Tuesday, May 21, 2019

Setting the record straight on the D'Hondt formula

A commenter on a previous thread has alerted me to a piece of polling analysis on Newsnet that is based on an entirely false premise.  The article claims that Best For Britain are wrong to suggest that the figures from their recent YouGov poll would translate into three SNP seats in the European Parliament, and that the correct figure should be two.  It also goes on to say: "Why Best for Britain have allocated 3 seats to the SNP when their poll results actually only give them just 2 is strange. Perhaps because of an unexplained adjustment or wider polling influence."

In fact, the Newsnet piece is wrong and Best For Britain are right.  The 38% of the vote that the SNP are given by the poll would comfortably be enough to win them three seats, and it would actually leave them not that far away from four.  This is not because of any "unexplained adjustment" or "wider polling influence" - it's simply because of how the D'Hondt formula works.  The Newsnet author wrongly believes that D'Hondt divides a party's vote by two every time it wins a seat, but that's not the case at all.  As Newsnet is a pro-indy website, this is clearly an honest mistake rather than anything malicious, but it's still important to set the record straight because it could lead to further confusion about how the voting system works.  (And Alex Cole-Hamilton would be only too delighted about that!)

The D'Hondt formula actually divides each party's original vote by the number of seats it has already won, plus one.  So this is how the calculation would play out if the Best For Britain poll happens to be accurate...

First count: SNP 38, Brexit Party 19.8, Greens 11, Labour 10.2, Conservatives 10, Liberal Democrats 7, UKIP 2, Change UK 2

SNP win first seat

Second count: Brexit Party 19.8, SNP 19 (38 ÷ 2), Greens 11, Labour 10.2, Conservatives 10, Liberal Democrats 7, UKIP 2, Change UK 2

Brexit Party win second seat

Third count: SNP 19 (38 ÷ 2), Greens 11, Labour 10.2, Conservatives 10, Brexit Party 9.9 (19.8 ÷ 2), Liberal Democrats 7, UKIP 2, Change UK 2

SNP win third seat

Fourth count: SNP 12.7 (38 ÷ 3), Greens 11, Labour 10.2, Conservatives 10, Brexit Party 9.9 (19.8 ÷ 2), Liberal Democrats 7, UKIP 2, Change UK 2

SNP win fourth seat

Fifth count: Greens 11, Labour 10.2, Conservatives 10, Brexit Party 9.9 (19.8 ÷ 2), SNP 9.5 (38 ÷ 4), Liberal Democrats 7, UKIP 2, Change UK 2

Greens win fifth seat

Sixth count: Labour 10.2, Conservatives 10, Brexit Party 9.9 (19.8 ÷ 2), SNP 9.5 (38 ÷ 4), Liberal Democrats 7, Greens 5.5 (11 ÷ 2), UKIP 2, Change UK 2

Labour win sixth seat

Final seat allocation: SNP 3, Brexit Party 1, Greens 1, Labour 1

14 comments:

  1. SNP vote should be divided by 4 in counts 5 and 6?

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    Replies
    1. I've actually divided it by 4 in those two counts, but you're right, the bit in brackets should say 4 rather than 3, so I'll correct that.

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  2. Hi James,

    Quick question how do you calcuate vote swing if both parties have lost vote share. I understand if both have gained.

    Party A: +6%
    Party B: +3%
    is it the difference between the two dived by 2 (6-3)/2=1.5% swing to Party A

    But would both negative be
    Party A -5%
    Party B -1%

    (5-1)/2=2 2% swing to party B?

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    Replies
    1. Yes, regardless of whether both parties are up, or both parties are down, you take the difference between the two figures and divide it by two. But if one party is up and one is down, you take an average of the two figures, so if party A is up by 7 and party B is down by 5, the swing is 6.

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    2. Thanks James

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  3. Hi James,

    Thanks for following up - that is the result that I calculated, and at each round.

    As mentioned previously I don't think there is anything mendacious involved from Newsnight, just a bit amateurish.

    God knows how they'd handle the AMS approach for Holyrood and, especially, the STV methodology used in local authority elections!

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  4. I’m confused. Some of the SNP calculations divide by the number of seats already won as opposed to “won+1”. Am I reading this wrong?

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    Replies
    1. The journey to "yes" episode 22?

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    2. Actually make that episode 25, 24 has just gone live on Wings.

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    3. Gavin: Yes, I think you're reading it wrong, as far as I can see they all divide by 'won+1'.

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    4. There seems to be something strange at the Third Count with the SNP division which is the same as at Second Count.

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    5. What's strange about that? The Brexit Party wins the second seat, so the SNP calculation remains the same on the third count as it was on the second count.

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  5. The Scottish sub-sample from the final EU Yougov poll has the SNP at 40% - it would get the SNP 3 seats. Tories and Labour are in single figures. Full details at :

    https://d25d2506sfb94s.cloudfront.net/cumulus_uploads/document/c6muz9lchd/TheTimes_190521_EPVI_w.pdf

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