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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?

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    A big reversal would affect every district...but less so in the gerrymandered ones as that's why they were gerrymandered in the first place, to lessen the chances of that happening. (That said, I'm not a statistician...so I could absolutely be wrong on this) – user1530 May 18 '17 at 15:52
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    @blip If you're going to say something so blatantly wrong, you should do so in an answer rather than a comment. It is absurd to say that most districts will be significantly affected by anything. Most districts are highly partisan, not because of gerrymandering but because most districts are in areas where gerrymanders don't matter. Five of the ten most partisan districts are in New York City (and the other five are in other cities). That's not a gerrymander. There's no way to draw New York City with more than two or three swing districts. – Brythan May 18 '17 at 22:15
  • IIRC TV Tropes said that Queensland, Australia had malapportionment that used to act in Labor's favour but subsequently acted in Sir Joh's favour. (Can't remember how to spell his surname) – Andrew Grimm May 18 '17 at 23:10
  • @Brythan if I think I may be blatantly wrong, I certainly wouldn't want to have people assume it's a proper answer (hence my gigantic disclaimer in my comment).n. – user1530 May 18 '17 at 23:27
  • 2 answers so far and no cites to 538 summaries on either gerrymandering or wave elections? – user4012 May 19 '17 at 2:03
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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)

  • A 51-to-49 outcome is a margin of two percent. – phoog May 19 '17 at 13:58
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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.

  • Good answer...especially pointing out that gerrymandering can be done in many different ways which would change how a change in political climate would affect it. – user1530 May 18 '17 at 23:29
  • "Some Democrats charge that partisan gerrymanders are increasing polarization, which is absurd" - I think it would help if you explain why this is absurd since you say you are contradicting "Some Democrats" when you say it is absurd. – Readin May 19 '17 at 4:40
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    What does this sentence mean? "The polarizing gerrymander is the incumbent gerrymander that occurs in a bipartisan gerrymander." – stannius May 19 '17 at 18:10
  • @stannius There are two main types of gerrymander. First, there is the partisan gerrymander where one party controls redistricting and tries to maximize the number of seats that they have and can hold. In this gerrymander, they spread out their own voters. Second, there is an incumbent gerrymander. This happens when either party can block redistricting, so they have to agree. In that case, they shore up incumbents of both parties, taking other party voters out and putting in the matching party. Incumbent gerrymanders increase polarization of both parties. – Brythan May 20 '17 at 1:18
  • Do you have a source regarding "Some Democrats allege that Republicans did a different kind of gerrymander in 2010?" I'd be interested in reading more about that, especially how that would work mathematically. – RaceYouAnytime May 20 '17 at 3:10
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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.

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