Notional results

Computing notional results is a useful technique for comparing two FPTP elections with each other. The problem it is trying to solve is that it’s really hard to do a meaningful comparison when the boundaries change, so psephologists calculate the notional results of the last election to have something to hold the new one up against.

So notional results basically means “this is what we think would have happened last time if the new boundaries had already been in place back then”.

Calculating accurate notional results isn’t really possible because we don’t know what each voter actually would have done if the boundaries had been different – it ignores tactical voting, for instance. However, for parliamentary elections they’re normally decent, because we tend to have access to the results on a ward basis. For instance, if Barrhead ward gets transferred from East Renfreshire to Paisley in a boundary change, we can subtract the ward figures from the former and add them to the latter and get a decent result.

So far, so good. Calculating notional results in local elections is much harder, however, because we don’t have access to any breakdown of the smaller areas. Furthermore, the STV voting system makes it even harder because the ballot papers are so different – how can you know what a voter would vote in a constituency with one SNP and one Green even if you knew what they voted in one with two SNP candidates?

As an example, if I had to calculate to 2012 notional results for my local ward, Newton Mearns North and Neilston, I would start with the closest 2012 equivalent, Neilston, Uplawmoor and Newton Mearns North, which elected four members last time. Here’s a graph of what happened:

So one Tory got elected easily in the first round. It then took the elimination of one SNP candidate to get the other one elected. Once the Green got eliminated, it pushed one Labour candidate above the quota, and once the last Tory got removed, it led to the last man standing, the second Labour candidate, to get elected.

Losing Uplawmoor has caused this ward to drop from four members to three. So what would have happened last time if the ward had already existed back then? It’s impossible to tell for sure, but the way I’d do it is to simply assume that the last Labour guy wouldn’t have got elected, resulting in one SNP, one Tory and one Labour. If Uplawmoor was really different from the rest of the ward (e.g., much more strongly Labour than the rest), one might change this, but you’d need to have solid evidence for this to do so.

If I repeat this exercise for all of East Ren, I end up with the following notional results:

Party	Ward 1	Ward 2	Ward 3	Ward 4	Ward 5	Total
SNP	1	1	1	1	0	4
Con	0	1	1	1	3	6
Lab	2	1	1	2	1	7
Ind	1	0	1	0	0	1

However, it’s really not an exact science. Especially the new ward 4 (Clarkston, Netherlee and Williamwood) is almost impossible to estimate because it’s a combination of most of two wards, including a really successful independent in one of them.

I don’t think my estimates seem too implausible because they all the same or slightly smaller than the actual results. (Smaller is good because the council got reduced from 20 to 18.) However, the BBC’s estimates seem really odd in comparison:

Party	Actual 2012 results	My notional results	BBC notional results	2017 results	Actual diff.	My notional diff	BBC notional diff.
SNP	4	4	6	5	+1	+1	-1
Con	6	6	5	7	+1	+1	+2
Lab	8	7	6	4	-4	-3	-2
Ind	2	1	1	2	–	+1	+1

In other words, according to the BBC’s notional results the SNP did a lot better five years ago than they actually did, and that means the change from 4 to 5 seats looks like a fall from 6 to 4 in their terms. I find it really odd because they’re assuming that a reduction in the size of the council would have resulted in more SNP councillors, not fewer.

If your calculations of notional results produce weird outcomes like this, I think it’d only be fair to publish the way you calculated them and emphasise that it’s your best estimate, not actual values. However, look how the BBC don’t mention the actual 2012 figures anywhere, and only write a small warning without any link to the underlying calculations:

If this was just a freak event, I wouldn’t be too bothered about it. It’s so hard to calculate notional results that they’re likely to come out somewhat weird in a few places. There seems to have been a systematic bias in their algorithm, however, making it look like the SNP did much better five years than they did, and that in turn has made it look like the SNP did badly this time.

Here are the national results:

	2012 actual seats	BBC 2012 seats	2017 actual seats	Actual change in seats	BBC change in seats
SNP	425	438	431	6	-7
Con	115	112	276	161	164
Lab	394	395	262	-132	-133
LD	71	70	67	-4	-3
Grn	14	14	19	5	5
Other	204	198	172	-32	-26

Note how the notional results are making the SNP’s rise from 425 to 431 councillors look like a fall.

It’s perhaps even clearer if we look at the share of seats rather than absolute numbers:

	2012 share of seats	BBC 2012 share of seats	2017 share of seats	Actual change in share	BBC change in share
SNP	34.8%	35.7%	35.1%	0.3%	-0.6%
Con	9.4%	9.1%	22.5%	13.1%	13.4%
Lab	32.2%	32.2%	21.4%	-10.8%	-10.8%
LD	5.8%	5.7%	5.5%	-0.3%	-0.2%
Grn	1.1%	1.1%	1.5%	0.4%	0.4%
Other	16.7%	16.1%	14.0%	-2.7%	-2.1%

So the BBC estimates that the SNP five years ago would have won 35.7% of the seats rather than 34.8% if the new boundaries had been in place back then (taking seats mainly from independent, but also from the Tories). This means that the new seat share of 35.1% looks like a 0.6% decrease rather than 0.3% increase.

For a voting system such as STV, I think it would be fairer to compare two elections by looking at what has happened to the actual number of seats and the share of the total.

Notional results may be a necessary evil in FPTP elections, but they can be strongly misleading under STV, as demonstrated convincingly by the BBC yesterday.