Some Basic Electoral Numbers

At the last general election, Labour won 44.4% of the vote in Great Britain and that secured them 419 seats or an overall majority in the Commons of 179. In the vast majority of those constituencies where the result was marginal or even semi-marginal, the Conservatives were in second place; they won 31.4% of the vote across Great Britain, 13% behind Labour, and secured 165 seats.

Labour can afford to lose 89 (net) seats and still retain a tiny overall majority. If it loses a net 90 or more, there will be a hung Parliament unless one of the other parties has gained so many seats as to have a majority of its own. Labour's 90th most vulnerable seat is Birmingham Yardley, one of the few where the Liberal Democrats are in second place, and where Labour led the Lib Dems by 14.1% of the vote. Therefore a swing of just over 7% from Labour to the second-placed party in every constituency would deprive Mr Blair of his majority.

However, it is more usual to think in terms of a uniform swing directly from one party to another, holding support of other parties constant. Traditionally, a seat is regarded as "marginal" if the majority is less than 10% of the votes cast, in other words which would be vulnerable on a swing of 5%. If there was a uniform swing from Labour to Conservative of 5%, so that the Conservatives captured all the "Labour marginals" on this traditional definition, Labour would still have 359 seats, an overall majority of 59, and the Tories would have only 237 - that is 72 more than they won last time, but would still be one of their worst ever results.

It would need a swing almost half as big again, 7.3%, to ensure that Labour lost 90 seats. In this case the key seat would be Ayr - intriguingly, a seat that the Conservatives have already captured from Labour in a Scottish Parliament by-election, although polling in the constituency at the time showed that electors in Ayr said they would vote very differently for Westminster from their voting for Holyrood.

A national uniform swing of 7.3% is the same as cutting the Labour lead over the Conservatives by 14.6%. But that is more than Labour led by at the last election! In other words, it would be possible for the Conservatives to have a marginal lead in votes and yet Labour still have an overall majority in the Commons - anything up to a 1.6% lead would not be enough. Shades of Al Gore and George Bush! It has happened before, by the way, in 1951, when Labour had the most votes but the Tories got an overall majority. (In February 1974, as well, the "wrong" party won, but although Labour had more seats though fewer votes than the Tories, neither party had a majority and in fact it seemed possible at first that the Tories might be able to remain in office with Liberal support, until the Liberals refused to play ball.) If the parties had an equal share of the vote, Labour would still have an overall majority of 19, and the Tories would just capture Hornchurch, while just failing to capture Batley and Spen.

The next important landmark comes with a 7.6% swing. If the Tories achieve this across the country, giving them a 2.2% lead in votes and allowing them to capture Erewash in Derbyshire, they would hold 265 seats in England, a majority of the English seats. This would potentially be of significance in the argument for an English Parliament and over whether Scottish and Welsh MPs should be entitled to vote on matters that only concern England when English MPs cannot interfere with such matters in Scotland and Wales. But note that if the Tories were to do well enough to win a majority in England, they would already have deprived Tony Blair of his overall majority in the Commons.

But suppose the Tories were, contrary to most people's expectations, to do better still. A uniform swing of just under ten (9.8%) would put the Conservatives and Labour level in the Commons, with 300 seats each: the Tories become the biggest party once their lead in votes exceeds 6.6%, but Labour remain the biggest party on any lead slimmer than that. Even that, of course, would not be enough to form a Conservative government, since it would leave the Lib Dems holding the balance of power and they would presumably prefer to keep Tony Blair rather than install William Hague in Number Ten. The key seat in this case, the target that would give the Tories 301, is Warrington South. If the Tories do well enough across the country to win Warrington South, they can expect to be the biggest party in the Commons.

Finally, for a Conservative overall majority the party needs a swing of 11.5%, or a ten-point lead, which would be enough to capture Vale of Clwyd. To put this in context, Attlee's Labour government in 1945 was elected by an 11.3% swing, which of course was ten years since the previous election. Tony Blair achieved a 10.3% swing in 1997. Only one other post-war election, that of 1979, has had a swing over 5%.

But what if, as has been the case in many recent by-elections and in the European elections two years ago, Labour's voters are reluctant to turn out and so don't pull their weight? Of course that would make a difference. If Labour has a national lead of 8% in the votes, on uniform swing they win 400 seats, for a majority of 141, and the Tories less than 200. But if Labour had an 8% lead in total support, but were only 95% as successful at turning out their voters as the other parties, Labour's majority would fall to 105; at 90% comparative turnout, the majority would be 69; and if the comparative turnout fell to 75%, the Tories would have a three-point lead in votes cast and Labour would be 21 seats short of a majority.

The big flaw in this argument is that it assumes that all the parties turned out their supporters equally well last time; but this is clearly not the case. Of those who didn't vote at the last election, disproportionately high numbers would have voted Labour had they voted at all; but most of that abstention was in safe seats where it didn't matter anyway. So a degree of lower Labour turnout is already accounted for in the 1997 figures - Labour won by 13% in votes, but their "real" lead was considerably higher. This pattern of turnout being lowest in the seats where it matters least is likely to be repeated (and it can be argued that it is precisely because the mid-term by-elections and European elections don't matter to voters that they have suffered low turnouts); so for the comparative Labour turnout to fall to 75% in the key marginals, the overall figure would probably need to be a great deal lower still.

And, in the same way, uniform national swing is a big assumption and unlikely to occur in practice. We are already beginning to notice regional patterns in the data which, if reproduced at the election, would significantly alter the fall of seats and, furthermore, at most recent elections the marginals have been out of step with the rest of the country. The more the parties concentrate their campaigning in those key seats, of course, the more that is likely to recur. But that is another story.