The article on this page examines the causes of the gap by consideration of the likely electoral geography at the next general election under the new boundaries.

- Observing the Gap
- Constituency sizes
- Differential Turnout
- Support Distributions
- Tactical Voting
- Conclusions

The following table shows clearly the existence and extent of the electoral gap between Labour and the Conservatives. The table varies the Con and Lab support figures around that. central case, keeping the LibDem support constant.

Con-Lab % | Con % | Lab % | Con Seats | Lab Seats | Con-Lab Seats |
---|---|---|---|---|---|

-10 | 29.88 | 39.88 | 177 | 388 | -211 |

-9 | 30.38 | 39.38 | 180 | 387 | -207 |

-8 | 30.88 | 38.88 | 182 | 387 | -205 |

-7 | 31.38 | 38.38 | 189 | 381 | -192 |

-6 | 31.88 | 37.88 | 196 | 375 | -179 |

-5 | 32.38 | 37.38 | 201 | 371 | -170 |

-4 | 32.88 | 36.88 | 214 | 359 | -145 |

-3 | 33.38 | 36.38 | 220 | 353 | -133 |

-2 | 33.88 | 35.88 | 227 | 346 | -119 |

-1 | 34.38 | 35.38 | 235 | 336 | -101 |

0 | 34.88 | 34.88 | 240 | 330 | -90 |

1 | 35.38 | 34.38 | 249 | 321 | -72 |

2 | 35.88 | 33.88 | 253 | 315 | -62 |

3 | 36.38 | 33.38 | 268 | 301 | -33 |

4 | 36.88 | 32.88 | 276 | 292 | -16 |

5 | 37.38 | 32.38 | 287 | 279 | 8 |

6 | 37.88 | 31.88 | 296 | 270 | 26 |

7 | 38.38 | 31.38 | 305 | 262 | 43 |

8 | 38.88 | 30.88 | 317 | 251 | 66 |

9 | 39.38 | 30.38 | 335 | 234 | 101 |

10 | 39.88 | 29.88 | 351 | 219 | 132 |

The columns of the table are:
### Useful rule-of-thumb

From the table's data, we can also get a useful approximation rule.
Each 1% change in the Con-Lab% difference is worth about 17 seats in the Con-Lab seat difference.

- The first column "Con-Lab %" is the lead (positive or negative) of the Conservatives over Labour in opinion poll terms.
- The next two columns are the supposed percentage support figures for both Con and Lab in that scenario.
- The next two columns, "Con Seats" and "Lab Seats", are the predicted number of seats won by each major party in the scenario.
- The last column, "Con-Lab Seats", is the difference in seats between the two parties.

The rows of the table are coloured red or blue according to the largest party. If the party has an absolute majority (326 seats or more), the colour has a darker hue.

We will use this *gearing* of 17 later.

We can confirm some key facts.

- Labour has a majority up to a Con-Lab% difference of zero.
- Conservative majority starts from a Con-Lab% difference of nine.
- The equal-seats point is around a Con-Lab% difference of five (precisely 4.9%)
- Around 4% on either side of the equal-seats point is a hung parliament

The motivation for the three parties in the next election is clear. Labour need to be in the darker-red area, which means doing at least as well as the Conservatives. The Conservatives need the darker-blue area, which needs about a 9% lead in the opinion polls. The Liberal Democrats would like a hung parliament, and would like the Conservatives to lead Labour by around 5% or so.

In one sense the electoral landscape is symmetric. There is a 4% buffer zone on either side of the equal-seats point. Beyond that zone, each major party can enjoy a parliamentary majority. But the equal-seats point is not symmetric. We would expect it to be at 0%, but instead it is at 4.9%. This is the "gap" that we have observed, and now have to explain.

The number of seats in Scotland is now controlled by the Boundary Commission for Scotland, but the Scotland Act 1998 requires them to make seats with the same average electorate as England. In its fifth report in 2004, it calculated the quota number of Scottish seats at 57, but nevertheless produced 59 in practice. The small seats of Orkney and Shetland, and Na h-Eileanan An Iar (Western Isles) contributed to the discrepancy.

Although the number of seats in Wales is set by the Parliamentary Constituencies Act 1986 to be at least 35 (which is now slightly too high), the rules also require the Boundary Commission for Wales to keep the number of seats approximately unchanged. In its fifth report (2005), the Boundary Commission for Wales kept the number of seats unchanged at 40.

Secondly, the Boundary Commission for England has to work with the electorates as at 2000. In the years since then, we would expect continued poplulation drift away from poorer (Labour) areas towards richer (Conservative) areas. This also over-represents Labour voters slightly.

Thirdly, it is not possible to have seats exactly equal, given that seats are made up of entire local election wards, and that some regard should be given to county, historic and natural boundaries.

We can estimate how much this over-representation is worth. Working with our base case of Con and Lab equal at 34.88%, we can weight each seat by its own electorate and count how many weighted seats each party wins. This alters the Con-Lab seat difference from -90 to -78, implying that uneven constituency sizes are worth 12 seats to Labour. Using our gearing of 17, we can think of this as about 0.7% of the total gap of 4.9%.

This is a major effect, but it has already been allowed for by the pollsters. They try to restrict their sampling to those most likely to vote. So non-voting Labour supporters will be ignored both by the opinion polls and (automatically) by the general election. So we should be comparing like-with-like and differential turnout will not matter. But the Boundary Commissions, rightly, do not ignore non-voters and they draw the seat boundaries to ensure equal numbers of electors in each seat, not equal numbers of actual voters. This means, rather elegantly, that Labour non-voters are represented as long as they live in a seat with a lot of Labour supporters anyway. However, it does also mean that safe Labour seats will contribute less than they should to the measured national support figures, and thus cause some "gap".

We can estimate how much gap is caused by this effect. We do this by estimating how many
votes would be cast for each party if the turnout in each seat was identical. Our formula for this is

where

to ensure an equal turnout of 80% in each seat. We can then calculate the national support figures by adding up the adjusted votes

This effect is legitimate. Labour is strongly handicapped by the failure of many of its supporters to vote, and this effect is a much smaller move in the other direction. This part of the gap is a direct consequence of the principle of having seats with equal electorates rather than equal turnouts. It is hard to argue with that principle, though it does result in safe Labour MPs being elected with fewer votes than equally safe Conservative MPs.

Compared to the total gap of 4.9%, we see that this effect (1.8% gap) plus the uneven constituency sizes (0.7% gap) accounts for about half the total gap. We can check this calculation intuitively by taking a simple average of each party's percentage support over all the seats (instead of adding up all the votes cast for the party). This gives a Labour lead of 2.46%, which is again about half the gap.

Here are two extreme examples for a party which has 35% support nationally. There are 632 seats (excluding Northern Ireland).

**1. Strong case** Suppose the party has 45% support in 492 seats, and 0% support in 140 seats. This has the correct
average of ( 45% x 492 + 0% x 140 ) / 632 = 35%. Usually 45% support in any seat is sufficient to win, so
the party will win about 492 seats and have a landslide majority of 334.

**2. Weak case** Instead, suppose the party has 30% support in 587 seats and 100% support in 45 seats. This also has the
correct national average of ( 30% x 587 + 100% x 45 ) / 632 = 35%. In a three-party system, 30% support in any seat
will always lose, so the party will win just 45 seats.

For those familiar with second moments of distributions, it is interesting to note that the standard deviations of these two distributions are almost identical. So the two distributions are equal in both first and second moment, but have completely different electoral outcomes.

We now work with a base case which has been adjusted for the effects of uneven constituency size and for
differential turnout. We do this by applying the explained gap of 2.46%, to give national support figures of
Con 36.11% and Lab 33.65%. This has the effect of ensuring that the average *percentage* support
in each constituency is 34.9% for both parties. The seat gap is now 49 which, as expected, is about half the
original seat gap of 90.

The histogram shows the distribution across seats of support for
both the Conservatives and Labour at this adjusted base case.
For instance, the peak of 110 for Labour at 45% means that there are
110 seats in which Labour's support is between 40% and 45%. Of those, all but 8 were seats which Labour won.

Thinking about the two extreme cases above, let us consider whether the parties have a relatively "weak" or "strong" distribution. The Conservatives have more seats than Labour in the weak area of 25%-35%. These seats are bad for the Conservatives because they "use up" many votes in seats which they do not win. Conversely Labour has more seats than the Conservatives in the strong area of 40%-45%. These seats are good for Labour because they can win the seat without spending too many votes. Both of these effects are good for Labour and bad for the Conservatives.

On the other hand, the Conservatives have more seats than Labour in the slightly strong areas of 50%-55%. Labour also "wastes" some votes in very safe seats with 60%-70% support. These effects are bad for Labour and good for the Conservatives.

We need to quantify these effects so that we can determine which are more important. We can look at the means and standard deviations of the distributions, but we do not expect this to reveal very much. Another simple measure is just to count how many seats have support above, say, 40% (marginal seat), 45% (winnable seat), or 50% (safe seat).

Party | Mean | Std dev | Num seats above 40% | Num seats above 45% | Num seats above 50% |
---|---|---|---|---|---|

Con | 34.86% | 13.2% | 336 | 256 | 183 |

Lab | 34.79% | 13.6% | 354 | 266 | 156 |

Con-Lab | 0.07% | -0.4% | -18 | -10 | 27 |

The table shows the relevant statistics for the two parties, as well as the difference. The surprising result is that the distributions are very similar. The means and standard deviations are very close, but even the number of marginal, winnable and safe seats are similar compared with the remaining gap of 49 seats. Labour lead by 10 seats over winnable or safer seats, so they have a slightly more favourable support distribution.

The main difference appears, not in the distribution, but in the number of seats won. Labour has been much more successful at winning the borderline seats in the 40% bucket, where it has won nearly half the possible seats. The Conservatives only win about one sixth of their possible seats.

The following two charts show all the marginal Conservative and Labour seats respectively. The result of each seat is shown as a column of 100% of all votes divided up into Con, Lab, LibDem and the rest (Nat, Min and Oth). The winning party is highlighted in a bolder hue.

And for the 88 Labour marginals:

We can see clearly that the Conservatives do not win many of their marginal seats, but Labour win quite a few of theirs. At first glance, it is hard to see any particular reason why this is. Looking more closely we see that Labour often win when the LibDems have good support, and the non-Labour vote is split. In Conservative seats, the non-Conservative vote is less often split, so the Conservatives usually lose. This suggests that tactical voting against the Conservatives may be taking place.

An informative statistic is that in the 18 Conservative marginal seats, where Labour was third, the Labour vote averaged just 12.04% and the Conservatives only won 2 of those seats. But in the 16 Labour marginal seats, where the Conservatives were third, the Conservative vote averaged 17.81% and Labour won 13 of the seats. It appears as if Labour supporters are quite ready, if Labour is trailing, to vote tactically to support the Lib Dems against the Conservatives. But Conservatives are less inclined to vote Lib Dem to stop Labour. So tactical voting by Labour supporters could be worth about 10 seats of the gap. Testing with a tactical unwind of 5% for third-placed Labour supporters in the election simulator confirms a change of 9 seats in the gap.

It is hard to estimate the amount of Lib Dem tactical voting against the Conservatives, if any. Speculatively, we attach a 1% tactical vote by third-placed Lib Dems in favour of Labour. This is partly a matter of judgement, though there is some weak numerial evidence. (The average support for third-placed Lib Dem candidates in Conservative marginals is about 1% less than that in Labour marginals.) The tactical voting feature of the election simulator values this gap effect at 16 seats.

Cause | Seat gap | Support gap % | Comment |
---|---|---|---|

Uneven seat sizes | 12 | 0.7% | Scotland and Wales are over-represented |

Differential turnout | 33 | 1.8% | Labour supporters don't vote in (safer) seats |

Support distribution | 10 | 0.5% | Differences in clustering of supporters |

Tactical voting by Labour supporters | 10 | 0.5% | Labour supporters vote LibDem over Con |

Tactical voting by Lib Dem supporters | 16 | 1.0% | LibDem supporters vote Lab over Con |

Total | 81 | 4.5% |

So we see that most of the gap has been explained. There is no single cause, but the two biggest effects are differential Labour turnout and tactical voting. In terms of the fairness or legitimacy of each of these effects, the following comments could be made:

**Uneven seat sizes**. The over-representation of Scotland and Wales seems not to be justified, especially since both of them now enjoy devolved government.**Differential turnout**. This follows from the principle of equal numbers of electors in each seat, whether they vote or not. So Labour seats often have a smaller number of voters who turnout, thus electing an MP with fewer votes than elsewhere. This is quite legitimate.**Support distribution**. This is probably due to luck, and it is a small effect which is not obviously driven by any systematic factor.**Tactical voting**. This is the concern of individual voters who make their own choices.

Looking forward to the next election, we can confidently assume that the uneven seat sizes and differential turnout will continue to operate. The support distribution might change, but it is a small effect anyway. But tactical voting could alter significantly between the 2005 election and the next one. If public sentiment switches from wanting to "keep the Tories out" to either neutrality or even a desire to punish Labour, then perhaps a third of the 90 seat gap could disappear.

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