Tactical Voting

As a progressively more adamant Europhile, I was pleased to learn that the UK would take part in next month’s European Parliament elections1. As an amateur psephologist, I was delighted.

Rather glibly, I responded to someone asking whether one needed to vote tactictally in these elections by saying “no, it’s PR, vote for who you want to get in”. But then I read a tweet thread explaining that that’s not quite true: because of the way regions are arranged, it’s not always the case that all votes are equal.

A poll

I’ve only been able to find one recent poll for the elections - perhaps unsurprisingly, since everyone was insisting they couldn’t possibly take place. Let’s make the entirely unreasonable assumption that the numbers Hanbury have reported are absolutely bang on, and see how the system would work in my region, the South West.

Hanbury has the numbers as:

LAB: 28.4% 
CON: 25.5% 
BRX: 16.8% 
LD:  13.4% 
TIG:  5.4% 
(5% bar)

… and the South West elects 6 MEPs.

The D’Hondt system takes the following steps:

  1. Divide each party’s vote share by one more than the number of seats so far allocated to it to get a dividend
  2. Allocate the next seat to the party with the highest dividend.
  3. Repeat steps 1 and 2 until you run out of seats.

In this (and pretty much every) case, we start with no seats allocated, so we divide everybody’s percentage by 1. The leading party is LAB, who take the first seat.

For the second seat, the dividends for everyone except LAB remain the same, but Labour’s dividend drops to 14.2% (putting them, for the moment, third). Since CON now has the biggest dividend (25.5%), they take the second seat.

For the third seat, the Conservative dividend drops to 12.75%, putting them temporarily in fourth. The dividends are now:

BRX (0): 16.8 
LAB (1): 14.2 
LD  (0): 13.4 
CON (1): 12.75 
TIG (0):  5.4

The Brexit Party takes the third seat, and their dividend drops to 8.4% and fourth place. Labour’s dividend for the fourth seat is highest, so they take it, dropping to 9.47% (and third place). After four seats being allocated, we have:

LD  (0): 13.4 
CON (1): 12.75 
LAB (2):  9.5 
BRX (1):  8.4 
TIG (0):  5.4

The penultimate seats will fall to the Liberal Democrats (dropping to 6.7%) and to the Conservatives (dropping to 8.5%). The final result would be:

LAB: 28.4% - 2 seats 
CON: 25.5% - 2 seats 
BRX: 16.8% - 1 seat 
LD:  13.4% - 1 seat 
TIG:  5.4% (5% bar)

… which looks pretty fair: Labour and the Conservatives have roughly double the support of the Brexit Party and the LibDems. Each seat, in the end, required 12.75% of the votes.

Deeper analysis?

To think about voting tactically, it’s worth thinking about “wasted” votes. How far away was each party from winning the final seat?

To work this out, we can divide each party’s vote share by the number of seats it ‘deserved’ - how many 12.75%s go into their polling numbers?

LAB: 2.23 
CON: 2.00 
BRX: 1.32 
LD:  1.05 
TIG: 0.42

The higher the decimal part of this, the closer you are to winning an extra seat.

In raw percentage point terms, The Independent Group2 are closest to winning an extra seat: they would require an extra 7.45 points to take the final seat from the Tories. I haven’t listed the Green and UKIP, who are both on 5%; they are next in line (7.75 extra points), followed by Brexit (8.7), Labour (9.85), the Lib Dems (12.1) and the Conservatives (12.75).

You can also consider a defensive strategy, looking at how far each party is from losing a seat, by comparing how many 9.47%s go into each party’s share. (That’s the leading remaining dividend).

LAB: 3.00 
CON: 2.69 
BRX: 1.77 
LD:  1.42

Here, the lower the decimal part, the closer you are to losing a seat. The Lib Dems are most at risk here; a drop of 4 points or so would see them lose the last seat to Labour. The Conservatives would need to drop about 6.5% to lose their second seat, and Brexit a bit more than seven points.

How to vote tactically

Depending on how your affiliation lies, you might choose to express a preference between two parties vying for the last seat rather than voting for a party some way behind (or ahead) - in the South West, the battle is between the Lib Dems and Labour (between whom I don’t have a strong preference), and it’s hardly marginal in any case.

In Scotland, by contrast, the three major parties are split 32.2-24.3-21.7 - and the system gives them two seats apiece. The last seat became Labour’s second rather than the SNP’s third by fractions of a percent - 0.35 more points for the SNP or 0.24 less for Labour would have seen a 3-2-1 split.

Voting for the party you like best is an absolutely fine strategy for elections - but if you want to vote in a way that maximises your chances of affecting the result, it pays to study the system and - in the Euros - choose between the two parties most likely to win the final seat.

* My code is available here: github.com/icecolbeveridge/dhondt
* I've previously written about the D'Hondt variant used in the Scottish Parliament elections.

Colin

Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008. He lives with an espresso pot and nothing to prove.

  1. Apparently, this is an undemocratic thing, and the EP is undemocratic []
  2. I don’t really know, or care, what they ought to be called []

Share

Leave a Reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Sign up for the Sum Comfort newsletter and get a free e-book of mathematical quotations.

No spam ever, obviously.

Where do you teach?

I teach in my home in Abbotsbury Road, Weymouth.

It's a 15-minute walk from Weymouth station, and it's on bus routes 3, 8 and X53. On-road parking is available nearby.

On twitter