Everyone knows that First Past the Post favours the largest party. At the last Westminster election, Labour managed to turn 34% of the vote into 63% of parliament – a full 29 percentage points more. Thankfully we don’t use this system in Holyrood, but even here the largest party still gets an uplift. In 2011, for instance, the SNP won 54% of the Scottish parliament on 44% of the vote – 10 percentage points more.

The Scottish Parliament is made up of constituency MPs elected under First Past the Post, and regional ‘additional’ members that are supposed to even out the distortions of the constituency results. So why does the Holyrood system still tend to favour larger parties?

After the 2011 Scottish election Professor Sir John Curtice and Dr Martin Steven looked at the results for our report The 2011 Scottish Parliament election In-depth. They found that there are three key features of the system that give rise to this tendency:

A regional, rather than a national, system of proportional representation

Scotland’s 56 additional members are not allocated in proportion to each party’s share of the list vote across the country as a whole. Rather, they are allocated separately in each of eight regions. The typical region contains nine constituency seats and seven regional ones. As a result, a party needs to win just over 1/17th of the vote, or 5.9%, in a region to be sure of winning a seat – and in practice is certainly likely to require more than 5%. Parties that cannot pass this de facto threshold remain unrepresented, leaving more seats to be allocated to other larger parties.

For example, in 2011, both the Liberal Democrats and the Greens struggled to win seats. In winning just over 5% of the vote the Liberal Democrats only managed to secure representation in four regions, leaving their vote elsewhere unrepresented. With only 4.4% of the vote this fate befell the Greens in six regions. Together with the fact that apart from the independent candidate, Margo MacDonald, in Lothian, none of the smaller parties or independent candidates managed to win any seats, despite collectively winning nearly 8% of the list vote across Scotland as a whole, a significant body of votes did not contribute to the election of any candidate, thereby leaving more seats to be allocated to larger parties including, not least, the SNP.

There are too many First Past the Post seats

Additional seats account for fewer than half the seats in all regions. As a result, if a party is particularly successful in winning constituency seats there may be insufficient additional seats for it to be possible to correct fully the disproportionality created by the outcome in the constituencies.

In the Lothians region in 2011, the SNP won eight of the nine constituency seats – and thus half of all the seats in the region – despite winning just over 39% of the list vote. Its proportionate entitlement was seven seats. The ‘extra’ SNP seat would otherwise have been won by the Liberal Democrats who, as a result, failed to secure any representation in the region.

The d’Hondt method favours larger parties

The regional seats are distributed using the d’Hondt method. This method tends to favour larger parties, making it particularly difficult for a party to win its first seat. Alternative methods are available that do not have this property. In particular, the Sainte-Laguë method treats both large and smaller parties equally.

The use of the d’Hondt system clearly favoured the larger parties and made it more difficult for smaller parties to secure representation. Taking the West of Scotland region as an example, both Labour and the SNP would have won one seat less, while both the Liberal Democrats and the Greens would have secured a seat instead of being left without any representation.

West of Scotland Region

For the sake of clarity, votes for smaller parties have been excluded.

Forming a more perfect parliament

Put together, each of these features played some role in generating the disproportionality in 2011. No electoral arrangement is perfect, and if there are improvements to be made, we should not be afraid to make them. While a full upgrade to the ERS’ prefered system, the Single Transferable Vote, is one option. Improvements can be made to the current system by changing the balance of seats, electing members nationally, or using a fairer voting formula. Either way, Scotland should look again at how its parliament is elected. Further reform would help make Holyrood more democratic, more representative, and better able to serve everyone in Scotland.

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Scotland’s Parliament has always been better at representing the political makeup of Scotland than Westminster. A parliament where votes mattered more, where power was shared, and where the political map reflected how people actually voted.

The regional list system is the way this happens. It balances out the warping effect of the constituency results and corrects the unfairness. But the way we count those regional votes matters just as much as the fact we have them.

Right now, Scotland uses the D’Hondt method to allocate regional seats. There is another option, Sainte-Laguë, that would do a better job of matching seats to votes. For the voter, the process would be exactly the same as it is now, but the results would be a better match to how Scotland voted.

How D’Hondt and Sainte-Laguë work

Named after their inventors, D’Hondt and Sainte-Laguë are ways of sharing out seats between parties. Each region elects a group of representatives. To decide who they are, they count up how many votes each party gets and the party with the most votes gets the first seat. Each time a party wins a seat, its total number of votes is divided by a number. The party with the biggest remaining number gets the next seat, and the process repeats.

The difference is the number we divide by. With D’Hondt, we divide by 1, then 2, then 3, and so on. This means big parties stay near the front of the queue for longer. With Sainte-Laguë, we divide by 1, then 3, then 5, then 7. That gives smaller parties a fairer chance.

D’Hondt’s method favours the biggest parties

While D’Hondt’s method is far fairer than First Past the Post, in practice, D’Hondt often over-rewards parties that have already done well in constituencies. That weakens the purpose of the regional seats, which are meant to balance things out.

You can see this clearly in Scottish Parliament history. In 2011, the SNP won a slim majority on 44% of the vote. That result was driven by constituency success, but D’Hondt limited how much the regional list could correct the imbalance. 

What Sainte-Laguë would change

A change to Sainte-Laguë’s method would spread seats more evenly and makes sure regional votes do what voters expect them to do. Countries like Norway, Sweden and New Zealand use Sainte-Laguë or close versions of it. These are stable democracies with strong parliaments and high public trust.

Sainte-Laguë would mean that the regional lists would do a better job at balancing out the distorting effect of the first Past the Post constituencies, and reduce the gap between the vote share and seat share of the bigger parties.

In 2011, polling expert Professor Sir John Curtice looked at what happened in the West of Scotland region, and what could have happened if we had used Sainte-Lague.

Source: The 2011 Scottish Parliament election In-depth Prof John Curtice & Dr Martin Steven. For the sake of clarity, votes for smaller parties have been excluded.

A small change with a big impact

This is not a radical redesign. It is a technical fix that honours the spirit of devolution.

Scotland chose a proportional parliament because it wanted cooperation, diversity and fairness. The Sainte-Laguë method fits that vision better than D’Hondt ever has.

If we care about making every vote count, we should care about how we count them.

Sometimes democracy improves not through grand reforms, but through getting the details right.

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When choosing a proportional voting system, one of the most important decisions is the number of MPs each constituency elects – its ‘district magnitude’. For example, rather than having three constituencies in Lewisham as we do now (Lewisham Deptford, Lewisham East and Lewisham West and Penge) each electing one MP each, under a proportional system you might have one constituency that covers all of Lewisham, but elects 3 MPs.

Whether you decide to make a Lewisham seat that elects 3 MPs or an Inner South London seat that elects 12, can affect everything from the overall proportionality of the elections to the relationship between MPs and their constituents.

But it is a game of trade-offs – larger constituencies mean more proportional results, but necessarily cover a larger geographic area and have been accused of being more distant from voters. So, what is the ideal constituency size and is there a perfect balance between proportionality and localness?

What is the ideal number of MPs per constituency?

Within European countries that use proportional representation, there is a fair bit of variation in terms of what size a constituency is. At the smaller end are Austria (median constituency = 4 seats), Spain (5), Switzerland (5.5) and the countries that use STV – Ireland (4) and Malta (5). Those with larger constituencies include Belgium (15), Finland (16) and Latvia (14).

Then there is the Netherlands that eschews constituencies entirely in favour of a single nationwide allocation of seats and the countries that use mixed-member systems, like Germany and Italy, which combine single-member constituencies with overlapping multi-member regions. But overall, most European countries have an average constituency size of between 4 and 15 seats.

The impact of constituency size on proportionality

The general rule with proportionality and constituency size is ‘the smaller the constituency, the less proportional the results’. This is largely due to smaller constituencies raising the effective threshold at which a party can win a seat, leading to more seats going to larger parties. You need a smaller share of the vote to win one of ten seats, than one of three.

But the relationship isn’t as simple as one extra MP means one extra unit of proportionality. To demonstrate this, I’ve projected every general election since 1997 onto several schemes of Party List PR – Micro (2-3), STV-size (3-6), Sub-county (3-12), County (6-20), Sub-regions (16-30) and Regions or Nations (18-84) – and averaged the results.

What’s most apparent is how non-linear the trade-off is between proportionality and constituency size. Even relatively small STV-size constituencies yield a significant level of proportionality for fairly little loss of localness. And once you go beyond an average constituency size of around 10, the improvements in proportionality become increasingly limited compared to a constituency’s continually increasing geographic area.

As the chart shows, the relationship between proportionality and constituency size is also intertwined with different electoral formulae. Choosing Sainte-Laguë over D’Hondt, for instance, allows you to have much smaller constituencies for the same level of proportionality.

Impact of variation of constituency size

But it isn’t just average constituency size that matters, it is also the range in size. And range varies from uniformity in Malta (all 5 member) and Croatia (all 14), through small variances in Ireland (3-5) or Iceland (7-11), to significant variation in Finland (7-36) and Portugal (2-48). The problem with high levels of variation is that it creates inequality between different areas, as it is easier to win seats in larger constituencies than in smaller ones.

This is compounded by the fact that larger constituencies are almost always big cities – meaning that small parties with an urban support base can be at an advantage compared to a similarly supported party with a largely rural votership.

But uniformity isn’t necessarily the answer either. Variably sized constituencies are able to coincide with ‘natural’ political communities (cities, counties, states, etc.) and are usually permanent (with the number of MPs they elect being refreshed every few years).

Constituencies of equal numbers of MPs are much less flexible – with boundaries having to be regularly redrawn, often with ‘natural’ political communities being split or unrelated ones merged to stay within population quotas. Generally, it is preferable to have at least some level of variation in constituency size, within certain parameters.

Strengthening the constituency link

The opposite end of the pole to proportionality is the MP-constituency link and there is always the concern by some that any increase to the size of constituencies will weaken that link. It is undoubtedly true that constituencies under any PR system will be larger in area and have a greater population than single-member districts, although the ratio of MPs to voters stays the same.

It is always worth noting that under most versions of PR proposed for Britain, every constituency outside of the Scottish Highlands would be smaller in area than the largest current constituency (Ross, Skye and Lochaber).

Internationally, the link between an MP and their constituents is hard to compare because it depends so much on national political culture. However, the evidence generally suggests that constituency work is highest in countries that have a combination of small constituencies and voting systems that emphasise individuals, such as Open List PR or the Single Transferable Vote. This has been particularly true with the latter – one study even finding that backbench Irish TDs did a bit more constituency work than their British counterparts.

Having a group of MPs that actually represent the voters can produce a stronger constituency link, than having a single MP only a minority voted for.

A 2011 paper by John Carey and Simon Hix that found that the ‘electoral sweet spot’ is an average district magnitude of between four and eight. There you achieve a relatively high level of proportionality without sacrificing much in the way of local representation.

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Looking at just Party List systems in western Europe, there is a lot of variation. We can see constituencies vary from four- or five-member districts to single nationwide constituencies, there are some countries that impose electoral thresholds and some where you vote for individuals as well as parties. But one of the most significant differences, is also the least visible – the equations that decide how the seats are actually allocated to the parties. So, just how do these electoral formulas work?

The D’Hondt Method

The most common electoral formula is the D’Hondt method (called the Jefferson method in the USA), which is used to elect many of Europe’s national parliaments as well as the regional seats in Scotland and Wales. Counting takes place in rounds, with the party with the highest total in each round winning the seat. D’Hondt works by dividing the number of votes cast for each party by the number of seats they have already won, plus one – so that after a party has won one seat their votes are divided by two, after they have won two seats their votes are divided by three, and so on. To get a look at how D’Hondt works, let’s apply it to the votes cast in Nottinghamshire at the last general election.

D’Hondt, Nottinghamshire 2019

Rounds	Con 258,794	Lab 204,011	LD 33,604	Brexit 15,728	Ash Ind 13,498	Green 10,375	Others 9,743	Running Total
1	258,794	204,011	33,604	15,728	13,498	10,375	9,743	+1 Con 🔵
2	129,397	204,011	33,604	15,728	13,498	10,375	9,743	+1 Lab 🔴🔵
3	129,397	102,006	33,604	15,728	13,498	10,375	9,743	+1 Con 🔵🔴🔵
4	86,265	102,006	33,604	15,728	13,498	10,375	9,743	+1 Lab 🔴🔵🔴🔵
5	86,265	68,004	33,604	15,728	13,498	10,375	9,743	+1 Con 🔵🔴🔵🔴🔵
6	64,699	68,004	33,604	15,728	13,498	10,375	9,743	+1 Lab 🔴🔵🔴🔵🔴🔵
7	64,699	51,003	33,604	15,728	13,498	10,375	9,743	+1 Con 🔵🔴🔵🔴🔵🔴 🔵
8	51,759	51,003	33,604	15,728	13,498	10,375	9,743	+1 Con 🔵🔵🔴🔵🔴🔵 🔴🔵
9	43,132	51,003	33,604	15,728	13,498	10,375	9,743	+1 Lab 🔴🔵🔵🔴🔵🔴 🔵🔴🔵
10	43,132	40,802	33,604	15,728	13,498	10,375	9,743	+1 Con 🔵🔴🔵🔵🔴🔵 🔴🔵🔴🔵
11	36,971	40,802	33,604	15,728	13,498	10,375	9,743	+1 Lab 🔴🔵🔴🔵🔵🔴 🔵🔴🔵🔴🔵
Elected	6	5

As the party with the most votes, the Conservatives would take the first seat. In the second round, the Conservative’s original vote tally has been divided by two (they have 1 seat, plus 1), Labour now has the highest tally so they win a seat. In the third round, Labour’s original votes are also now divided by two (they have 1 seat, plus 1) so the Conservatives return to having the highest total and take a second seat. In the next round, their original tally is divided by three (their 2 seats, plus one). This continues until all the seats are filled, with the Conservatives winning six seats and Labour five.

The Sainte-Laguë Method

D’Hondt’s biggest competitor is the Sainte-Laguë method, used in countries such as Germany, New Zealand and Sweden. Sainte-Laguë works in much the same way as D’Hondt, though the votes are divided by twice the number of seats won, plus one. This has the effect of slightly improving proportionality between parties and being more favourable to smaller parties. Applying Sainte-Laguë to Nottinghamshire would allow the Liberal Democrats to take a seat at the expense of Labour.

Table B: Sainte-Laguë, Nottinghamshire 2019

Rounds	Con 258,794	Lab 204,011	LD 33,604	Brexit 15,728	Ash Ind 13,498	Green 10,375	Others 9,743	Running Total
1	258,794	204,011	33,604	15,728	13,498	10,375	9,743	+1 Con 🔵
2	86,265	204,011	33,604	15,728	13,498	10,375	9,743	+1 Lab 🔴🔵
3	86,265	68,004	33,604	15,728	13,498	10,375	9,743	+1 Con 🔵🔴🔵
4	51,759	68,004	33,604	15,728	13,498	10,375	9,743	+1 Lab 🔴🔵🔴🔵
5	51,759	40,802	33,604	15,728	13,498	10,375	9,743	+1 Con 🔵🔴🔵🔴🔵
6	36,971	40,802	33,604	15,728	13,498	10,375	9,743	+1 Lab 🔴🔵🔴🔵🔴🔵
7	36,971	29,144	33,604	15,728	13,498	10,375	9,743	+1 Con 🔵🔴🔵🔴🔵🔴 🔵
8	28,755	29,144	33,604	15,728	13,498	10,375	9,743	+ 1 LD 🟠🔵🔴🔵🔴🔵 🔴🔵
9	28,755	29,144	11,201	15,728	13,498	10,375	9,743	+1 Lab 🔴🟠🔵🔴🔵🔴 🔵🔴🔵
10	28,755	22,668	11,201	15,728	13,498	10,375	9,743	+1 Con 🔵🔴🟠🔵🔴🔵 🔴🔵🔴🔵
11	23,527	22,668	11,201	15,728	13,498	10,375	9,743	+1 Con 🔵🔵🔴🟠🔵🔴 🔵🔴🔵🔴🔵
Elected	6	4	1

With the most votes, the Conservative win the first seat. In the second round, their original total has been divided by three (Double their seat count, plus one), and Labour now has the highest total and wins the next seat. This process continues until all the seats are full.

Comparing the Formulas

	Votes	% Vote	FPTP Seats		D’Hondt Seats		Sainte-Laguë Seats
Conservative	258,794	47.4%	8	72.7%	6	54.5%	6	54.5%
Labour	204,011	37.4%	3	27.3%	5	45.5%	4	36.4%
Liberal Democrat	33,604	6.2%					1	9.1%
Brexit Party	15,728	2.9%
Ashfield Independents	13,498	2.5%
Green Party	10,375	1.9%
Others	9,743	1.8%

With Nottinghamshire, both electoral formulas produce different results but are, unsurprisingly, all more proportional than the actual First Past the Post result. However, different allocations aren’t guaranteed and, if we applied the same process to Cheshire, we would get the same results under both formulas.

The differences between the formulas are heightened when you have smaller constituencies and the differences that do appear add up across the country. Sainte-Laguë usually produces the most proportional results and D’Hondt is slightly less proportional on account of a moderate bias towards larger parties, though it is still vastly more proportional than FPTP.

Just as every electoral system is a compromise between proportionality, voter choice and local representation, there is no simple way to declare one electoral formula the best. But they all are an improvement on Westminster’s broken First Past the Post system.

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