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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