The Scottish Parliament Under Sainte-Laguë

I have often looked at Scottish election results, and to cut a long story short the Scottish Parliament is elected on a form of Additional Members System, with the constituency Members of the Scottish Parliament being elected by the First Past The Post that we all know and 13,013,123 of us love, and the regional MSPs being elected on party lists using the d'Hondt system.

There are possible variations, and one method of allocating list seats is the Sainte-Laguë method.

In the d'Hondt system, a quotient is calculated by dividing the number of votes a party has by one more than the number of seats it has at that point, and the party with the highest quotient gets the next seat - and its quotient is recalculated as a result.

In the Sainte-Laguë system, the quotient is calculated by dividing the number of votes by one more than twice the number of seats a party has. So if a party has one seat, its quotient is one-third the number of votes, if it has two seats, the quotient is one-fifth etc.

D'Hondt has a reputation for a bias towards the larger parties, and when used at the upper-tier in a constituency-based system, we end up with a form of AMS which favours parties that are larger and/or who are successful at winning constituencies. Both these effects detract from proportionality.

One way to compare is to take an election with 1,000 voters - 501 vote for party A, 299 for party B and 200 for party C. We can then look at how many seats each party would win depending on how many seats there are to be filled:

System	Sainte-Laguë			D'Hondt
Party	A	B	C	A	B	C
1 seat	1	0	0	1	0	0
2 seats	1	1	0	1	1	0
3 seats	1	1	1	2	1	0
4 seats	2	1	1	2	1	1
5 seats	3	1	1	3	1	1
6 seats	3	2	1	3	2	1
7 seats	4	2	1	4	2	1
8 seats	4	2	2	5	2	1
9 seats	4	3	2	5	2	2
10 seats	5	3	2	5	3	2
11 seats	6	3	2	6	3	2
12 seats	6	4	2	6	4	2
13 seats	6	4	3	7	4	2
14 seats	7	4	3	7	4	3
15 seats	8	4	3	8	4	3
16 seats	8	5	3	8	5	3
17 seats	9	5	3	9	5	3
18 seats	9	5	4	10	5	3
19 seats	9	6	4	10	5	4
20 seats	10	6	4	10	6	4

One thing to note is that when there are 3, 9, 13 or 19 seats to be filled in this scenario, the results for Sainte-Laguë are in hold. If d'Hondt has the feature that it is disproportionate by favouring larger parties, then Sainte-Laguë overcorrects this, as there are cases where A - with more votes than B and C combined - has fewer seats than the combined total of B and C. Hence despite having a majority of the votes, A could end up being out-voted by B and C co-operating.

However, if B and C had run a joint list or had been allowed to link lists, then at no point would they have between them more seats than A. From this, does it mean that parties should not co-operate this way under Sainte-Laguë?

The hard and fast rule is - it depends.

Now consider a situation where there are 4 parties - A gets 501 votes (as before), while B gets 399, C 60 and D 40. In one scenario, C and D run separately, while in the second, they run a joint list (or link lists):

Scenario	No pact between C and D				Pact between C and D
Party	A	B	C	D	A	B	C/D
1 seat	1	0	0	0	1	0	0
2 seats	1	1	0	0	1	1	0
3 seats	2	1	0	0	2	1	0
4 seats	2	2	0	0	2	2	0
5 seats	3	2	0	0	3	2	0
6 seats	3	3	0	0	3	3	0
7 seats	4	3	0	0	3	3	1
8 seats	4	3	1	0	4	3	1
9 seats	4	4	1	0	4	4	1
10 seats	5	4	1	0	5	4	1
11 seats	6	4	1	0	6	4	1
12 seats	6	5	1	0	6	5	1
13 seats	6	5	1	1	7	5	1
14 seats	7	5	1	1	7	6	1
15 seats	7	6	1	1	8	6	1
16 seats	8	6	1	1	8	6	2
17 seats	8	7	1	1	8	7	2
18 seats	9	7	1	1	9	7	2
19 seats	9	8	1	1	9	8	2
20 seats	10	8	1	1	10	8	2

What we see here is that by co-operating formally, C and D ensure that the first seat is won at an earlier stage (the seventh available seat rather than the eighth) but the second seat is won at a later stage (the sixteenth seat rather than the thirteenth).

It appears that if - based on the number of seats available and the predicted level of support - neither of two parties would win a seat on their own, then it is sensible to co-operate. On the other hand, if it is clear both parties would win a seat on their own, then co-operation can become counter-productive.

With that out the way, let's have a look at the May 2011 election. Under d'Hondt, we get the result:

Party	Constituency MSPs	Regional MSPs	Total MSPs
Scottish National Party	53	16	69
Labour	15	22	37
Conservatives	3	12	15
Liberal Democrats	2	3	5
Greens	0	2	2
Independent	0	1	1

However, if Sainte-Laguë had been used instead, we would get:

Party	Constituency MSPs	Regional MSPs	Total MSPs
Scottish National Party	53	11	64
Labour	15	19	34
Conservatives	3	12	15
Liberal Democrats	2	5	7
Greens	0	7	7
Independent	0	1	1
Respect - The Unity Coalition	0	1	1

Instead of an overall majority, the SNP would be running an administration that was just short of an overall majority, against a heavily divided opposition.

The changes in individual MSPs would be:

Region	Elected under d'Hondt	Would have been elected under Sainte-Laguë
Glasgow	Anne McTaggart (Lab)	George Galloway (Respect)
Highlands & Islands	Mike Mackenzie (SNP)	Eleanor Scott (Green)**
Lothian	Neil Findlay (Lab)	Margaret Smith (LD)*
Scotland Central	Unchanged
Scotland Mid & Fife	Annabelle Ewing (SNP)	Mark Ruskell (Green)**
Scotland North East	Mark McDonald (SNP)	Martin Ford (Green)
Scotland South	Charles Brodie (SNP)	Alis Ballance (Green)
Scotland West	Margaret McDougall (Lab)	Ross Finnie (LD)*
	Stuart McMillan (SNP)*	Steen Parish (Green)

An asterisk indicates someone who was a sitting MSP at the time of the election. A double asterisk indicates a "retread" - in this case Scott and Ruskell return to represent regions they represented between the May 2003 and May 2007 elections.

There are some things to note. Currently, the SNP has regional MSPs for every region apart from Lothian. Under Sainte-Laguë this would extend to Scotland Mid & Fife and Scotland North East.

The Liberal Democrats would also have retained 2 MSPs - Smith and Finnie - who have served since the first election.

In Glasgow, there would have been the return of former MP Galloway to this city. He had decamped to Bethnal Green & Bow for the May 2005 general election, but was defeated in Poplar & Limehouse at the May 2010 general election. In March 2012 he returned to the House of Commons by winning the by-election in Bradford West. Interesting whether he would have gone down that route if he were an MSP at the time.

Next, we can look at the 2007 election, which under d'Hondt produced the result:

Party	Constituency MSPs	Regional MSPs	Total MSPs
Scottish National Party	21	26	47
Labour	37	9	46
Conservatives	4	13	17
Liberal Democrats	11	5	16
Greens	0	2	2
Independent	0	1	1

As we know, with a narrow lead in votes and seats, the SNP eschewed any deal with the Liberal Democrats and/or the Greens, and formed a minority administration. Under Sainte-Laguë, the story would have been different:

Party	Constituency MSPs	Regional MSPs	Total MSPs
Labour	37	8	45
Scottish National Party	21	21	42
Conservatives	4	14	18
Liberal Democrats	11	5	16
Greens	0	6	6
Independent	0	1	1
Solidarity - Scotland's Socialist Movement	0	1	1

Despite coming top in terms of votes, this sees the SNP take second place. The outgoing Labour/Liberal Democrat administration finds itself 4 seats short of an overall majority, opening up the prospect of a "traffic light" coalition with the Greens.

The changes in individual MSPs would be:

Region	Elected under d'Hondt	Would have been elected under Sainte-Laguë
Glasgow	Bill Kidd (SNP)	Tommy Sheridan (SSSM)*
Highlands & Islands	David Thompson (SNP)	Eleanor Scott (Green)*
Lothians	Unchanged
Scotland Central	John Wilson (SNP)	Graham Simpson (C)
Scotland Mid & Fife	Richard Simpson (Lab)**	Mark Ruskell (Green)*
Scotland North East	Nigel Don (SNP)	Shiona Baird (Green)*
Scotland South	Aileen Campbell (SNP)	Chris Ballance (Green)*
Scotland West	Unchanged

As before an asterisk indicates someone who was a sitting MSP at the time of the election, and a double asterisk a retread or potential retread. In this case, Richard Simpson had been elected as the constituency MSP for Ochil at the May 1999 election, being defeated by the SNP's George Reid at the 2003 election.

Now we move on to the most interesting Scottish election - that of 2003. Under d'Hondt, the result was:

Party	Constituency MSPs	Regional MSPs	Total MSPs
Labour	46	4	50
Scottish National Party	9	18	27
Conservatives	3	15	18
Liberal Democrats	13	4	17
Greens	0	7	7
Scottish Socialist Party	0	6	6
Independents	2	1	3
Scottish Senior Citizens' Unity Party	0	1	1

If the election had been held using Sainte-Laguë, then the result, again, would have been different:

Party	Constituency MSPs	Regional MSPs	Total MSPs
Labour	46	3	49
Scottish National Party	9	13	22
Conservatives	3	15	18
Liberal Democrats	13	4	17
Greens	0	9	9
Scottish Socialist Party	0	9	9
Independents	2	1	3
Scottish Senior Citizens' Unity Party	0	1	1
Pensioners' Party	0	1	1

Hence, under Sainte-Laguë, there would still have been a Labour/Liberal Democrat minority administration, albeit with a smaller majority.

The changes in individual MSPs would be:

Region	Elected under d'Hondt	Would have been elected under Sainte-Laguë
Glasgow	Unchanged
Highlands & Islands	Rob Gibson (SNP)	Steve Arnott (SSP)
Lothians	Unchanged
Scotland Central	Linda Fabiani (SNP)*	Stan Blackley (Green)
Scotland Mid & Fife	Bruce Crawford (SNP)*	Linda Graham (SSP)
	Tricia Marwick (SNP)*	George Rodger (PP)
Scotland North East	Richard Baker (Lab)	John Sangster (SSP)
Scotland South	Unchanged
Scotland West	Stewart Maxwell (SNP)	Steve Burgess (Green)

As previously, an asterisk indicates someone who was a sitting MSP at the time of the election.

Out of the additional SSP politicians, one thing to speculate on is how they would have responded in September 2006 to the split leading to the formation of Solidarity by Sheridan and Rosemary Byrne, MSP for Scotland South. It seems that Arnott would have become Solidarity's third MSP. The last information I have concerning Graham has her listed as SSP in 2007, and in May 2007, Sangster - who went on to become Chair of Inverurie Community Council - contested the Inverurie & District ward of Aberdeenshire Council, with no party label.

Rodger was the leader of the Pensioners' Party.

It is interesting to note that under Sainte-Laguë, both the Greens and SSP would have MSPs from every region.

And this brings me on to the inaugural election of 1999:

Party	Constituency MSPs	Regional MSPs	Total MSPs
Labour	53	3	56
Scottish National Party	7	28	35
Conservatives	0	18	18
Liberal Democrats	12	5	17
Greens	0	1	1
Scottish Socialist Party	0	1	1
Independent	1	0	1

Under Sainte-Laguë, it would have been:

Party	Constituency MSPs	Regional MSPs	Total MSPs
Labour	53	2	55
Scottish National Party	7	25	32
Conservatives	0	17	17
Liberal Democrats	12	5	17
Greens	0	4	4
Socialist Labour	0	2	2
Scottish Socialist Party	0	1	1
Independent	1	0	1

One thing to note is that Socialist Labour - formed by Arthur Scargill in protest at the move to the centre Labour was following under the then Prime Minister Tony Blair - did better than the SSP in terms of votes, and really it was only the SSP's strong support in Glasgow that gave it an MSP, while Socialist Labour didn't - I will return to this later.

The changes in individual MSPs would be:

Region	Elected under d'Hondt	Would have been elected under Sainte-Laguë
Glasgow	Sandra White (SNP)	Kay Allan (Green)
Highlands & Islands	Rhoda Grant (Lab)	Eleanor Scott (Green)
Lothians	Unchanged
Scotland Central	Linda Fabiani (SNP)	Raymond Stead (Soc Lab)
Scotland Mid & Fife	Bruce Crawford (SNP)	Graeme Farmer (Green)
Scotland North East	Unchanged
Scotland South	David Mundell (C)	Louise McDaid (Soc Lab)

We can look at how the parties fare from election-to-election under the two systems, by looking at the number of seats they would have gained or lost if the elections were held under Sainte-Laguë:

Party	1999	2003	2007	2011
Labour	-1	-1	-1	-3
Scottish National Party	-3	-5	-5	-5
Conservatives	-1	0	+1	0
Liberal Democrats	0	0	0	+2
Greens	+3	+2	+4	+5
Scottish Socialist Party	0	+3	N/A	N/A
Socialist Labour**	+2	N/A	N/A	N/A
Independent (Margo MacDonald)*	N/A*	0	0	0
Scottish Senior Citizens' Unity Party	N/A	0	N/A	N/A
Pensioners' Party**	N/A	+1	N/A	N/A
Solidarity - Scotland's Socialist Movement**	N/A	N/A	+1	N/A
Respect - The Unity Coalition**	N/A	N/A	N/A	+1

[* In 1999, MacDonald was elected as an SNP MSP for Lothians, but by the 2003 election had left the SNP and stood for re-election as an Independent on a "party list" comprising of solely her name. The other Independent MSPs elected have both been from constituencies - Dennis Canavan in Falkirk West in 1999 and 2003; and Jean Turner in Strathkelvin & Bearsden in 2003.]

An "N/A" indicates that the party in question neither won any regional seats under d'Hondt, not would it have won any regional seats under Sainte-Laguë.

Parties with a double asterisk are ones that have never had any elected MSPs - although Solidarity ended up with a couple of MSPs via divisions in the SSP.

As we can see, it's smaller parties like the Greens who do better under Sainte-Laguë. Most countries that use proportionalish representation subdivide the country, and what we see here is the Greens doing just well enough to get over the hurdle in most - and sometimes all - regions, which is lower for Sainte-Laguë than d'Hondt.

The SNP seems to be hit badly by Sainte-Laguë. They were (until 2011) in an interesting position. They were the second party which found it hard to win constituencies and so relied heavily on regional seats. In 2011 they not only won most constituencies, but often did well enough to pick up extra regional seats. But under Sainte-Laguë it becomes harder for a constituency-rich party to win regional seats, due to the lower quotient. Labour didn't really have this problem as they tended to win only a few regional seats, which would be in areas where they were low on constituencies.

For all their support for proportional representation, the Liberal Democrats were in the strange position in Scotland that they benefitted from FPTP, and so only win a few regional seats. In 2011 they are reduced to being another minor party a la the Greens, and so would benefit from Sainte-Laguë.

The big story of 2003 was the breakthrough for the Greens and the SSP. Under Sainte-Laguë, the Greens would already have been more established. But, if Socialist Labour already had a couple of MSPs, compared to the SSP being a parliamentary one-man band, would it be Socialist Labour that disaffected Labour voters turned to in 2003, rather than the SSP? Running the 1999 election on Sainte-Laguë alters the political landscape and this would have been reflected in how people voted in later elections.

For ecample. take the June 1999 election to the European Parliament, and how, under d'Hondt, the UK Independence Party and the Greens gain Members of the European Parliament. The June 2004 election saw UKIP rise past the Liberal Democrats into third place. There are various reasons, but one of them has to be that voters now saw that under a proportional system UKIP could win - the political equivalent of "nothing succeeds like success".

What is interesting about the 2003 results is how, under Sainte-Laguë, fractured the opposition to a Labour/Liberal Democrat administration would be. The SNP and Conservatives would only be 4 seats apart.

If we consider the results of the June 2001 general election in Wales, then we see the Conservatives being the second largest party in terms of votes but stuck on 0 seats, as they were at the May 1997 general election. In Scotland, however, winning Galloway & Upper Nithsdale from the SNP brings them up to 1 seat.

At the 2005 general election, the Conservatives start doing better in Wales with 3 MPs, than Scotland with just 1 MP again.

Moving on to the 2010 general election, the Conservatives, with 8 MPs, become the second-largest party in Wales, but in Scotland remain in fourth-place with still just 1 MP.

If we look at the May 1999 election to the Welsh Assembly, we see the Conservatives down in third place, with 9 Assembly Members to Plaid Cymru's 17. The May 2003 election sees this gap narrow as Plaid Cymru are down to 12 AMs and the Conservatives are up to 11.

Moving on to May 2007, and the gap has widened slightly, with Plaid Cyrmu up to 15 AMs and the Conservatives up to 12 - but Labour and Plaid Cymru forming a coalition administration in July that year ensures the Conservatives become the Opposition.

If we then look at the May 2011 election, then we see the Conservatives - with 14 AMs - have overtaken Plaid Cymru - with 11 AMs - to become Wales' second party.

Bearing in mind that even as late as the April 1992 general election, the Conservatives were Scotland's second party in terms of votes and MPs, it is interesting to reflect whether an election result which put them and the SNP nearly neck-and-neck could have led to a Welsh-style revival of fortunes.

If the Scottish Parliament had used Sainte-Laguë from the beginning, then the way people cast their regional votes could have been very different to how they were actually cast.