Electoral Reform- Are The New Constituencies Fair?

Last year saw the passage of the Parliamentary Voting Systems & Constituencies Act 2011 which, among other things, reduces the House of Commons from 650 to 600 MPs at the May 2015 general election. One little thing is that the new boundaries have to be approved by the House of Commons, and there is nothing to stop them being rejected, in which case the next election would be held on the current boundaries.

When new constituencies are proposed, various people and groups draw up notional results, which are simply what the result would have been if the new boundaries were used. I will go with the ones drawn up by Electoral Calculus. Other people have other results, but with minor variations depending on how you do the calculations. There may be differences on how hyper-marginals (such as Chesterfield, Rochdale South or Workington & Keswick) end up, but no-one really disagrees that these will be the big battleground seats.

The Conservative stance is the more equally sized constituencies are fairer and are a complete electoral reform in themselves (which to me sounds like the Labour stance that removing the hereditaries from the House of Lords was a complete reform in itself and nothing further was needed).

But is this correct? First look at the vote share:

Conservative 36.97%

Labour 29.66%

Liberal Democrat 23.56%

And now the seat share:

Conservative 48.58% (307 out of 632)

Labour 40.82% (258 out of 632)

Liberal Democrat 9.02% (57 out of 632)

You're probably going to ask why, if there are 650 constituencies, I am using 632. These are the figures for Great Britain.

Incidentally, I did recently hear the wonderful sarky comment that the Liberal Democrats now have proportional representation as their support has plummeted so it now reflects their share of seats! Hmm.

We can now deduct the vote share from the seat share:

Conservative +11.61%

Labour +11.16%

Liberal Democrat -14.54%

So, as we might expect, the Conservatives and Labour get more seats than they would under a proportional system, and the Liberal Democrats get less. We can measure the disproportionality by squaring and summing the differences:

11.61 x 11.61 + 11.16 x 11.16 + 14.54 x 14.54

This gives us:

134.79 + 124.55 + 211.41 = 470.75

This is the magic number that shows how (dis)proportional a result is. In a pure proportional system it would be zero.

Now look at the seat share under the new constituencies:

Conservative 50.86% (297 out of 584)

Labour 39.56% (231 out of 584)

Liberal Democrat 8.22% (48 out of 584)

Again, ignoring the 16 Northern Ireland constituencies. A quick look implies that the new boundaries help the Conservatives and hurt Labour and the Liberal Democrats. We can, as before, deduct the vote share from the seat share:

Conservative +13.89%

Labour +9.90%

Liberal Democrat -15.34%

And, as before, measure the disproportionality by squaring and summing the differences:

13.89 x 13.89 + 9.90 x 9.90 + 15.34 x 15.34

This gives us:

192.93 + 98.01 + 235.32 = 526.26

So, the new boundaries give a more disproportional result that the current ones. However, there is another way of measuring fairness, which is to assume an even swing and equalise the votes of the two main parties. Under the current boundaries, if the Conservatives and Labour each got 33.31% of the vote, then Labour would have a lead of 53 seats- 8.15% of the total, while under the new boundaries, Labour would have a lead of 36 seats- 6.00% of the total.

Under either the current or new boundaries, if the Conservatives and Labour tie in votes, then Labour is in the lead and can form a minority Government- and indeed a Conservative/Liberal Democrat Government would be forced to form confidence and supply deals with regional parties to survive.

So we have a curious situtation- the new boundaries seem to, by one measure, favour the Conservatives, and by another favour Labour. The reason is that the Conservative seat lead is based on electoral sand.

Just do a 0.5% swing to Labour, and we see 7 seats fall to Labour. Not much, but try a 1% swing, and get the Conservatives losing 14 seats and Labour gaining 14 (with the Liberal Democrats losing 2 to Labour but balancing that with 2 gains from the Conservatives).

Noe try a 2% swing, and we see that the Conservative lead in seats has nearly vanished. The Liberal Democrats could legitimately choose to go either way.

Under the new boundaries, Labour can be 2.89% behind the Conservatives and be the largest party and needs to be 3.67% ahead to have an overall majority. Note that at this point, the Govermment has got 55.04% of the vote- a stronger endorsment of a sitting Government than even the November 1935 election- and still loses

Under the current boundaries, things are a bit better for Labour, as they can be 4.09% behind the Conservatives yet be the largest party in the House of Commons, and only needs to be only 2.77% ahead to have an overall majority.

What about the Conservatives? Under current boundaries, they need to be 10.65% ahead of Labour to have an overall majority, while under new boundaries, they need only be 7.57% ahead.

It is clear that even after equalising constituency size, the bias towards Labour that has been around for about a quarter of a century continues- reduced, but still there.