It’s not all that hard to count to 331, but, as we can see above, there’s more than one way to get there.

In the aftermath of the general election, it fell to me to check the paper’s giant map of the seats won and lost across Britain on 7 May. In particular, the graphics department wanted to know how many gains – gross gains, that is: gains before losses – had actually been made, so that they could list them all around the map. Out of a total of 650 parliamentary seats, that seemed like an elementary request. Or so I thought, until I found that two reliable sources (the Guardian, top, and the BBC, above) were giving completely different figures.

To take the Conservatives as an example, both sources have them winning 331 seats in total. But the Guardian has them gaining 38 seats from other parties (and losing 10), while the BBC has them gaining 35 (and losing 11). How can that be? No wonder graphics was puzzled: I was too.

Clearly, since they imply net gains of 28 and 24 seats respectively, the two sums can’t even be working from the same base figure of constituencies held before the election. So what figures are they using? Subtracting the net gains from the total of seats now held – 331 – is an obvious place to start. That reveals that the Guardian (331 – 28) is working on a basis of 303 Conservative seats already held, while the BBC (331 – 24) is working on a basis of 307.

Hmm. Odd. Can we relate either of those two figures to data about the previous election? Time for a quick trip to the Electoral Commission’s website, where we find that … oh:

Now we have a third figure for seats won in 2010: 306. What’s going on? Can we not even agree on a figure for the number of seats the largest party in the country holds from one general election to the next?

And then, after slightly longer than one cares to admit, the light began to dawn. The clue to the Electoral Commission figure is down at the bottom of the graphic: “Speaker (1)”. The Speaker of the House of Commons is an apolitical figure who votes only in the most exceptional of circumstances; nonetheless, he or she is still notionally an MP who stands for election as a representative of one of the parties. And the current Speaker, John Bercow, is a Conservative: the Tory MP for Buckingham. So if you add him to the Conservative total, you get 307: the same as the BBC’s figure. And then it all starts to become a lot clearer.

Clearly, the BBC is using the data from the 2010 election as its basis point. So what is the Guardian using? One obvious possibility is that it is factoring in changes to the makeup of the Commons that have taken place since 2010. Can we account for the discrepancy by looking at byelection results in the last parliament?

According to parliament.uk, there were 21 byelections in the last parliament. Three of them resulted in the Conservatives losing a seat, and all three are still reasonably memorable events for political wonks: author Louise Mensch’s unexpected resignation from her seat in Corby in 2012, which resulted in a Labour win; and the high-profile defections of Douglas Carswell and Mark Reckless from the Tories to Ukip in the runup to the election, when both incumbents won their seats back under new colours.

That reduces the number of seats the Tories held in parliament from 307 to 304, which is getting closer to the Guardian’s figure. Could it be that the Guardian is simply discounting the Speaker’s seat? It seems not: the election interactive is clear that it is talking about all 650 seats in the country, not 649 as would be the case if Buckingham were excluded.

It’s only when, exploring the interactive, you discover the striking fact that ultra-safe Tory seat of Kensington is described as a “gain” that you find the last missing piece. Sir Malcolm Rifkind, the former foreign secretary and MP for Kensington, was suspended by the Conservative party, and ultimately decided not to stand for re-election, after being caught in a cash-for-access newspaper sting in February. Technically, therefore, as a sitting MP who has had the party whip withdrawn, he counted as a seat lost before the election, and therefore a Tory “gain” (from an “independent”) when his successor duly won. So the Guardian’s total, omitting Mensch, Carswell, Reckless and Rifkind, is also correct: 303.

So who’s right? In short, everyone. The BBC is working on a previous-election basis, using unmodified figures from the 2010 ballot. The Guardian is using eve-of-election figures, reflecting the actual position of the parties on the day before the country voted in 2015.

Both approaches have their strengths and weaknesses. If you work on an eve-of-election basis, you’re using running totals based on the quality of your own electoral research and arithmetic. If you work only on the official previous-election numbers, the maths is simpler, but you have to remember the “byelection factor”: some triumphant regainings of marginals lost in midterm will actually be “holds” for your purposes, and some routine victories for the winners of half-forgotten byelections actually “gains”.

If you’re wrestling with British electoral totals (and you might not be for another five years … although who knows?), here’s a table covering four of the most likely problems you may encounter (click to enlarge). As to how 2020’s calculations will go, if the major boundary changes and seat reductions planned by the Tories go through in this parliament – heaven only knows.

Tags: general election 2015, majorities, worked examples