Levelling Seats

One of my interests is electoral systems - don't knock it; on many job applications for analyist roles I have written about this interest and emphasised how I use Excel for it - and one of the issues that has confused me is that of levelling seats. Now, I understand the basic idea - to ensure that election results are more proportional, but the application of it was confusing.

I'll take as my starting point the June 2009 elections to the European Parliament for the United Kingdom. The United Kingdom elects 73 Members of the European Parliament (in 2009 we actually elected 72, but in December 2009, an extra seat was awarded to the West Midlands.

Sweden uses a levelling seat system for its general elections, with 39 of the 349 members chosen this way. If we keep the same ratio then we would expect 8 MEPs to be elected on levelling seats. The remaining 65 MEPs would be elected on a regional basis:

Region or nation	MEPs	Current MEPs	Reduction
Eastern England	6	7	1
East Midlands	5	5	0
London	7	8	1
North East England	3	3	0
Northern Ireland	3	3	0
North West England	7	8	1
Scotland	5	6	1
South East England	9	10	1
South West England	6	6	0
Wales	3	4	1
West Midlands	6	7	1
Yorkshire & Humberside	5	6	1

Next we're going to do something which will seem odd at first - we will consider the Europarties rather than the national parties in cases where national parties are in a Europarty. The reasons for this will become apparent in a moment. But for now, the results would be:

• Alliance of European Conservatives & Reformists - 25 (Conservative 24, Ulster Unionist Party 1)
• Party of European Socialists - 12 (all Labour)
• UK Independence Party - 11
• Alliance of Liberals & Democrats for Europe - 10 (all Liberal Democrat)
• European Free Alliance - 3 (Scottish National Party 2, Plaid Cymru 1)
• European Green Party - 2 (both Green Party of England & Wales)
• Sinn Féin - 1
• Democratic Unionist Party - 1

We can look at which MEPs elected in 2009 would not have been elected at this stage:

Region or nation	MEP	Party
Eastern England	John Agnew	UK Independence Party
London	Marina Yannakoudakis	Alliance of European Conservatives & Reformists
North West England	Nick Griffin	British National Party
Scotland	Catherine Stihler	Party of European Socialists
South East England	Catherine Bearder	Alliance of Liberals & Democrats for Europe
Wales	John Bufton	UK Independence Party
West Midlands	Anthea McIntyre	Alliance of European Conservatives & Reformists
Yorkshire & Humberside	Andrew Brons	British National Party

With these out the way, we now work out which parties get the 8 levelling MEPs. We are used to using d'Hondt for list systems, so this is the approach I will take here. Note that it doesn't really matter how the earlier members were elected before we get to this stage - for example, we could have levelling Members of the Scottish Parliament elected once all the first-stage MSPs had been elected under the Additional Members System.

The basic principle is to add together all the votes for the parties, and allocate the extra MEPs - so we divide the total vote for each party by one more than the number of MEPs it has. When we do this we find that the European Green Party and the British National Party are entitled to 3 levelling MEPs each, and the English Democrats and the Christian Party are each entitled to 1 levelling MEP. There is something intutive here - these are the minorish parties who just fail to win a seat in the regions, but add together their votes across the nation and we see they get enough to win seats.

Note that we are using the Europarties here - it could be possible that when we look at the Party of European Socialist vote, they are entitled to a levelling MEP in Northern Ireland, and so Labour voters in Great Britain would be helping elect a Social Democratic & Labour Party MEP. Notice I mentioned a levelling MEP in a particular place. Levelling members are not meant to represent the whole nation.

For the next stage is to find out where these levelling MEPs will represent. And to do this we use the Sainte-Laguë method in an unusual way. For each party that is entitled to levelling MEPs, we look at its vote and seats region-by-region, and work out a quotient of the number of votes divided by one more than twice the number of seats. The region with the highest quotient gets that party's first levelling MEP - and the process is repeated if more than one is to be elected.

For the parties with no MEPs in the first round and only entitled to one levelling MEP, it is simple. It is the region where they got their most votes. For the English Democrats, this is South East England, and the winner would be Steve Uncles, who was unsuccessful in his bid to become Kent's Police & Crime Commissioner - note that even though he would represent just South East England, he would owe his place to the votes his party got across the whole of England.

For the Christian Party, this is London and the levelling MEP would be George Hargreaves.

For the European Green Party and the British National Party it is a bit more complicated. But we find for the former the levelling MEPs are Ricky Knight in South West England, Rupert Read in Eastern England and Peter Cranie in North West England.

The British National Party would see Griffin and Brons elected as levelling MEPs, along with Simon Darby in the West Midlands.

So, the regional distribution would be:

Region or nation	First stage MEPs	Levelling MEPs	Total MEPs	Gain/Loss
Eastern England	6	1	7	0
East Midlands	5	0	5	0
London	7	1	8	0
North East England	3	0	3	0
Northern Ireland	3	0	3	0
North West England	7	2	9	+1
Scotland	5	0	5	-1
South East England	9	1	10	0
South West England	6	1	7	+1
Wales	3	0	3	-1
West Midlands	6	1	7	0
Yorkshire & Humberside	5	1	6	0

And that is how levelling seats are worked out.

Now, I did state earlier that it doesn't really matter how the earlier members were elected before we get to the levelling seats stage. Basically, all that it's interested in is how many votes a party has nationwide and how many seats that party has before the levelling seats are worked out.

With the Additional Members System in the United Kingdom, the lower-tier are always elected by Single Member Plurality. But it doesn't have to be - there could be all single-member constituencies using the Alternative Vote, or some multi-member constituencies using Single Transferable Vote. Take, for example, the May 2011 election to the Scottish Parliament and consider the Scotland North East region. 10 constituency members and 7 additional members elected using the d'Hondt system. But it doesn't have to be 10 constituencies - there could be just 7, with 5 of them returning 1 MSP, Aberdeen & North Kincardine returning 3 MSPs and Dundee returning 2 MSPs. When the allocation of additional members are worked out, all that matters is the regional vote and number of constituency MSPs for each party.

And that brings me on to how levelling seats would work with AMS. Note that they would not create a third tier of MSPs, rather that they would be an extra set of regional MSPs. If we look at the 2011 Scottish election, we get:

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

Scotland is divided into 8 regions, which return between 8 and 10 constituency MSPs, and 7 regional MSPs. This gives us 129 MSPs in all. With the Swedish ratio, we would expect 14 levelling seats. We can round this up to 16 - equivalent to 2 levelling seats per region.

The first step is to simply allocate 5 regional MSPs for each region - so the sixth and seventh regional MSPs are not elected at this stage (but might be later). So, the MSPs who lose their seats at this stage are:

Region	MSP	Party
Glasgow	Bob Doris*	Scottish National Party
	Anne McTaggart	Labour
Highlands & Islands	Jean Urquhart	Scottish National Party
	Mike MacKenzie	Scottish National Party
Lothian	Neil Findlay	Labour
	Gavin Brown*	Conservative
Scotland Central	John Wilson	Scottish National Party
	Clare Adamson	Scottish National Party
Scotland Mid & Fife	Willie Rennie	Liberal Democrat
	Annabelle Ewing	Scottish National Party
Scotland North East	Lewis Macdonald*	Labour
	Mark McDonald	Scottish National Party
Scotland South	Jim Hume*	Liberal Democrat
	Charles Brodie	Scottish National Party
Scotland West	Stuart McMillan*	Scottish National Party
	Neil Bibby	Labour

[* MSP at the time of the election]

As we see, reducing the number of regional MSPs by 2 per regions sees the loss of 9 Scottish National Party, 4 Labour, 2 Liberal Democrat and 1 Conservative MSP, giving a result of:

Party	Constituency MSPs	Regional MSPs	Total MSPs
Scottish National Party	53	7	60
Labour	15	18	33
Conservatives	3	11	14
Liberal Democrats	2	1	3
Greens	0	2	2
Independent	0	1	1

Now we'll look at how many levelling seats each party needs, but we'll do something different. In European countries that use levelling seats, it is common for them to be allocated on a more proportional system than then previous seats. So, with the regional seats allocated on d'Hondt, in this example we shall allocate the levelling seats to the parties using Sainte-Laguë. When we run this, we find that Labour, the Liberal Democrats and the Greens are all entitled to 4 levelling seats, the Conservatives entitled to 3, and the Scottish National Party to 1. Using the method above, we can then allocate them out:

Region	MSP	Party
Glasgow	None
Highlands & Islands	Eleanor Scott**	Green
Lothian	Neil Findlay	Labour
	Gavin Brown*	Conservative
	Ann Henderson	Labour
	Margaret Smith*	Liberal Democrat
Scotland Central	None
Scotland Mid & Fife	Willie Rennie	Liberal Democrat
	Mark Ruskell**	Green
Scotland North East	Lewis Macdonald*	Labour
	Hugh Campbell-Adamson	Conservative
	Martin Ford	Green
Scotland South	Jim Hume*	Liberal Democrat
	Derek Brownlee*	Conservative
	Marie Rooney	Labour
	Alis Ballance	Green
Scotland West	Stuart McMillan*	Scottish National Party
	Ross Finnie*	Liberal Democrat

[* MSP at the time of the election]

[** Former MSP]

One thing to note about levelling seats is that they are not distributed evenly across the regions.

The overall result with this would be:

Party	Constituency MSPs	Regional MSPs	Total MSPs
Scottish National Party	53	8	61
Labour	15	22	37
Conservatives	3	14	17
Liberal Democrats	2	5	7
Greens	0	6	6
Independent	0	1	1