# Why is the efficiency gap (to measure Gerrymandering) higher when the voter repartition is perfectly uniform?

The efficiency gap, as explained in Stephanopoulos and McGhee (2015), measures Gerrymandering using the notion of wasted votes (see a quick overview at How the Efficiency Gap Works (PDF)). This measure is the main argument used currently by the plaintiffs at the supreme court for the Wisconsin case of Gerrymandering.

But it seems there is an issue, in the case of a hypothetical population, where voters are perfectly uniformly spread on the territory, such as in any possible district of any possible possible voting map, 51% of the population vote for the Party A, and 49% for the Party B. In this case, there is no Gerrymandering possible: any election for any possible map will give all the seats for the Party A. But using the efficiency gap, if I have well understood, it will give a maximal measure of the Gerrymandering (close to 50%).

In that case, how can this metric be used as a measure of Gerrymandering? How do the proponents of this metric deal with that issue?

EDIT : The math behind the example. Let's imagine 10 districts with 100 people in each (so 1000 people in total). In each district, the Party A will have 1 wasted vote (everything above the majority), and the Party B will have 49 wasted votes. So in total: 10 wasted votes for the Party A, 490 for the Party B.

``````EfficiencyGap = (WastedVote_PartyB - WastedVote_PartyA)/TotalVotes
= (490-10)/1000
= 48%
``````

Source: Stephanopoulos, N.O., and McGhee, E.M. (2015). Partisan Gerrymandering and the Efficiency Gap. The University of Chicago Law Review 82, 831–900.

• Would you mind showing your math? I get about 50% for that situation Commented Oct 17, 2017 at 17:16
• Yes, sorry for that, it is around 50% (which is, as I understand it, still the maximum you can obtain), you are right, I edit my question. Commented Oct 17, 2017 at 17:19
• Since a map like you propose cannot exist in reality, I imagine proponents of this measure would simply draw the map to minimize the gap. In some cases, it would probably look just as wiggly, if not worse, than some of the maps currently used. Commented Oct 17, 2017 at 17:36
• After having read the paper I find the quote "... unless states could show that the gaps either resulted from the consistent application of legitimate policies or were inevitable due to the states' political geography." So it seems they do address and dismiss this issue.
– user9389
Commented Oct 18, 2017 at 15:55

### Efficiency gap

In that case, how can this metric be used as a measure of Gerrymandering ? How do the proponents of this metric deal with that issue ?

Handwaving. They assume that over the course of several election cycles, the vote would go differently. Either the incumbent would get more than 51% of the vote or the challenger would sometimes win. That's because that's what normally happens. Incumbents normally win unless the challenger has some kind of advantage that year.

There's also a theoretical problem with really unbalanced districts requiring gerrymandering. For example, if Salt Lake City is roughly even in voters and the rest of Utah is overwhelmingly Republican, then the wasted Republicans could outnumber the wasted Democrats in a 4-0 split. Because excess votes in winning by too much is as bad as losing votes in the efficiency gap.

### Gerrymandering

The primary problem is that gerrymandering is not a measurable thing. Start with the fact that gerrymandering is not just one thing. It is a collection of different behaviors, united by how people feel about them. Things that can be called gerrymandering:

1. Giving the district an odd shape (e.g. like Gerry's salamander).
2. Splitting up a municipality or county unnecessarily.
3. Putting too many voters of a group in one district (packing).
4. Putting not enough voters of a group in one district (cracking).

The problem is that these things can be contradictory. The most even shape might be to split an entity across two districts. If we keep the city together and want to keep the rest of the county in one district, we tend to have to shape it like a doughnut (with a hole in the middle). In one district, it might take 60% minority by population to ensure 55% by registration and 50% by actual voter. But in another district, they may call that same proportion packing.

For example, let's look at the 12th congressional district in North Carolina in 2016. This district was 44.6% black, less than half. Yet the argument was that this district packed too many black voters into one district. So the courts mandated that they crack the district and distribute its voters among other districts.

Gerrymandering is a charge that politicians use to complain about districts that are not favorable to them. Republicans point out that the districts drawn in Illinois and Maryland are unfair to them. Democrats counter that districts drawn in North Carolina and Ohio are unfair to them. Libertarians and other third parties point out that every geographic districting plan is unfair to them.

### Bias

The genius of the efficiency gap is that unlike distance from proportionality, it favors Democrats without favoring third parties or Republicans in Democratic states. So it reinforces the two party hegemony. They don't even bother giving examples including third party candidates.

The first thing to notice is that the efficiency gap doesn't diagnose any states as having anti-Republican gerrymanders. This is because the threshold they chose doesn't see anti-Republican gerrymanders in states like Illinois and Maryland.

The second thing is that it doesn't show states that have a Republican minority. For example, Massachusetts is roughly 25% Republican, but Republicans have no seats in the state.

The third thing is that independents and third parties get no help from the efficiency gap. For example, independents make up about 25% of Massachusetts and also have no seats in the House of Representatives. And in states like California and Texas, there are enough Libertarians (and possibly Greens in California) to make up at least one seat.

As a statistic, the efficiency gap currently helps Democrats a lot. It might help Democrats less after an election like 2008, but right now it would shift districts towards the Democrats in some states. It does so without providing any help for third parties or independents. As such, in my opinion, it distracts from real reforms and props up the two party system. It perpetuates many of the inequalities of the current system and encourages the courts to get involved in each and every districting.

### Proportionality

There isn't a lot of data showing them doing their work. The original paper does not include real calculations on real data, merely on examples. And most news articles don't include more than a mention of the final results. But since posting this, I have found two articles that at least tell us what states this method identifies as being the most gerrymandered. In 2012, that was Florida, Michigan, North Carolina, Ohio, Pennsylvania, Texas, and Virginia.

In 2016, that was North Carolina, Pennsylvania, Michigan, New York, and Texas. Note how three states dropped off the list in those four years: Florida, Ohio, and Virginia. Florida redistricted, but Ohio and Virginia did not. One state was added: New York. The total number of seats affected (outside of the threshold) was seven in 2016 in the five states.

New York is an interesting case. It is actually rather absurd to view it as a Republican gerrymander. In 2011 (when redistricting was being done), New York had a Democratic governor and one Democratic-controlled legislative chamber. It had one legislative chamber (the Senate) that was split evenly between the parties. As a result, Republicans could block a plan but couldn't force one. So rather than being a pro-Republican gerrymander, it is better thought of as a bipartisan plan.

Efficiency gap analysis identifies New York as a pro-Republican gerrymander. Why? Primarily because Democrats do really well in some districts of New York City while Republicans are only moderately dominant in any district. Another reason is size. 6% of 27 is two seats. Finally, the efficiency gap is biased. If we look at New York in 2016, we would see that Republicans were actually underrepresented. They won 33% of the seats but took 36% of the vote.

That statistic is even worse in California. There we find that Republicans won fourteen seats (26%) despite winning 36% of the vote (nineteen seats). So a proportionality standard would give a pro-Democratic gap of five. But the efficiency gap is zero seats.

### Alternatives

Meanwhile, a proportional system like Single Transferable Vote (STV) could eliminate the very concept of redistricting. Each state would be a separate bucket but within the state, any voter could vote for any candidate. Voters would have their choice of candidates. Candidates would not be able to choose their voters, as every geographic district system allows. Candidates would only be able to choose how and where they marketed themselves to voters.

Is a candidate the local candidate? Is the candidate the ideological candidate, who best matches the voter? Is the candidate some kind of compromise? Voters could choose how to pick among those options.

If the problem is wasted votes, then let's not minimize the difference in wasted votes between two arbitrary groups. Let's minimize them at a larger scale. With STV, the total wasted vote is less than the number of voters for one district (because everyone else gets one of the candidates on their list). With the efficiency gap, the wasted vote is always 50%. The only difference is whose vote is wasted.

This would still leave some decisions to states. Do they use traditional STV? Or one of the Condorcet-compliant alternatives? Or something else (that may not have been developed yet)? I'm not crazy about List forms of proportionality (they reduce the advantage of good candidates), but some places like them. States would have room for choice and experimentation within the constraints.

That would allow true freedom of association, unlike the efficiency gap, where politicians still choose how their voters associate. They only face more constraints.

• The argument isn't "if it's not perfect, it must be gerrymandering." The gerrymandered districts can be configured with surgical precision through data analysis and computer modeling. What's also possible is that through the use of computer modeling, we can evaluate thousands and thousands of possible permutations. It's not that "this configuration wastes votes." It's "out of all possibilities, the configured district maps consistently fall at the statistical probability extremes for wasted vote coefficient." Just like with a scientific experiment, we remove random chance via significance. Commented Oct 17, 2017 at 21:15
• What would be considered non-gerrymanding of African-Americans, assuming they registered and voted at the same rate as others? Every seat having 22% African Americans? 22% of seats being 100% African-American? 43% of seats having 51% African-Americans? 45% of seats having 49% African-Americans? Giving African-Americans a majority in Democratic primaries? Commented Oct 18, 2017 at 1:07
• I agree with the overall viewpoint of this answer, but I disagree with the tone, which I feel has an anti-Democrat bias (as opposed to an anti-efficiency-gap bias). Commented Oct 18, 2017 at 1:17
• @AndrewGrimm Going off the rulings where gerrymandering was ruled against (e.g. 12th congressional district in North Carolina as referenced in the article), the reason it was ruled against is that the Federal court found that "race was the predominant factor in drawing those lines but state legislators lacked justification in using that practice", "The record is replete with statements indicating that race was the legislature’s paramount concern". So presumably as long as any other basis was used to redistrict, and it cannot be demonstrated race was, it would be considered non-gerrymandering. Commented Oct 18, 2017 at 1:22
• A STV system that works well: you first vote for a person and if he/she doesn't go through the vote transfers to the party. Commented Oct 18, 2017 at 7:10

Addressing the question in the title, uniformity isn’t increasing the efficiency gap. Take your example to another value, if 70% of population voted for Party A, 30% for Part B, and the districts are still completely uniform, but the efficiency gap is now .10. (30 wasted Party B votes and 20 wasted Party A votes in each district for a total difference of 300 – 200 = 100. 100/1000 = .10). Here, everything is still uniform, but the efficiency gap is different. The large efficiency gap is cause because almost half of your population’s vote didn’t result in any seats won.

(Interesting fact: Past 75% of the population voting for Party A, the efficiency gap is actually negative. This is addressed in the original paper in the limitations section.)

Reading into your question, you mention ‘there is no Gerrymandering possible’. The authors define gerrymander as ‘simply a district plan that results in one party wasting many more votes than its adversary’. This did happen in your example, so using the definition provided by the authors, this does count as gerrymandering. Everything seems to line up with the authors intent and your example.

The 51-49 split is but one of the weaknesses of the Efficiency Gap. And the EG is not about wasted votes, either. This video explains it better... It shows a different (better) way to calculate the EG.