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On gerrymandering

Sparked by yesterday's discussion, this is cut and pasted from my website, and records a discussion between me, Jim Riley and others on Usenet (remember that?) back in August 1999, demonstrating that requiring a rigid ratio between electors and representatives is not a safeguard against gerrymandering; if anything, the reverse.

I started the bidding with the old chestnut about dividing the mythical county of Tymanagh with a population of 60% Yugoslavs and 40% Belgians into three single-seat constituencies. There are as it were 1.8 seats' worth of Yugoslavs, and 1.2 seats' worth of Belgians.

diagramA 'fair' result is clearly that the Yugoslavs should win two seats and the Belgians one; this picture illustrates just one possible arrangement that would bring that about.
diagramBut since the Yugoslavs are a majority overall, it will usually be possible - in fact, it will usually be easier - to create three seats with Yugoslav majorities.
diagramOn the other hand, if the Yugoslavs are sufficiently geographically concentrated, this can be turned against them by creating a homogenous Yugoslav seat, leaving the Belgians a 60/40 advantage in the other two seats

I concluded by stating that:

"Setting strong constraints on the size of electoral districts doesn't make gerrymandering very much more difficult at all. In fact if it's not compensated by other geographical constraints it can make it even easier to incorporate the next little village of Belgians just to make up the numbers."

Gerry Cunningham responded sceptically:

"Nice, if you're dealing with FPTP [ie first-past-the-post, UK or US-style]. Now let's see it with multi-seat STV."

So I came up with these two examples, illustrating how you could engineer different results where you had 80,000 voters, electing eight representatives by STV, and again 60% Yugoslavs (total of 48,000) and 40% Belgians (total of 32,000). Of course the "fair" result is that the Yugoslavs should win five seats and the Belgians three.

diagramBut if the Belgians are drawing the boundaries, you might find you have:

1) Tymanagh North-East, a 3-seat constituency, total electorate 30,000, 15,100 Belgians and 14,900 Yugoslavs.
The quota is 7,500 so it elects 2 Belgians and 1 Yugoslav.
2) Tymanagh South-West, a 5-seat constituency, total population 50,000, 16,900 Belgians and 33,100 Yugoslavs.
The quota is 8,334 so it elects 2 Belgians and 3 Yugoslavs.

Total result: Belgians 4, Yugoslavs 4.


However if the Yugoslavs are in charge (which after all is more likely) you could get:

1) Tymanagh North-West, a 3-seat constituency, total population 30,000, 7,300 Belgians and 22,700 Yugoslavs.
The quota is 7,500 so it elects no Belgians and 3 Yugoslavs.
2) Tymanagh South-East, a 5-seat constituency, total population 50,000, 24,700 Belgians and 25,300 Yugoslavs.
The quota is 8,334 so it elects 2 Belgians and 3 Yugoslavs.

Total result: Belgians 2, Yugoslavs 6.

Jim Riley did it much more elegantly with some ascii maps which I have turned into pretty colours here. He had 65% Yugoslav and 35% Belgians (to be more exact, 144 blocks of which 94 were Yugoslav and 50 Belgian), electing nine representatives by STV.

diagramUsing 3-seaters we can have:

Tymanagh North (65%/35%), Tymanagh South (65%/35%), and Tymanagh Mid (67%/33%) each return 2 Yugoslavs and 1 Belgian.

Totals - Yugoslavs 6, Belgians 3 - the "fair" result.

Tymanagh West (100%/0%) returns 3 Yugoslavs, while Tymanagh North (48%/52%) and Tymanagh South (48%/52%) each return 1 Yugoslav and 2 Belgians.

Totals - Yugoslavs 5, Belgians 4.

or switching to a 4-seater and a 5-seater:
Tymanagh West (81%/19%) returns 4 Yugoslavs, while Tymanagh East (53%/47%) returns 3 Yugoslavs and 2 Belgians.

Totals - Yugoslavs 7, Belgians 2.

All 3 of Jim's plans have an identical number of represented per representative in all districts. The districts are compact with regular boundaries. In fact, plans B and C, which produce the most deviation from the popular vote are more compact than plan A. (Thanks to Jim for letting me reproduce his schemes.)

Of course this is all a bit unrealistic in two respects. First, nowhere in the world insists on such a degree of accuracy in the ratio between representatives and population/electorate (and we'll just ignore that last distinction for now). Populations move all the time in the real world, and tolerances of 5% within a given region are usual; 10% is not unreasonable. The more members per constituency, the easier it is to make a difference.

But second, which largely cancels out the first point, with margins as tight as these, the gerrymanders are very vulnerable to differential turnout and even more so to people of one tribe voting for candidates from another, or failing to transfer their votes down the line.

It is intrinsically more difficult to gerrymander proportional systems to get the result you want. Usually all you can hope to affect is where the 'last seat' in each constituency goes.

The problem with any single-seat system is that every seat is the last seat in that constituency!


( 2 comments — Leave a comment )
Jul. 7th, 2010 03:01 pm (UTC)
Nowhere in the world insists on such a degree of accuracy in the ratio between representatives and population/electorate

My understanding is that the US requires all districts within a state to be exactly the same size -- you can check this on http://en.wikipedia.org/wiki/List_of_United_States_congressional_districts.
Jul. 8th, 2010 01:35 pm (UTC)
5% is way too rigid. A 10 or even 12.5% deviation given the smaller seat sizes compared to the USA would seem much more practical. It's also absurd that they're not allowed to take population projections into account, even when they come in the form of hard evidence in the shape of new electorate figures during the review. I read the 1980s review a couple of years ago and despite all the evidence that Milton Keynes was mushrooming, they stubbornly refused to allow for that. In contrast, in exactly the same review, they initially awarded Glasgow 10 seats even though it had a quota of 10.70 on the grounds that the electorate was falling and that other options would increase the number of seats from the magic 71 figure then in existence.

In the Milton Keynes example, the commission got it badly wrong and were forced to split it in a rare interim review in 1992. In Glasgow their initial instincts were right but such a fuss was kicked up at the review about them breaking their own rules that they backed down and gave Glasgow and 11th seat which was duly abolished a decade later.

The coalition's problem is that they've started with a faulty assumption. The number of votes needed to elect a Labour MP is less than what's needed to elect a Conservative so this must be due to unequal electorates instead of differential turnouts. The real solution to the problem would be to make attendance at polling stations compulsory on polling day. However as this would bring out more Labour voters it's not going to be considered.
( 2 comments — Leave a comment )

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