# How surpluses are distributed

#### Brendan Burgess

##### Founder
Apparently some expert was on the radio and has confused people.

This is my understanding of the process - a Returning Officer has confirmed my understanding of it.

First count

The quota is 8,000

John gets 7,500
Peter gets 7,000
Robert gets 6,000
Derek gets 5,000

(I have used 8,000 as the quota for simplicity - that would not be the actual quota)

Mary has exceeded the quota by 2,000 votes.

All Mary's 10,000 votes are sorted by candidate

John gets 5,000 second preferences
Peter gets 2,000 second preferences
Robert gets 1,000 second preferences
Derek gets 500 second preferences
No 2nd preference: 1,500

So John gets 50% of the surplus or 1,000 votes
Peter gets 30% of the surplus or 600 votes
etc.

The actual mechanism

Out of John's pile of 5,000 2nd preferences (Where Mary got the first preference), 1,000 ballot papers are selected from the top of the transfer pile and added to his pile of first preferences but are kept as a separate pile for future counts.

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#### Brendan Burgess

##### Founder
Later count surpluses

The quota is 8,000 still.
John was on 7,500 on the first count.
He has now got 1,000 votes so he has a surplus of 500 votes.

The 1,000 votes transferred from Mary to John are sorted in sub-parcels.

Peter gets 600
Robert gets 200
Derek gets none
No 3rd preference 200

So the surplus is distributed as follows:
Peter 300 (50% of 600)
Robert 100
Non-transferable 100

The top 300 of the sub-parcel of 600 which went
Mary 1
John 2
Peter 3

are now added to Peter's pile.

"An elected candidate's surplus is distributed based on the next available preferences for continuing candidates contained in the last parcel of votes that brought the elected candidate over the quota.

All the votes in the last parcel of votes received by the elected candidate are sorted into sub-parcels according to the next available preferences, setting aside those that do not transfer to any candidate. The total number of transferable papers is calculated.

Where the number of transferable papers is greater than the surplus (which it usually is in the early stages) , only a proportion of them can be included in the surplus distribution. This proportion is calculated by working out the ratio of the surplus to the total number of transferable papers and applying that ratio consecutively to the total number of next preferences for each candidate still in the running. This calculation gives the number of next preferences for each candidate that should be included in the surplus distribution. The resultant number of next preferences for each continuing candidate to be transferred as part of the surplus distribution is taken from the top of his/her sub-parcel of next preferences made up from the last parcel of votes received by the elected candidate."

Dept of Environment Guide edited by me for clarity

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#### cremeegg

##### Frequent Poster
I am with you up to this.

This proportion is calculated by working out the ratio of the surplus to the total number of transferable papers and applying that ratio consecutively to the total number of next preferences for each candidate still in the running.
Which are the transferable papers, Marys had 10,000 first prefs. John had 5,000 first prefs.

What is the total number of transferable papers, (assuming the voters voted all the way down the ballot).?

Is it 15,000 ?

#### Brendan Burgess

##### Founder
This is a bit technical and you don't need to worry about it.

"Where the total number of transferable papers is less than the surplus,
all the
transferable papers are included in the surplus distribution. As the transfer of these
papers leaves the elected candidate with more than a quota of votes, that number of
non-transferable votes equal to the difference between the number of transferable
papers and the surplus is removed from him/her. The papers concerned are designated
as “non-transferable papers not effective” because they are no longer credited to any
candidate. The quota of votes retained by the elected candidate for the duration of the

The quota is 9,000 still.
John was on 8,500 on the first count.
He has now got 1,000 votes so he has a surplus of 500 votes.

The 1,000 votes transferred from Mary to John are sorted in sub-parcels.

Peter gets 300
Robert gets 100
Derek gets 50
No 3rd preference 550

The surplus is 500.
The total number of transferable votes is 450 which is less than the 500 surplus, so all are transferred, i.e.
Peter gets 300
Robert gets 100
Derek gets 50

#### Brendan Burgess

##### Founder
Which are the transferable papers, Marys had 10,000 first prefs. John had 5,000 first prefs.
I have rewritten the first post to give the full first post count which might make it clearer.

5,000 papers were marked
Mary 1
John 2

What is the total number of transferable papers, (assuming the voters voted all the way down the ballot).?
The transferable papers are those which show a 2nd preference . There were 1,500 which went 1 Mary and nothing else. They are her non-transferable votes.

#### Protocol

##### Frequent Poster
The quota is 8,000

First count

John gets 7,500
Peter gets 7,000
Robert gets 6,000
Derek gets 5,000

Mary has exceeded the quota by 2,000 votes, and so is elected, okay.

All Mary's 10,000 votes are sorted by candidate

John gets 5,000 second preferences
Peter gets 2,000 second preferences
Robert gets 1,000 second preferences
Derek gets 500 second preferences
No 2nd preference: 1,500

So John gets 50% of the surplus or 1,000 votes
Peter gets 30% of the surplus or 600 votes
etc.

The actual mechanism

Out of John's pile of 5,000 2nd preferences (Where Mary got the first preference), 1,000 ballot papers are selected from the top of the transfer pile and added to his pile of first preferences but are kept as a separate pile for future counts.

So let me get this straight, if you gave 1st to Mary, and 2nd to John, you are one of 5,000 identical votes, BUT, only 1,000 of these 5,000 actually get transferred.

So there is just a 20% chance that your actual vote will transfer.

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#### Brendan Burgess

##### Founder
So let me get this straight, if you gave 1st to Mary, and 2nd to John, you are one of 5,000 identical votes, BUT, only 1,000 of these 5,000 actually get transferred.

So there is just a 20% chance that your actual vote will transfer.
Look at it this way.
80% of your vote was used to elect Mary.
She didn't need the other 20% so it went to John.

Brendan

#### ajapale

##### Moderator
Thanks Brendan,protocol, for the explaination of how the surplus works.

I heard that man on the radio and he was good in most respects with the exception of the mechanics of the surplus. It's a difficlult thing to explain verbally on the radio. Also it didn't help that the interviewer was behind the curve and was still grappling with the concept of the quota as the interviewee was trying to explain the surplus.

I think an infographic style presentation might make it easier for people to visualise how the PR STV system works.

Does anyone know what happens an elimination or surplus in the case of a dead heat?

#### trojan

##### Frequent Poster
Thanks Brendan,protocol, for the explaination of how the surplus works.

I heard that man on the radio and he was good in most respects with the exception of the mechanics of the surplus. It's a difficlult thing to explain verbally on the radio. Also it didn't help that the interviewer was behind the curve and was still grappling with the concept of the quota as the interviewee was trying to explain the surplus.

I think an infographic style presentation might make it easier for people to visualise how the PR STV system works.

Does anyone know what happens an elimination or surplus in the case of a dead heat?
How does the 1000 votes get selected?

#### ajapale

##### Moderator
Out of John's pile of 5,000 2nd preferences (Where Mary got the first preference), 1,000 ballot papers are selected from the top of the transfer pile and added to his pile of first preferences but are kept as a separate pile for future counts.
They are selected from the top of the pile.

#### Ceist Beag

##### Frequent Poster
Just to extrapolate on Brendan's example. If the second preference is already elected or eliminated am I right in saying that it will go to the third preference and so on until either a remaining candidate is listed or no further preferences remain?

#### elcato

##### Moderator
I think you also need to make it clear that if no-one is deemed elected (reached the quota) at any of the counts the votes of the lowest person are taken and they are eliminated.

#### Brendan Burgess

##### Founder
Just to extrapolate on Brendan's example. If the second preference is already elected or eliminated am I right in saying that it will go to the third preference and so on until either a remaining candidate is listed or no further preferences remain?
Yes.

#### Brendan Burgess

##### Founder
I think you also need to make it clear that if no-one is deemed elected (reached the quota) at any of the counts the votes of the lowest person are taken and they are eliminated.
Hi Elcato. This is not meant to be a guide to the whole system. Just a guide to how surpluses are distributed.

Brendan

#### orka

##### Frequent Poster
Out of John's pile of 5,000 2nd preferences (Where Mary got the first preference), 1,000 ballot papers are selected from the top of the transfer pile and added to his pile of first preferences but are kept as a separate pile for future counts.
So because the process to select the 1,000 second preference votes is, to an extent, random - does this mean that the result could be different on recounts? If so, surely close calls could turn out to be actually incorrect? Giving rise to recount after recount...

#### trojan

##### Frequent Poster
So because the process to select the 1,000 second preference votes is, to an extent, random - does this mean that the result could be different on recounts? If so, surely close calls could turn out to be actually incorrect? Giving rise to recount after recount...
I think i read somewhere that these votes are kept in a seperate bundle so as they can be checked in event of a recount.

#### Brendan Burgess

##### Founder
trojan is correct - they keep the selected votes in a separate bundle.

It would be very unusual for the randomness to have an impact.

Take the biggest surplus, which was probably the 7,165 for for Michael Healy-Rae

It was distributed absolutely proportionately, so Danny Healy-Rae got 3,835,

So, 3,835 papers were taken out at random from Michael Healy-Rae's transfers to Danny

which gave Danny a surplus of 613

The 3,835 were distributed absolutely proportionately, which resulted in

Brendan Griffin 139 (so he got 23% of the 3,835)

Martin Ferris 116

Let's say a different selection of the 3,835 papers had been taken, and Brendan Griffin only got 10%. Then he would have got about 60 votes fewer.

It would have made no difference as he was over 4,000 votes clear of the last person to be not elected.

For the randomness to affect the outcome, the following would all have had to happen

1) A very large surplus - rare enough
2) A very skewed selection affecting - we don't know
3) A very tight race for the last place - rare enough

A human counting error would be far more likely.
It's also possible that errors by the guys in the polling booths, not perforating the ballot papers properly would affect it more.

Brendan

#### Brendan Burgess

##### Founder
So because the process to select the 1,000 second preference votes is, to an extent, random
This would have very little impact.
In most cases, the 1,000 votes will not elect the next candidate, so their third preferences will not come into play.

They would come into play if that 2nd preference candidate were to be eliminated.

#### 44brendan

##### Frequent Poster
Brendan Griffin 139 (so he got 23% of the 3,835)
Should that not be 23% of the 613?

#### Brendan Burgess

##### Founder
Michael transferred 3,835 to Danny.

These were put into sub-parcels and Brendan Griffin got 882 votes.

That is 23% of 3,835.

Danny had 613 to transfer, so 23% of them went to Brendan Griffin.

Brendan