The BBC has just published an article explaining its controversial claim that the SNP actually lost seats at last week’s council elections, despite going from 425 to 431. The analysis was carried out by Prof. David Denver of Lancaster University, and we’d asked him about it yesterday.

He’d very kindly sent us a copy of the same article he’d sent the Beeb. We attach it below. We’ve highlighted in bold the only bits that didn’t make it into the BBC piece.

When the boundaries of Parliamentary constituencies change, it is clearly vital for analysts to have an idea of what the results of the previous election would have been had the new boundaries been in force and had people voted exactly as they did in their old constituencies.

There is a well-established way of doing this.

Since constituencies are made up of wards we can redistribute votes in old constituencies to newly-created ones making use of local election results. I have done this for Scottish constituencies after every boundary revision since 1980.

This year, I had a go at doing the same for Scottish wards for which new boundaries came into force in 2017. The problem is, of course, that there are no smaller divisions of wards for which we have voting figures which could be re-assembled in to the new wards.

Of the 354 new wards created, 151 were unchanged as compared with 2012, 34 had very small changes and 68 had what I defined as ‘minor’ changes – involving up to 10% of the electorate.

For these, the only differences between actual and notional results registered were if the number of councillors to be elected changed.

If the number declined by 1 then the last candidate to be elected in 2012 was deducted; if the number increased then the next candidate who would have been elected was added. Published detailed breakdowns of the various count stages allow this to be done.

For wards which experienced a ‘major’ change (10-30% of electorate involved) or could be described as ‘new’, I scrutinised maps of the old and new wards to ascertain which parts of old wards made up the new.

I then transferred votes proportionately from the old to the new (and sometimes using local knowledge and past experience of local elections) to get an estimate of how things would have worked out in the latter.

This is certainly a rough and ready way of doing things but there doesn’t appear to be any alternative.

The overall result of this exercise was as follows:

Actual seats/Notional seats

Con 115/112

Lab 394/395

LibDem 71/70

SNP 424/438

Ind 201/194

Green 14/14

Other 4/4

Total 1223/1227

The SNP increase of 14 is largely explained by increases in the number of councillors to be elected. In five councils (Aberdeen, Aberdeenshire, Edinburgh, Glasgow, North Ayrshire, and North Lanarkshire) my estimates gave the SNP 16 extra seats compared to the actual 2012 results – but there was an increase of 25 in the number of seats available in these council areas.