Parliamentary Voting System and Constituencies Bill - Analysis of Boundaries

This page first posted 12 September 2010

The coalition government has introduced a Bill to change the way that constituency boundaries are drawn up and to hold a referendum on changing the voting system from first-past-the-post to the Alternative Vote scheme. This bill is called the Parliamentary Voting System and Constituencies Bill. This article analyses the impact of the proposed changes to constituency sizes and boundaries. We look at the AV system in another article.

1. Introduction and recent boundary changes

The current system of drawing up electoral boundaries in the United Kingdom has been relatively uncontroversial and has generally avoided party-political distortions. In this respect, the United Kingdom has enjoyed a more stable and less partisan method of electoral re-districting than other established democracies. The comparison with the United States, where politicians have considerable influence over constituency boundaries and where many electoral districts have convoluted shapes to achieve partisan electoral advantage, provides a useful warning.

The first change to the historic constituency boundaries was made by the Great Reform Act (formally the Representation of the People Act) of 1832. This removed the "rotten boroughs" with very small electorates and created new seats in the fast-growing cities of the industrial revolution. Even today, a review of boundaries is still needed from time to time to reflect changing population patterns. People gradually move away from unpopular areas towards more popular areas and so the Westminster constituencies need to change their boundaries to equalise their electorates.

Popular opinion worries about "sharp practice" when electoral boundaries are re-drawn, but the actual UK experience has been more benign. The work of redrawing the boundaries is done by four independent Boundary Commissions. Each nation in the country - England, Scotland, Wales and Northern Ireland - has its own Boundary Commission. Each Commission periodically draws up proposed new boundaries within its region, acting within its guiding statutes, and tries to equalise the electorate of each constituency. The Commissions also have regard to local government boundaries and try to keep each constituency within the same county, city or London borough.

The proposed boundaries are then open to discussion, comment, and counter-suggestion by the public. In practice, the main respondents are representatives of the major political parties. There can then be a local inquiry led by an Assistant Commissioner to air the issues, and then a final report will be produced. The Commissions have a generally good record of impartiality and resistance to political pressure. As an example, their decisions for West Yorkshire were successfully defended in the High Court against a challenge by Ed Balls MP and others in 2006.

Boundary Reviews currently have to take place between every 8 and 12 years. Recently there have been three major reviews:

The fifth review was accelerated in Scotland by the Labour government to reduce the number of Scottish seats from 72 to 59. This reflected the recent devolution of powers to the Scottish Parliament and partially addressed the West Lothian Question. This decision was both an example of good administration and also politically selfless, in that most of the 13 abolished seats were Labour-held.

2. Equal-sized constituencies

In an ideal world, every constituency would be of exactly equal size. However a number of factors prevent exact equality from being achieved. These include: So in practice there is an element of variation between the electorates of different seats. To think about this more clearly, it would be good to have a way of measuring this variation between seats. One way to do this is by calculating a measure of "size deviation". This is given in percentage form, where a size deviation of, for example, 10% means that the vast majority of seats have an electorate which is within 10% of the average seat size. The precise definition is given in the Appendix A below.

2.1 Size deviation at recent elections

The bar chart shows the size deviation of constituencies at various elections in the last 30 years. Elections are marked by date, possibly modified by "ob" (old boundaries) or "nb" (new boundaries) if there was a Boundary Review around that time.

We can see that the deviation increases between boundary reviews as the population shifts itself around the country. But the deviation decreases at each boundary review. For instance the 1992 election had a deviation of 20% with the old boundaries, which reduced to 14% with the new boundaries.

At the most recent election in 2010 the deviation was 12% which is relatively low. This means that most seats are within 12% of the average seat size. There has been a long-term improvement in the deviation over the review cycle.

3. Current effect of size inequality

Having seats of different sizes does introduce some unfairness into the system. We can estimate the amount of this unfairness by calculating how many seats would have been won at the recent 2010 general election if seats has been more equally sized.

3.1 Four-nation effects

Let us begin by looking at the four constituent parts of the country - England, Scotland, Wales and Northern Ireland. Each has its own Boundary Commission, which draws the boundaries for the seats within its own area. But the numbers of seats in each area are (effectively) set by Parliament and not by the Commissions. So population drift between the four areas is not compensated for at the boundary reviews, which allows inequalities to develop.

The table shows the current number of seats for each nation alongside the "fair" number of seats set in proportion to their population.

 Current SeatsPopulation-weighted
Northern Ireland1817-1

So England is under-represented at Westminster (by 2.4%), Scotland and Northern Ireland are slightly over-represented (by around 7% each) and Wales is significantly over-represented (by 20%).

An simple and effective way of reducing seat-size inequality would be to set the number of seats for each of the four regions to be in proportion to their population. Without any further modification of seats, this would have had an effect on the 2010 election result. The table below shows the changes:

PartyActual Result

The Conservatives gain around five seats and Labour lose three seats. This should be expected because the Conservatives are relatively stronger in England than in Wales, so a transfer of seats from Wales to England is beneficial to them. But Labour also win seats in England too, so the translation effect is not as large as if every Welsh seat were Labour and every English seat were Conservative.

3.2 Full seat equality

We can also calculate what the result of 2010 general election would have been if all seats were equally sized, to within the 5% maximum deviation proposed by the Bill. This would approximately equalise every seat, and also make the nations' seat numbers to be population weighted as well.

PartyActual Result

There is only a modest change of a handful of seats, equivalent to about 3 seats changing hands, compared with the Equal-Nations result above.

4. The Bill's Proposals

The Bill makes four main proposals in regard to seat boundaries and their reviews
  1. All seats' sizes to be within 5% of the average seat's electorate.
  2. Boundary Reviews must take place every 5 years, rather than within 12 years.
  3. The total number of seats be reduced from 650 to 600.
  4. Two seats: Orkney and Shetland, and Na h-Eileanan An Iar (Western Isles) be kept unchanged.

4.1 Maximum deviation of 5% in seat size

This proposal would direct the Boundary Commissions to make all seats' sizes lie within plus or minus 5% of the national average seat size. The benefits of this proposal are: The drawbacks of this proposal are: The example of island constituencies is already well known. Both the Isle of Wight (electorate 109,966) and Ynys Mon/Angelsey (electorate 50,075) are well outside the proposed permitted range of 66,705 to 73,727 voters, and would have to be partly merged with mainland seats.

But more seats would be affected by crossing county, district or borough boundaries. In London, for instance, 53 out of the current 73 seats do not lie within the 5% range, but changing that would require substantial cutting across borough boundaries, which has historically been avoided where possible.

It is not obvious that the benefits of the 5% maximum deviation rule outweigh its substantial costs.

4.2 Increasing the frequency of Boundary Reviews

This proposal would increase the frequency of Boundary Reviews. They currently happen around every 12 years and the Bill proposes to make this every 5 years. Again there are benefits and costs to this. The benefits are: The downsides are: Constant change of seat names and definitions would further weaken the bond between voters and their MP. Most voters do not keep up with the Boundary Commissions deliberations and reviews, and need time to get acquainted with new seat names and boundaries. It is possible that new seat definitions every election would reduce voter engagement and turnout and diminish their "ownership" of the electoral process.

On balance, this proposal achieves a modest benefit at a potentially large cost and is not beneficial.

4.3 Decreasing the size of the House of Commons

The proposal is to decrease the size of the House of Commons from 650 to 600 members. The arguments here are more clear cut. In favour: Arguments against: Overall this is a sensible and useful measure, even if its motivation is a little obscure.

4.4 Protecting Orkney & Shetland and the Western Isles

These are two remote Scottish seats, both of them small in electoral terms. Orkney and Shetland has an electorate of 33,085 and Na h-Eileanan An Iar (Western Isles) has an electorate of 22,266. The national average seat size is 70,216. Orkney and Shetland is about half of the correct size, and the Western Isles are less than a third of the right size.

If the Western Isles were merged with the existing adjacent seat of Ross, Skye and Lochaber then the total seat would be the correct size. The Scottish Boundary Commission has previously recommended action along these lines.

Similarly, if Orkney and Shetland were merged with the existing seat of Caithness, Sutherland and Easter Ross, then the total seat would also be about the correct size.

Currently, the Western Isles seat is held by the Scottish National Party with a 13% majority and Orkney and Shetland is strongly held by the Liberal Democrats. If the seats merged as above, the net effect would be to remove one seat from each of the SNP and the Liberal Democrats.

The idea of equality and fairness which informs the other measures of the Bill would naturally cause these two seats to be abolished and merged together with neighbouring parts of Scotland. This holds especially since other parts of the Bill allow geographical boundaries to be crossed.

There is a suspicion that the special terms granted to these seats are driven by political considerations, since it goes against the spirit of the rest of the Bill. Why should a voter on Lewis be worth three times as much as one on Skye? Why should a voter in Kirkwall or Lerwick be worth double a voter in Thurso or Wick?

5. Conclusions

On the basis of the analysis above, the conclusions on the boundary proposals in the Bill are: A future article on the proposed switch to the AV voting system will appear in due course.


A. Definition of "Size Deviation" of seats

To define this, we start by looking at the set of electorates of the vast majority of the seats. We use the 80% of the seats (currently 520 seats) closest to the average size, and discard the smallest 10% of seats and the largest 10% of seats. We do this because the very extreme seats, both large and small, are quite special and can distract attention from the behaviour of the "normal" seats.

The "size deviation" is defined to be the half-width of this set divided by the average seat size. This percentage gives a measure of the spread of seat sizes away from the average.

Example 1983: As an example, in 1983 the average seat size was 64,920 voters. The vast majority (80%) of seats had sizes between 53,612 and 74,659. The "size deviation" is equal to (74659 - 53612) / 64920 / 2 = 16.2%. So most seats are within plus or minus 16.2% of the average seat size.

Statisticians give this quantity the jargon-rich name of the semi inter-decile range.

B. Useful links

Some relevant web links: Please let us know of other links that Electoral Calculus readers might find useful.
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