Does gerrymandering risk tidal wave reversal?

Question

The voting population of gerrymandered districts is distributed so as to provide "safe" margins of victory in many districts while "wasting" opposition votes concentrated in a few districts. What happens if there is a big reversal of the political winds? It seems imaginable that under such circumstances previously safe margins would become unsafe and produce a very large change of electoral outcomes from those predicted in ordinary circumstances.

Put in a few words, could gerrymandering be productive in ordinary times but very counterproductive in unusual circumstances? Has this question been examined by modeling or other systematic analysis? Is this question relevant to the 2018 House elections?

Answer 1

Yes, it definitely could happen.

The mathematical version of gerrymandering is easily expressed in integer programming, as shown here (for people who like MIPs).

In its simplest version (without geographical considerations and vote uncertainty), the gerrymandering problem amounts to a simple partitionning problem. Let us assume you are a daredevil (there is no voter uncertainty) and want a margin of 1%. You want as many districts as possible with a percentage of voters for party A at 51 %. The number of delegates (districts) from party B has to be minimized.

In algorithmic terms, assuming building a district is like putting voters in big bags of equal size, the optimal solution is given by:

• Build districts with 51 % of voters for party A and 49% of voters for party B

• When you do not have enough voters for party A, build districts with voters of party B only (and the few )

This can give you for instance:

• for an area with 51 % (or more) of voters for party A, 100% of delegates for party A

• for an area with 25.5 % of voters for party A, 50 % of delegates for party A

and so on.

Now assume party A has a bad term, and 2 % of the voters change their minds and decide to vote for party B. If they are equally distributed between districs, you would end up with 100 % of representatives for party B. Here you have your tidal wave reversal.

In practice, the number of voters who change their minds is more likely to be decribed by a distribution function (I feel like a Rayleigh distribution would describe it well, and be used by most statisticians as a "default" distribution if there is no additional knowledge). But even if the "change of minds" differs between districts, you will have a significant shift. The worst case scenario is if the "change of minds" keeps a "gerrymandered" solution such as described above. In that case, with a minority party A, you will get twice as big a shift in representatives than in opinion change (if 2% of voters change their minds, at least 4% of representatives will be changed).

This answer concerns an "ideally gerrymandered area", politicians are usually more cautious when it comes to this sport. The margins may be larger. I also ignored the fact that districts come in finite number (4 % of representatives does not exist if you have 10 districts for instance)

Answer 2

It did happen. In the US in 2006, the Democrats took the House of Representatives after twelve years of Republican control. Four years later the Republicans took back the House. Both were wave elections (34 seats in 2006 and 64 in 2010). Then there was a redistricting, which Democrats complain that Republicans gerrymandered. Republicans then lost seats in the next election.

Source: Wikipedia

The 2006 election was an example of partisan gerrymandering gone wrong. A number of districts in places like Ohio and Pennsylvania were just Republican enough that a popular Republican could hold them. Republicans weren't popular in 2006. Democrats took the House. In 2010, Democrats weren't popular. Republicans took the House back.

Types of gerrymander include partisan (maximizing the number of seats for one party or the other) and incumbent (making safe seats for incumbents of both parties). Some Democrats charge that partisan gerrymanders are increasing polarization, which is absurd. The polarizing gerrymander is the incumbent gerrymander that occurs in a bipartisan gerrymander.

Some Democrats allege that Republicans did a different kind of gerrymander in 2010, creating extra safe partisan districts. Perhaps we'll see in 2018. If they're right, then even if Donald Trump is historically unpopular, the Republicans should hold the House. They have to hope that they are wrong.

Answer 3

This does not only apply to gerrymandering but any way to skew a voting system.

To see this, let’s first make a few simplifying assumptions:

• We have a pure two-party system.
• Votes somehow assign seats to votes in some parliament.
• The status quo is an equally divided parliament (see this answer of mine, why this is a generally valid assumption even in an unfair voting system).
• The goal is to have the majority in the parliament.

Now let’s look at the general number of seats a party receives in dependence on its votes. Mind that these are generic curves, not reflecting an individual election. If you so wish, this smoothens the noise caused by effects of individual elections, e.g., candidate-specific specialities, short-lived hot topics, etc. In general, this is about the typical case – you can always find a particular (atypical) voting outcome where effects are reversed.

In a proportional representation system or even an ideal plurality voting system, the portion of seats received by a party is identical to the portion of votes (1). Now, suppose our party changes the system to their advantage (2), be it via gerrymandering or some other manipulation. In our scenario, changes of power happen when we cross the 50% seats (blue line). In the unfair system (2), this crossing happens with a steeper slope. This slope quantifies how prone our system is to landslides: The steeper the slope, the bigger the effect of a single vote.

Thus, any skewing of the voting system makes the system more prone to landslides. Now, you may ask what if there is a dent in the curve causing the 50% line being crossed at a smaller slope (3). However, such a curve is usually not generic in the above sense: A slight change in the political landscape, regional effects, etc. may easily shift the dent in the curve up- or downwards (thus increasing the slope). For this curve to be generic, there must be some weird mechanism in the voting system that ensures that the dent is always at 50% seats.

Now, let’s turn to gerrymandering. If our party used gerrymandering in its favour, we can specify things a bit (2 → 4). We have two strong increases of our party’s seats in dependence of the votes it receives: One at low percentages where it wins over the cracked districts and one at very high percentages when it wins the packed ones. However, this does not change that the 50% line is crossed at a higher slope than for a fair system (1).

For ideal bipartisan gerrymandering, we have a different situation (5): Now, we have a decreased slope at the 50% crossing as the current seats are relatively secure for either party. If we take this as it is, the chance of landslides is decreased. However, it is questionable if this is really generic (like for Case 3). If the political landscape slightly changes, the 50% crossing moves up- or downwards and thus to a region of larger slope.

This is an inherent effect: If you want to decrease the slope at any point, you have to increase the slope elsewhere – the average slope must be 1. Thus changes happen more abruptly – if they happen. And from this point of view, our initial assumption that this about getting the majority is not necessary anymore.

Answer 4

Yes.

In my opinion (and apparently in the opinions of some key legislators in several Southern states of the U.S.), gerrymandering encouraged by the Voting Rights Act eventually creates a situation where large numbers of districts "snap" from electing white Democrats to electing white Republicans. This pattern has been seen, one or a few states at a time, for decades.