So, the Chancellors debate has been had, Easter is on the way, and the UK local government elections have already been scheduled for May 6. So unless Gordon Brown is proposing to take the British people to the polls twice in a month — and hey, any addled decision is possible in these conditions — it can be assumed we are five weeks away from the UK elections.

It would seem most likely that Brown will announce it immediately after the Easter break — unless he is so crazy as to go before (see above caveat, etc) — though technically he could go with a campaign period of as little as 16 days.

Up for grabs are 650 seats in a first-past-the-post system (down from 659, after Scotland’s haul was reduced by 13). Northern Ireland has 18 seats, Wales 40, Scotland 59 — and England a whopping 533. Of these around 200 are concentrated into the small south-east region, including London, an enormous tilt towards a single, fairly sameish region.

The Labour party holds 345 seats, the Conservatives 193, and the Lib-Dems 63, the Scottish National Party with seven, Plaid Cymru (Welsh nationalist)  with three, the Democratic Unionist Party’s eight, Sinn Fein’s five, the three from Northern Irish SDLP (moderate Catholic), and a left-wing Respect member. Then add the 10 independents plus one independent Labour and another independent conservative. Three seats are currently vacant (this is all fluid due to members being expelled, small party reps quitting and rejoining, etc).

Those figures should remind people of the reality behind some of the stonking swing figures — Labour remains by far the largest party. Their absolute majority is around 55 (it varies depending on whether you count the speaker and three deputies as voting members or not), but losing that, even by a fairly substantial drop, is far from certain to pitch them out of power.

That they will lose their majority is virtually certain. There are about 21 Labour-to-conservative seats that would change on a uniform swing of 1.5%, enough to make the non-Labor numbers slightly higher than Labour, at 321 seats to 235. But of course that is meaningless, because the chances of all parties, plus independents, getting behind the conservatives is non-existent.

At around a 3% swing, with the cut-off seat being South Ribble — chosen from among half a dozen because I like the name — Labour’s current majority ratio of 36-33% to the Tories is reversed. However, Labour would still retain its largest party status with 295 to 265 seats or thereabouts — the Conservatives however could put together a majority with the Lib-Dems that a Labour deal with the minor parties could not undo.

At about 4.25%, with the cut off being the magnificently middle of everywhere seat of Dudley South, the Tories become the largest party on 36/31% vote split, yielding around 285 seats to 275. After that every 0.5% further to the right yields another 10 to 15 seats. But it isn’t until they get to a 7% swing across the board that the Tories claim a majority in their own right, with 330 to 230 or thereabouts.

Seven per cent is a big swing — but of course swings tend to be more dramatic in FPP three-way elections, with the possibility of a split difference concentrating the mind wonderfully. Furthermore, this model assumes a simple exchange of Labour for Conservative votes, leaving the Lib-Dem vote unchanged at 22% for the sake of simplicity. (There’s a handy swing calculator here, and some good electoral mapping at The Telegraph here.)

That is quite possible if there is a double-shift — disgusted leftish Labour voters going to the Lib-Dems, while other Lib-Dems move onto the Tories, thus keeping the vote the same while recycling its constituent voters.

When you plug the numbers in any way other than a Lib-Dem static vote, but retain a 7% swing, then the Tory majority evaporates. If the Lib-Dems lose 2% of their 22.5% vote for a 7% swing making the Tory/Labour/LD vote 40/31/20.5, then it comes out around 315/255/50 seats, leaving the Tories 10 seats short of a majority.

Conversely if the Lib-Dems did better, gaining 24% of the vote for a 38/29/24 split, it would see them gaining only around 305-310 seats, a good 15-20 shy of a majority.

You have to start plugging in some pretty big numbers, swinging the Tories into a 43-44% vote share before they start to really get a 60-0 majority on these figures. That’s the 10% swing they’d get if the current upper-limit polls are correct — but it’s been a long time since they’ve gone higher than 10%.

At those sort of figures, the crudity of the model being applied doesn’t matter — the Tories would have a working majority. But in any situation that suggests a majority around 10 or so, or a hung parliament, and two types of questions start to intervene.

The first is how useful a simple zero-sum model is of a three-way party split, when that has to cover a multiplicity of different circumstances and, also at some point, acknowledge the degree to which a three-way race generates insoluble complexity. The second factor to bring into consideration is the particular way in which a swing from to or from the third party breaks.

For example, the Lib-Dems have a stronghold in Cornwall, Devon and parts of the West Country — as well as in select major urban contituencies. In the west they’re really pseudo-Tories — a party that developed out of local non-conformist church traditions, in the absence of major industrial development. In urban areas, they simply represent the Left at the electoral level — especially when issues like Iraq and civil liberties come to the floor. Not only is this a nightmare for the party leaders, it means there is no easy way to summarise voter shift across the country — as one can do, for example, with the 2-3% of votes that slide back and forth between Labor and the Greens in Australia.

For anyone with any spark in them, one hoped-for result is obvious. Realistically speaking there will be a 6-8% swing away from Labour. If 2% of it goes to the Lib-Dems, and if it is deep enough in individual places to get an extra person from Cymru, Respect, the Greens in Brighton, or one of the independents up, then there is the prospect the Tories could get close enough to a majority to be able to put one together with selected minor parties, leaving the Lib-Dems out of it.

Alternatively, if Labour fell short but not fatally so, it might only be able to put together a majority with the Lib-Dems and selected other minor parties. One among several scenarios we’ll examine tomorrow…