Wednesday, November 19, 2008

Geek post: electoral maths and beating the BNP

During a conversation about why the Greens were the best vote to keep out the BNP at the European election next year I started to get sucked into a discussion on the glorious D'Hondt system that we use in these elections in the UK. It's difficult to do in a few words so I thought I'd go into a little more detail. I'll post on something more exciting later, I promise!

Anyway, let's look at how this bugger works because it isn't simple. For the voter things are pretty easy. Each region has a ballot paper and you vote for the party of your choice, broadly the more votes each party gets the more MEPs are elected from their list. But when it comes to working out exactly how many Euro MPs are elected it gets a bit more tricky. Wikipedia puts it like this;

After all the votes have been tallied, successive quotients or 'averages' are calculated for each list. The formula for the quotient is \frac{V}{s+1}, where:

  • V is the total number of votes that list received; and
  • s is the number of seats that party has been allocated so far (initially 0 for all parties in a list only ballot, but includes the number of seats already won where combined with a separate ballot, as happens in Wales and Scotland).

Whichever list has the highest quotient or average gets the next seat allocated, and their quotient is recalculated given their new seat total. The process is repeated until all seats have been allocated.

Believe it or not that is as clear an explanation as you're likely to get, but let me put it another way anyway. You have a set number of seats per region and you elect each seat in turn. Every time you elect someone that party's "quotient" (which was originally the number of votes they got) is downgraded - first you halve the original vote, then you third it, then quarter it, etc. Then whichever party has the highest quotient gets the next place and their vote is downgraded until you've filled all the seats.

OK. Let's look at London last time to see it in practice. They were nine seats to fill and was the number of votes the main parties got;

Tory 504,941
Labour 466,584
Lib Dem 288,790
UKIP 232,633
Green 158,986
Respect 91,175
BNP 76,152

I'm going to go through this seat by seat - bear with me. You can use the table below if it helps (numbers in bold have succeeded in getting someone elected).
  1. So the Tories came top they get seat number one and you half their (to 252,471).
  2. Labour now have the most they get second place and you half their vote (to 233,292).
  3. Lib Dems next and you half their vote (to 144,395).
  4. Now the Tories "quotient" is the highest and they get their second MEP and their quotient becomes one third of their original vote (or 168,314)... and so on...
Tory 504,941 (1)
252,471 (4)
168,314 (7)
Labour 466,584 (2)
233,292 (5)
155,528 (9)
Lib Dem 288,790 (3) 144,395

UKIP 232,633 (6)

Green 158,986 (8)

Respect 91,175

BNP 76,152

Simple, huh?

Now, at the next election London will only have eight seats to play for, and UKIP and Respect will be entirely out of the running - massively increasing the potential for a BNP MEP (not withstanding their current hilarious difficulties). Which means, in regards to keeping the BNP out, it's all a battle for eighth place - the place that the Greens currently hold.

Now if the results for the major parties are similar to last time then Labour and the Tories need three votes to add one to their quotient in this range, the Lib Dems two and all the minor parties one. That means that voting Labour or Tory is one third as potent as voting Green (and voting Lib Dem just half).

This basic formula holds true in every region of England without exception, even for those areas where the Greens have not yet won a seat, it's still a battle for last place and one vote for a Green is the most mathematically powerful vote you can cast for that seat under D'Hondt. And they need to be because each BNP vote is also worth three times that of a Labour vote in June, which is a steep hill to fight against.

There is a real chance that the fascists could gain their first MEP at this coming Euro election and I think that's something we should try to prevent if we can. Ballot for ballot the best anti-fascist vote is a Green vote - which by happy coincidence also allows you to vote for peace, progress and a sustainable economy at the same time - that's a win / win situation if ever I heard one.


The Sentinel said...

Vote Green!

Vote for Keith Bessant!!!

Malc said...

I'm okay with the theory - its about the battle for 8th place. But - in your example (London) how are UKIP out the running?

Also, Respect took 91,000 votes in London... UKIP over 200,000. Okay the seats are cut to 9, which on that basis, it would be Labour that miss out (if the vote stays the same).

I think my point is this: The BNP would have to pick up more than 80,000 votes in London to win a seat and at the same time Labour would have to lose out considerably. Why are you worried?

Jim Jay said...

Because at the last Euro elections they had an unprecedented vote (partly a Kilroy / Joan Collins thing) which wont be repeated - UKIP's performance since having a swathe of MEPs elected has been very poor and the group fractured spectacularly.

They just wont manage anything like this vote again and, I suspect, this vote will be carved up between the BNP and the Tories.

Since this election though the BNP has won a seat on the London assembly and built some base for itself. Its weak turnout last time wont be repeated - it's just about whether they can top their assembly vote. An extra 80,000 is not out of the question because many of the 232,633 UKIP voters will be tempted by the BNP.

If the vote was identical it would be Labour that lost out - but with UKIP and Respect out of the picture we cannot be sure that the BNP will not be strong enough to get that last place.

HelloKnitty said...

That was great! I almost think I understand it- picking up my canvassing gear as we speak!

Anonymous said...

This almost makes my posts on CPZs and speed humps seem more palatable! I'd forgotten about the RESPECT vote last time round - surely Greens should be able to get some of that this time? And quick plug for the Re-Elect Jean Lambert MEP Facebook group and page if I may . . .

adolfo said...

The field-work for the Communication Research poll yesterday took place, like today’s ICM survey, from October. CR, like Mori does not use past vote weighting but has a very fierce “squeeze” question to try to get a response from those who say they will vote but won’t name a party.

scott redding said...

Geek challenge: you could go through the 2004 London mayoral and 2004 European results, and then compare all of that to the 2008 London mayoral and council results, and predict more accurately how the vote distribution may change, i.e. Green strengths and BNP strengths.

Say the UKIP vote collapses. I mean, if they drop by 70 000 votes, and if 50 000 of those votes go BNP, they still get the 8th or 9th position, and the BNP are on 126 000.

And I think Sue's right about some of the Respect vote coming our way. Even if only 10 000 of their votes shift to us, then that leaves the Green vote on 168 000. With Paddick's performance in the elections (-5% on 2004), some of the Lib Dem vote may shift our way too.

How large would the Tory vote need to be to threaten 9th place, the Boris effect?

Matt Sellwood said...

I'm not that worried about the BNP in London. The North-West is a different kettle of fish. I AM worried about our seat in London, but more because I think we could lose it to a major party, as opposed to the fascists.

I reckon that if turnout is about 35%, we'll need around 190,000 votes to be absolutely and totally sure of re-election. That IS doable, because over 200,000 people voted for us on the Assembly List earlier this year. The challenge will be getting those people to vote, and reminding them that they voted Green last time...


P.S. And yes, of course it will be more difficult, because at least some of those people will have voted Green as part of a 'progressive package' of Ken for Mayor, Labour for constituency, Green for list. But at least they have voted for us before....

Matt Sellwood said...

BTW, Sue and Scott, the current rumble is that RESPECT will stand in 2009 in London. I think we can assume that they are likely to get about 60,000 votes (what they got in the Assembly list), which is 30,000ish down from what they got in the 2004 Euros.

I'm not convinced that that vote will necessarily shift to us though? It is largely coming from the areas where we are weakest as a London party.

Of course if RESPECT could be persuaded not to stand at all, I think that would be a net benefit to us. Not convinced they are persuadable though, really.


Jim Jay said...

Two quick geek questions answered (not the huge one about comparing all london boroughs!)

UKIP's vote will only have to decrease by less than 80,000 votes (or one third) to lose them their MEP - but it's likely they will get less than a quarter of their vote last time.

On these figures (but lets work with that) they'd need a 32,000 boost in their quotient for number four - which is 128,000 votes... or a 25% increase.

Not going to happen thankfully.

Peter said...

I geekily disagree with you in the strongest possible terms. Such a strategy could backfire spectacularly if you ever convinced enough people to follow it.

Humour me a second. Let's assume that your exhortation to vote Green tactically to keep out the BNP is listened to and acted upon by tons of people who reckon it's a great idea.

It's so successful that the percentage results for the next London euro elections are:

Con 31
Lab 21
LD 8
BNP 7.8
Green 15
Others 12.2

The Green boost comes mostly from anti-fascist Labour and LD supporters who switch to keep the BNP out.

Run it through a D'Hondt calculator, and Tories get the 1st, 3rd and 6th seats; Labour the 2nd and 5th seats; Greens the 4th seat; LibDems the 7th seat; and the BNP, erm, the 8th seat. OOPS - And why? - because the Greens have stacked up loads of wasted votes which would have been better being retained by Labour to stop the BNP.

Because of uncertainty of outcome, tactical voting of this sort should play a very minimal role in the d'Hondt system. The extent of it should be to avoid voting for parties which have no hope of being elected (Socialist Pensioners Party or whatever). That aside, you should vote for your preference, and encourage all anti-fascists to do the same.

By all means use your tactical argument on people who'd otherwise vote for one of the Socialist alternatives - tell them they might assist the BNP if they don't vote Green.

But, apart from that, you just have to cross your fingers that the BNP doesn't poll highly and, if they do, that the 'wasted' votes of anti-fascists are split proportionally among the larger parties to stop the BNP gaining a seat.

Make sense??

Jim Jay said...

Yep, makes sense, very clearly explained and the figures are right as you put them. Thanks. However, I'm going to disagree for two reasons.

First on where the 'wasted' votes are.

Under your stats the Greens would have had to receive 0.6% more votes to take the BNP's seat, the Lib Dems 7.7%, Labour 2.7% and Tories just 0.2%. So under your figures the Green and Tory votes are still the most strategically important in denying the BNP a place.

Secondly (and more importantly) it rests on particular assumptions that don't seem very plausible given our current political climate.

Last time the Lib Dems got 81% more votes than the Greens, in your example the Greens get almost twice the Lib Dems. Obviously I think that would brilliant - I just don't believe it will be the case.

Your example rests on the Green support rocketing but falling short by just a fraction of a percentage point of gaining a second MEP. That's a very precise outcome and, I suspect, an unlikely one.

More likely is that Green and BNP support will both increase by a steady, but realistic amount. The question is will the BNP overtake the Greens, replacing the most progressive MEP with the most reactionary candidate.

nb Peter Cranie has been coincidentally writing on the same subject, although in a less geeky way.

nnb and of course if enough people vote BNP it doesn't matter how the votes are distributed.

Peter said...


even taking a more realistic scenario, your tactics could hand the seat to the BNP.

Try a more moderate

C 31
L 23
LD 12
G 10
BNP 7.8

with the Greens only gaining 1-2% from anti-fascist Labour voters. Even that could be enough for the BNP to gain a seat which otherwise Labour would have won.

The slogan "vote Green to tactically beat the BNP" might benefit the Green Party, but it's very dubious whether it would help or hinder the stated objective.

Jim Jay said...

Well, these figures are more realistic and as I said if the BNP get enough votes it wont matter what the distribution of the other votes are.

Of course it's possible that the final vote might reveal something unexpected like this - but it still relies upon a precise set of circumstances (ie that the BNP get 7.8 rather 7.74%)- it seems to me we have to fuse the maths with what's likely to happen.

If the Green vote quadrupals then the argument does not hold, but it's not likely, alas. The most likely scenario is that the Greens are vying for the 8th (and last) place, as are the BNP.

So not only would the Green vote block the BNP but because, unlike the other parties, it will be their first MEP elected in the list each vote is still two to three times stronger.

ModernityBlog said...


good analysis, very sobering