make it easier to gain a multi-seat advantage, even with a smaller gap, and those just happen to be more Republican.
    – Bobson
    Commented Jul 1, 2018 at 6:27
  • Actually, I just found this article which says that it's "7% OR 2 seats", in which case there are several Democratic gerrymanders as well as more Republican ones.
    – Bobson
    Commented Jul 1, 2018 at 14:17
  • Regarding the Maryland 6th district, why was it taken to court twice? What I don't understand is why this was taken to court, how the court ruling would change the results, and why this math is related to any of these two points. Commented Jul 1, 2018 at 20:43
  • I understand the math behind the 7% and the wasted votes. I don't understand how the court ruling would change the math, which would then change the results. Commented Jul 1, 2018 at 20:44
  • Efficiency gaps for the diagrams, treating Blue as the positive value: 1: -10%. 2: 30%. 3: -30%.
    – Bobson
    Commented Jul 2, 2018 at 5:16

The Efficiency Gap does not measure Gerrymandering. It is a measure of Proportional Representation(2x). Forget about wasted votes, the Efficiency Gap is best understood using the equation:

EG = (% statewide seats - 50) - 2*(% statewide voteshare - 50)

Therefore, if your party has 51% of the statewide vote and 52% of the seats, the EG=0. The EG is also zero if your party has 60% of the statewide vote and 70% of the seats.

But, if your party has 60% of the statewide vote and 60% of the seats, EG=-10, which indicates that your state has been Gerrymandered. Think about that. A 60-60 state is Gerrymandered? That makes no sense.

  • Actually, a result of -10 means that the advantage is towards the other party. That means a state where one party wins 60% of the vote and gets 60% of the seats is actually disadvantaged relative to the other party. Why? Remember that we have first-past-the-post elections. If you had 60% (or even 51%) of the vote in every single district, you should have 100% of the seats. Drawing the lines such that you don't actually have all of them means that you've granted the other party seats they wouldn't normally have. Hence the -10.
    – Bobson
    Commented Jul 1, 2018 at 14:27
  • Of course, then all of the other party's votes would be wasted, driving up the gap in your favor. I don't know why their math works out so that voteshare counts double (I haven't read their paper), but I presume it's related to the first-past-the-post nature of elections.
    – Bobson
    Commented Jul 1, 2018 at 14:33
  • 1.Yes, I know what the -sign stands for. I was making a statement that a 60% D state that has 60% Ds in the legislature is considered Gerrymandered. This shows the absurdity of using the Efficiency Gap to determine if a state has been Gerrymandered. 2. If you had 60% of the vote in every district, thus 100% of the seats, EG = (100-50)-2(60-50) = +30. 3. Again, the Efficiency Gap measures Proportional Representation, not Gerrymandering. 4. The Efficiency Gap has nothing to do with first past the post. The 2x relation can be derived from the way the author defined wasted votes.
    – Ray J
    Commented Jul 1, 2018 at 23:41

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