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The Maths Behind GE 2016 (or 2013/14/15...)


livingstone

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Mar 3, 2004
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OK folks, rather than take random stabs in the dark about who might win what number of seats, I always think its better to examine what the polls say, but also the historical trends around how particular parties manage to convert votes into seats. We all know (or should…) that in our system, seats don’t allocate exactly proportionately. So the Christian Solidarity Party might achieve 1% of the vote but win 0 seats. The Greens are an example of small party bias in our system, where despite getting 2% of the vote, they did not win 2% of the seats.

So smaller parties tend to have negative seat bonuses – i.e. they win a smaller proportion of the seats than they do votes. Larger parties tend to have positive seat bonuses, i.e. winning a higher proportion of seats than votes.

The simplest way I’ve found to compare bonuses over time is to divide the proportion of seats won by the proportion of the vote won. This will give you a figure that hovers somewhere around 1.00 – where it’s dead on 1.00, then the party won the exact same proportion of seats and votes. Put in context, in elections since 1979, (comparing only FF, FG, Labour and SF) the highest bonus has been 1.27 (Fine Gael in 2011) and the lowest has been 0.23 (SF in 1997…I didn’t count SF before 1977 – if I did, I expect the seat bonus would have been lower still).

I did this for the four parties from 1977 to the 2011 election to figure out if there are patterns, and modelled current party ratings based on each seat bonus. There are patterns. The first is that there are some aberrations – elections whose circumstances were so unique that they produced out of the ordinary results. Fine Gael’s bonus of 0.83 in 2002 and Fianna Fail’s bonus of 0.69 in 2011 were both products of very unique elections.

Beyond the aberrations though, there are other patterns – with the exception of 2011, Fianna Fail has always had a positive seat bonus, ranging from 1.01 to 1.18, and Fine Gael with the exception of 2002, FG has only had one other negative bonus, of 0.95 in 1977. Otherwise, FG has had a positive bonus between 1.02 and 1.27. Labour have had four negative bonuses, but three of those have been extremely close to 1.00 at 0.99 (three times) and 0.98 (once). Interestingly, with Labour, the lower their share of the vote, the higher their bonus. So in 1987, when they did disastrously, they had a bonus of 1.11. Likewise, in 2002 and 2007 when their performance was worse than, say, 1997, they had a bonus of 1.11 and 1.19 respectively (compared to 0.98 in 1997). In Labour’s best election result to date before 2011 (1992), they had a mediocre bonus of 1.00. In fact, with the exception of 2011, the pattern is clear that Labour’s seat bonus is higher when their poll numbers are lower, which suggests that Labour (a) has a core level of seats which correspond to a core level of vote, and (b) when Labour attracts extra votes, they have been historically poor at maximising those votes into seats.

As for SF, their bonus has steadily risen, from 0.23 in 1997 to 0.85 in 2011. Unlike with other parties, SF has a clear trajectory as they become less transfer repellent, so it’s entirely plausible that they might reach unitary bonus (i.e. 1.00) at the next election.

So what does this tell us about the next election?

Nothing concrete, but we can probably predict that the next election won’t have the same historic circumstances as 2011. Why? Because in 2011, you had a hated Government who bore 100% of the responsibility for the mess, and an opposition with clean hands who the public were willing to embrace. In 2015/16, you will have a pretty unpopular Government but one which can legitimately claim that most responsibility lies with one of the main opposition parties, so there will not, I believe, be the same collapse in Government support that you saw in 2011. I think 2016 will be much closer to 1987 in terms of circumstances – i.e. an unpopular Government but an opposition that is only tepidly supported.

That being the case, I looked at each parties highest and lowest bonuses – although I excluded 2002 for FG and 2011 for FF on the basis that I believe that they were aberrations. For Sinn Fein, I’ve assumed 1.00 as their maximum, and 0.85 as their minimum, because frankly, there’s no way SF are going back to a bonus of 0.23.

Based on a 158 Seat Dail, and based on the last RedC poll, the seat ranges would be as follows:

FG – 42-56
Labour – 16-21
FF – 33-39
SF – 26-30

For comparison’s sake, in a 166 seat Dail, the range would be:

FG – 44-59
Labour – 17-22
FF – 35-41
SF – 27-32

What’s also interesting, though, is to compare bonuses for parties JUST when they were in a similar role – i.e. emerging from Government for FG and Labour, and emerging from opposition for FF. This comparison isn’t applicable to SF.

If you do that, then things improve slightly for Labour (in terms of seat floor, at least), because they’ve historically had higher bonuses emerging from Government, and also better for FF, because they’ve historically had decent bonuses emerging from opposition, so the range is:

FG – 42-52
Labour – 17-19
FF – 36-39

In a 166 seat Dail, this would equate to:

FG – 44-54
Labour – 18-20
FF – 38-41

So, as a summary? In a trimmed down Dail, based on current numbers, I think we’re looking at FG in the high-forties, Labour in the high teens, FF in the mid- to high-thirties and SF in the high-twenties.

That would probably put a FG/Labour coalition out of reach. Likewise a FF/SF coalition. The only viable options that I can see would be FG/FF or FF/SF/Lab.


(NB – this obviously comes with a health warning. Polls are snapshots and polling figures could change. Also, events, dear boy, events may move the next election from being standard to being an aberration in terms of bonuses – this analysis is really based on if an election were held today).
 


PO'Neill

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I'd agree with your analysis about SF getting 26-30, but their's not a hope we'll get into coalition with FF, not a chance. In the long term SF's ambition is to take FF and Labour's votes, not join with them. However FF and FG will not have the slightest problem bedding down with each other in the next Govt to I think eventually merge as Fine Fail or Fianna Gael or whatever. Two cheeks of the one ar$e regardless.
 

farnaby

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Fine Fail or Fianna Gael or whatever. Two cheeks of the one ar$e regardless.
"Gael Fail" would capture it nicely I reckon.

Nice analysis livingstone. It would be interesting to factor in a new party making a grand entrance PD-style - a possibility if things go from bad to worse.
 

livingstone

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"Gael Fail" would capture it nicely I reckon.

Nice analysis livingstone. It would be interesting to factor in a new party making a grand entrance PD-style - a possibility if things go from bad to worse.
Maybe, but difficult to see where it would come from. The left is already well represented. The closest to a new left-wing party might be if the cut-off Labour TDs and others formed a new Social Democratic party that rejects the sort of austerity of the Government but also the craziness of SF and ULA etc.

More likely though, might be a Shane Ross/Stephen Donnelly 'liberal' party in the style of the early PDs. But I don't see where its membership comes from. Certainly not the opposition - SF TDs wouldn't be that way inclined, and FF TDs don't have the intellectual heft for a serious new party. Labour TDs would also be unlikely to be so minded - so it would have to be a rump of FG, and there's no real indication of any dissatisfaction from an economically and socially liberal element of FG - in fact I'd imagine the only difficulty FG might have is if some social conservatives rebel on abortion or issues like gay marriage if they arise - but a rump built on social issues alone won't be able to make a real impression.
 

emulator

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Surely Independents will come into the equation a lot more the next time ? that, or as posted already a new party.

Meath East, which must be held before the end of May, will give an idea of what's going on.... once you filter out the sympathy vote that FG will no doubt be going for.

My spidey senses are telling me that there will be a GE this year.....
 

livingstone

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24,398
Surely Independents will come into the equation a lot more the next time ? that, or as posted already a new party.

Meath East, which must be held before the end of May, will give an idea of what's going on.... once you filter out the sympathy vote that FG will no doubt be going for.

My spidey senses are telling me that there will be a GE this year.....
Agreed re independents - I'd expect them (independents and others - ULA etc) to be around high-teens up to maybe 20. But on the figures I posted - FG/Lab would be around 65-70 and FF/SF would also be around 65-70. FF/Lab would be around 55-60.

A majority would be 79.

In that case, I think any possible coalitions will be too far from a majority to survive long with independent support. For that reason, I think the only stable options would be FG/FF and FF/SF/Lab (and I use the word 'stable' lightly in the latter case...).
 

PO'Neill

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Agreed re independents - I'd expect them (independents and others - ULA etc) to be around high-teens up to maybe 20. But on the figures I posted - FG/Lab would be around 65-70 and FF/SF would also be around 65-70. FF/Lab would be around 55-60.

A majority would be 79.

In that case, I think any possible coalitions will be too far from a majority to survive long with independent support. For that reason, I think the only stable options would be FG/FF and FF/SF/Lab (and I use the word 'stable' lightly in the latter case...).
FF/SF or FF/SF/Lab - not a hope, SF has no interest whatsoever in alligning it self with Fine Fail.
 

hellsbells

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ff/fg a certainty after the next election . Well matched they are ,should have no problems putting

eh eh policy differences behind them for a few years at the trough .
 

Davidoff

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1,485
Interesting analysis.

The striking thing about those numbers is the range for FF.

On a good day they might beat FG. On a bad day they could lose second place to SF.

Long way to go though.
 

cillian32

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FF/SF or FF/SF/Lab - not a hope, SF has no interest whatsoever in alligning it self with Fine Fail.
If SF were the bigger party....all bets are off ! We cant afford to keep electing FF or FG led goverments.
 

cillian32

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If only Tommy O Brien was here to give his opinion......Otherwise known as (Simonsays):D over at Political world .org
 

farnaby

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Maybe, but difficult to see where it would come from. The left is already well represented. The closest to a new left-wing party might be if the cut-off Labour TDs and others formed a new Social Democratic party that rejects the sort of austerity of the Government but also the craziness of SF and ULA etc.

More likely though, might be a Shane Ross/Stephen Donnelly 'liberal' party in the style of the early PDs. But I don't see where its membership comes from. Certainly not the opposition - SF TDs wouldn't be that way inclined, and FF TDs don't have the intellectual heft for a serious new party. Labour TDs would also be unlikely to be so minded - so it would have to be a rump of FG, and there's no real indication of any dissatisfaction from an economically and socially liberal element of FG - in fact I'd imagine the only difficulty FG might have is if some social conservatives rebel on abortion or issues like gay marriage if they arise - but a rump built on social issues alone won't be able to make a real impression.
You're right that a new party won't be a breakaway from the current lot - I'm thinking more of something like the abortive "Democracy Now" group pre-2011 GE. Pro-reform, anti-vested interest. Mostly new faces plus a few independents. Unlikely to make a PD-level impact, I'll concede.
 

statsman

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Joined
Feb 25, 2011
Messages
56,218
OK folks, rather than take random stabs in the dark about who might win what number of seats, I always think its better to examine what the polls say, but also the historical trends around how particular parties manage to convert votes into seats. We all know (or should…) that in our system, seats don’t allocate exactly proportionately. So the Christian Solidarity Party might achieve 1% of the vote but win 0 seats. The Greens are an example of small party bias in our system, where despite getting 2% of the vote, they did not win 2% of the seats.

So smaller parties tend to have negative seat bonuses – i.e. they win a smaller proportion of the seats than they do votes. Larger parties tend to have positive seat bonuses, i.e. winning a higher proportion of seats than votes.

The simplest way I’ve found to compare bonuses over time is to divide the proportion of seats won by the proportion of the vote won. This will give you a figure that hovers somewhere around 1.00 – where it’s dead on 1.00, then the party won the exact same proportion of seats and votes. Put in context, in elections since 1979, (comparing only FF, FG, Labour and SF) the highest bonus has been 1.27 (Fine Gael in 2011) and the lowest has been 0.23 (SF in 1997…I didn’t count SF before 1977 – if I did, I expect the seat bonus would have been lower still).

I did this for the four parties from 1977 to the 2011 election to figure out if there are patterns, and modelled current party ratings based on each seat bonus. There are patterns. The first is that there are some aberrations – elections whose circumstances were so unique that they produced out of the ordinary results. Fine Gael’s bonus of 0.83 in 2002 and Fianna Fail’s bonus of 0.69 in 2011 were both products of very unique elections.

Beyond the aberrations though, there are other patterns – with the exception of 2011, Fianna Fail has always had a positive seat bonus, ranging from 1.01 to 1.18, and Fine Gael with the exception of 2002, FG has only had one other negative bonus, of 0.95 in 1977. Otherwise, FG has had a positive bonus between 1.02 and 1.27. Labour have had four negative bonuses, but three of those have been extremely close to 1.00 at 0.99 (three times) and 0.98 (once). Interestingly, with Labour, the lower their share of the vote, the higher their bonus. So in 1987, when they did disastrously, they had a bonus of 1.11. Likewise, in 2002 and 2007 when their performance was worse than, say, 1997, they had a bonus of 1.11 and 1.19 respectively (compared to 0.98 in 1997). In Labour’s best election result to date before 2011 (1992), they had a mediocre bonus of 1.00. In fact, with the exception of 2011, the pattern is clear that Labour’s seat bonus is higher when their poll numbers are lower, which suggests that Labour (a) has a core level of seats which correspond to a core level of vote, and (b) when Labour attracts extra votes, they have been historically poor at maximising those votes into seats.

As for SF, their bonus has steadily risen, from 0.23 in 1997 to 0.85 in 2011. Unlike with other parties, SF has a clear trajectory as they become less transfer repellent, so it’s entirely plausible that they might reach unitary bonus (i.e. 1.00) at the next election.

So what does this tell us about the next election?

Nothing concrete, but we can probably predict that the next election won’t have the same historic circumstances as 2011. Why? Because in 2011, you had a hated Government who bore 100% of the responsibility for the mess, and an opposition with clean hands who the public were willing to embrace. In 2015/16, you will have a pretty unpopular Government but one which can legitimately claim that most responsibility lies with one of the main opposition parties, so there will not, I believe, be the same collapse in Government support that you saw in 2011. I think 2016 will be much closer to 1987 in terms of circumstances – i.e. an unpopular Government but an opposition that is only tepidly supported.

That being the case, I looked at each parties highest and lowest bonuses – although I excluded 2002 for FG and 2011 for FF on the basis that I believe that they were aberrations. For Sinn Fein, I’ve assumed 1.00 as their maximum, and 0.85 as their minimum, because frankly, there’s no way SF are going back to a bonus of 0.23.

Based on a 158 Seat Dail, and based on the last RedC poll, the seat ranges would be as follows:

FG – 42-56
Labour – 16-21
FF – 33-39
SF – 26-30

For comparison’s sake, in a 166 seat Dail, the range would be:

FG – 44-59
Labour – 17-22
FF – 35-41
SF – 27-32

What’s also interesting, though, is to compare bonuses for parties JUST when they were in a similar role – i.e. emerging from Government for FG and Labour, and emerging from opposition for FF. This comparison isn’t applicable to SF.

If you do that, then things improve slightly for Labour (in terms of seat floor, at least), because they’ve historically had higher bonuses emerging from Government, and also better for FF, because they’ve historically had decent bonuses emerging from opposition, so the range is:

FG – 42-52
Labour – 17-19
FF – 36-39

In a 166 seat Dail, this would equate to:

FG – 44-54
Labour – 18-20
FF – 38-41

So, as a summary? In a trimmed down Dail, based on current numbers, I think we’re looking at FG in the high-forties, Labour in the high teens, FF in the mid- to high-thirties and SF in the high-twenties.

That would probably put a FG/Labour coalition out of reach. Likewise a FF/SF coalition. The only viable options that I can see would be FG/FF or FF/SF/Lab.


(NB – this obviously comes with a health warning. Polls are snapshots and polling figures could change. Also, events, dear boy, events may move the next election from being standard to being an aberration in terms of bonuses – this analysis is really based on if an election were held today).
Interesting analysis, and it looks fairly accurate. The only problem is that we have no idea what the actual figures in the real election will be.
 

livingstone

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Interesting analysis.

The striking thing about those numbers is the range for FF.

On a good day they might beat FG. On a bad day they could lose second place to SF.

Long way to go though.
To be fair, the FG 'low' figure of 42 or 44 is entirely influenced by their negative bonus in 1977. Since 1977 (with the exception of 2002, which I've excluded) they've always had positive bonuses (and actually, they've been pretty healthy bonuses as well). The reason I left 1977 in FG's figures is that I can't think of any especially unusual circumstances that would have contributed to their negative bonus.

Sure, the outgoing Government in 1977 were unpopular, but not abjectly hated (as with FF in 2011). Unlike 2002, I can't 'explain away' the 1977 negative bonus, so I left it in. So while, of course, FG may replicate that negative seat bonus, I don't actually think they will. So while FG have a very large range, I think their actual result will be in the upper half of that range.
 

Con Gallagher

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Sure, the outgoing Government in 1977 were unpopular, but not abjectly hated (as with FF in 2011). Unlike 2002, I can't 'explain away' the 1977 negative bonus, so I left it in.
I presume the Tullymander was a factor - as was the popularity of Jack Lynch (with the introduction of US style electioneering). 1977 was an outlier as much as 2011. I can't forsee any parallels in the next general election (though the next local elections will be different with a strange preference for larger constituencies)
Electoral (Amendment) Act 1974 - Wikipedia, the free encyclopedia
 

livingstone

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Interesting analysis, and it looks fairly accurate. The only problem is that we have no idea what the actual figures in the real election will be.
Of course. My plan would be to update the model with each opinion poll and update this thread.

My confidence in opinion polling is pretty high compared to some posters, so I reckon that the opinion polls just before the election will be a decent indicator of final FPVs - I'm mostly interested to see if the model can correctly predict the seat range at any given level of support.
 

Heligoland

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FF/SF or FF/SF/Lab - not a hope, SF has no interest whatsoever in alligning it self with Fine Fail.
I wouldn't be so sure. The reps from outside Dublin don't have nearly the problem with FF that the Dubs have, and the prospect of taking the salute outside the GPO in 1916 would be very tempting for some of them.

You have to remember that SF shares power in Stormont with some really unsavoury characters, and it also has to deal with Tories swanning over from London. Having to put up with someone like Micheal Martin might not be such a daunting prospect in comparison.
 

rockofcashel

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I presume the Tullymander was a factor - as was the popularity of Jack Lynch (with the introduction of US style electioneering). 1977 was an outlier as much as 2011. I can't forsee any parallels in the next general election (though the next local elections will be different with a strange preference for larger constituencies)
Electoral (Amendment) Act 1974 - Wikipedia, the free encyclopedia
What is strange about larger constituencies ?

In fact, a lot more Dail constituencies should be larger, just as they were in the early years of the State, when the founders of the State actually cared about plurarity and proportionality.

Larger constituencies offer better hopes for smaller parties to enage in the political process and win seats. The only parties who will have a problem with larger constituencies are FF and FG, both of who are in line for significant seat losses in the local elections in 2014.

On the other hand, the party likely to gain most from the increase in seat numbers is SF and to lesser extent the Labour Party... with a lot of Independents likely to consider their chances as well.

On current figures, for example.. a 4 seater like the Cashel LEA, currently returned 2 FG, 1 FF, 1 Indo... A 7 seater for Cashel Municipal District Area would return 1/2 FG, 1/2 FF, 1 SF, 1 Lab, 1/2 Indos... more smaller parties and Indo's getting a chance.. but no gain for bigger parties
 
Last edited:

statsman

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Of course. My plan would be to update the model with each opinion poll and update this thread.

My confidence in opinion polling is pretty high compared to some posters, so I reckon that the opinion polls just before the election will be a decent indicator of final FPVs - I'm mostly interested to see if the model can correctly predict the seat range at any given level of support.
Fair enough.
 

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