Saturday, 5 August 2017

Barnett Formula: Keeping it Simple

My last (long and complicated) blog attempted to explain how the Barnett Formula affects the devolved nation's Block Grant funding over time. In particular it looked at the impact of different relative population growth rates and how the Barnett Formula has been applied in practice as opposed to how it was expected to work. So if you're interested in the how and the why of these dynamics, please read Calling Time on the Barnett Formula.

Free from the burden of explaining quite why all of these things happen, I wanted to take the opportunity to now write a simpler blog which simply demonstrates what happens under various circumstances in a way which I hope will be easier for the casual reader to digest.

My medium of choice will, of course, be the graph.

Simply put: annual application of the Barnett Formula increases each devolved nation's Block Grant by an amount calculated to give the same per capita increase to the devolved budget as that applied to England's comparable spend1.

To achieve this the formula therefore depends fundamentally on the relative population sizes and how they change over time - so to understand the Barnett dynamics we need to understand how these population proportions (devolved nation vs England) have changed over time.

This graph shows us that since Barnett was implemented in 1978 Scotland's population proportion has been consistently falling (because Scotland's population has been growing more slowly than England's) . Wales' proportion was stable through the 80s and early 90s and has only recently started to decline. Northern Ireland's actually grew slightly through the 80s and 90s and has stabilised more recently. These relative population growth differences entirely explain the differences we're about to see between the devolved nations when we model the impact of the Barnett formula over this period.

The next factor we need to consider is the actual nominal growth in spending in England in those areas where comparable spend is devolved. This is a hard number to get precisely right over such a long time period2 but for illustration purposes we'll use the actual annual growth rates for all public spending in "rUK" (where rUK = UK - Scotland)3. This matters because higher nominal growth accelerates convergence (and there were some high inflation years in this time-frame and nominal growth has clearly slowed dramatically in recent years).

The only other assumption we need is how much higher the (illustrative) devolved category spend per capita was for the devolved nation in 1978 when this all started. For illustration purposes I've chosen to use a fairly representative figure of 20%4.

So based on actual population changes and assuming the above nominal spend increases, we can now see how application of Barnett would affect that 20% premium in spend per capita over time for each of the devolved nations. Here's the graph:

The blue dashed line shows how "true" application of Barnett would have caused Scotland's spend per capita premium to have converged towards England's. Note that the uptick in recent years shows the premium is actually growing: this happens when absolute nominal spend/capita increases in England are small (as they have been) and Scotland's population proportion continues to fall5.

The solid blue line shows the benefit that Scotland achieved because "until 1992, the 1976 population estimates were used for the Barnett Formula"6, so "as applied" the Barnett Squeeze (which causes convergence in Spend per Capita between nations) was partially alleviated. As I said in my last blog on this topic: imagine the howls of grievance we'd hear if failure to apply the Barnett Formula as agreed had resulted in a 2.2% detriment to the Block Grant instead of a 2.2% benefit7.

The red lines show Wales. Because the population proportion didn't materially change between 1978 and 1992 the "true" vs "applied" Barnett Formula issue makes no material difference. What is clear is that simply because of the different trend in population proportion, Wales has seen a far more marked squeeze in Spending than Scotland.

The green lines show Northern Ireland. Because NI's population share was actually growing between 1978 and 1992 the impact of Barnett as applies (vs "true" Barnett) was to exacerbate the Barnett Squeeze. The Barnett Squeeze for NI is worse overall purely because of the different trend in NI population proportion vs Scotland or Wales.

So there we have it. The Barnett Formula was never intended as a long-term solution8 and - as I explored in my previous blog - there are strong arguments for changing to a system which is a) fairer between the devolved nations and b) fairer to the devolved nations insofar as there is a sound needs-based argument for maintaining per capita spend premia in some departments.

As I also argued last time: the easiest way to ensure spend is distributed based on need is not to devolve that spend so that e.g. social protection spend is allocated to individuals based on their need, not where they live.


1. This is a simplification; if you care for the more complicated detail see > Calling Time on the Barnett Formula

2. As the House of Commons briefing paper succinctly puts it: "it is hard to verify the extent to which the Barnett Squeeze is happening, largely due to a lack of comparable data". My previous blog Calling Time on the Barnett Formula provides a more detailed explanation of the complexities

3. This is mainly because I have these figures to hand and they're suitable for a realistic illustration. If one was so inclined one could dig out the England only figures, but that still wouldn't be giving us the spend just on departments which are devolved (which changes over time anyway) - this assumption is fine for illustrative purposes as it captures macro trends of inflation and general public spending policies. My rUK data series only goes back to 1981 (SNAP data), so for 1979 and 1980 only I simply assume inflation growth (inflation was high then: 13.4% and 18.0%).

4. In 1998/99 (the earliest year that GERS breaks spend out to this level) Scottish spend per capita on (the predominantly devolved areas) of [health + education + transport] was 20.1% higher than rUK.

5. Imagine the increase is zero: in this case neither England nor Scotland's absolute spend would increase, but because Scotland's poulation grows less quickly than England's, our spend per capita relatively increases

6. As per the House of Commons Briefing Paper, page 11 [and discussed in more detail in Calling Time on the Barnett Formula]

7. That being the impact of not updating the population proportions up to 1992

8. Because of my last blog and some happy happenstance, I have recently spoken with some people who were there and involved when the Barnett Formula was put in place. I think it's a fair sumary to say it was only ever intended as a short-term fix to avoid what were perceived as tedious department by department negotiations between the Scotland Office and the Treasury; the assumption was always that something better would be put in place within a handful of years.

For those who care about the spreadsheet mechanics, here's a snapshot of the "true" Barnett model

Bikes, Maths and The Big Pig

This morning I posted a question on Twitter to test how easily people get confused when thinking of averages. Within a few hours I had over a thousand answers, enough to confirm my hypothesis that the answer is "pretty easily".

[You can check the current live result here; the thread below is fun if you like that sort of thing]

Here's where I'd normally say something like "the correct answer is of course that it's impossible". That's the point of this test though - it's not obviously impossible because the majority of people intuitively went for the wrong answer.

I think the reason why this happens is interesting, but let's first quickly explain why the correct answer is that it's impossible.

The easiest way to explain is by illustration. In fact the reason I posed the question in the way I did was because I once actually experienced precisely this scenario when cycling on Majorca. I recognise this seems almost too good to be true, so for the doubters out there here's the Strava map of that ride and route profile.

The peak itself is known as "Puig Major" - I'm sure I'm not the only cyclist to have ground my way up there thinking Puig Major must mean "Big Pig" in Spanish1.

As you can see from the chart above it's precisely 10 miles up the hill. So if  - as in fact I did, back when I used to be fitter than I am now - you average 10 mph on the way up, it takes 1 hour to reach the summit.

At this point the impossibility of the challenge hopefully does become obvious. The total journey up and back down again is 20 miles, so to achieve a 20 mph average you'd clearly have to do the whole journey in an hour ... but you've already used all that hour just to get to the top of the hill.


The answer is of course2 true independent of the actual distance involved. It's easy enough3 to prove algebraically that it's impossible to double your average speed after you've covered half the distance of your journey (because you'd need to complete the second half of your journey in zero time):


I think part of the reason why most people instinctively get this wrong is explained in Kahneman's "Thinking, Fast and Slow" - we have a tendency to intuitively use the data that's closest to hand rather than taking the time to think if it's the right data.

So in this example we easily know it's the same distance up as it is down, so we instinctively calculate the total average as being the distance-weighted average of the two speeds (i.e. "half at 10 mph + half at 30 mph = all at 20 mph").

The problem is that we can't calculate average speed by weighting the two "halves" by distance, we have to weight them by time spent. So it would be correct to say "half the time at 10mph + half the time at 30 mph = all the time at 20mph" - but if you were to spend as long at 30 mph as you did at 10 mph, you'd travel 3x as far on the journey down!

The generic rule here - well worth remembering when sanity checking analyses - is you weight averages by the denominator not the numerator. Speed = Distance / Time, so to average two speeds you weight the total by the time spent at each speed, not the distance traveled


Having come this far I can't resist a little physics addition to this problem: why is it harder to achieve the same average speed on a hilly course than a flat one?

The potential energy you invest in to go up a hill you get back coming down, so you might think it should be just as easy to achieve the same average speed on a hilly course (that ends where it starts) as you could on a flat one. Cyclists will know this simply ain't so.

The answer is (at least in part4) to do with wind resistance being a function of the square of your speed: if you go twice as fast you incur four times the drag.

Let's imagine we went up our hill at 10 mph and down it at 30mph. We now know how to calculate our average speed: we spend 60 minutes at 10 mph and 20 minutes at 30 mph, so our average speed is 15 mph (10 x 60/80 + 30 x 20/80 = 7.5 + 7.5 = 15).

Now let's compare the wind-resistance work involved in doing a flat 20 miles at a constant 15mph with our up-and-down-the-hill alternative.

Work = Force x Distance

Distance is the same in both cases, Force is proportional to the square of speed.

The average square of speed in the flat scenario is easy = 15^2 = 225

The average (correctly weighted by time) square of speed in our hilly scenario = 100 x 60/80 + 900 x 20/80 = 75 + 225 = 300

We do 33% more wind-resistance work on our hilly ride.


OK, enough - I'm off to find somewhere flat to ride my bike5.

1. disappointingly it in fact just means "big hill"
2. here I go again
3. and again

4. there will be other moving-part speed-related friction factors which the existence of gears makes complicated
5. I live in East Lothian, that's not going to happen

Thursday, 3 August 2017

Calling Time on the Barnett Formula

The "fiscal framework" which governs how funds are allocated across the four nations of the UK (often simply referred to as the Barnett Formula, which underpins it) has never quite worked as intended and is frankly well past its sell-by date.

If we're to have a sensible discussion about how the fiscal framework could be improved, we first have to understand what happens currently and why.

It's hard to explain this in a way that doesn't quickly become mind-achingly complicated or simply too dull to hold the attention of all but the most obsessively curious. With that in mind, I'll try to separate the core arguments from the explanations, use illustrative examples with realistic figures and put stuff the analytically minded might want to understand into separate, smaller notes.

Note: this is a bit of a beast of a blog post: if you want the simple version with clear graphs, try the later post Barnett Formula: Keeping it Simple

The Barnett Formula & The Fiscal Framework

  1. The Barnett Formula (used to calculate the Block Grant) was designed to cause convergence of per capita spending between the four nations of the UK, an effect known colloquially as the "Barnett Squeeze"

  2. The fact that Scottish population growth has been slower than English population growth has to some extent dampened the expected Barnett Squeeze - but it's still happening

  3. In the years from 1978 to 1992 the formula was applied "incorrectly" in a way which was materially to Scotland's advantage

  4. In pure spend per head terms, Scotland has benefited from the fact that Social Protection has remained predominantly reserved (and therefore continues to be allocated based on need rather than subject to the Barnett Squeeze)

  5. Wales has suffered a worse Barnett Squeeze than Scotland due to the fact that its population growth has not lagged as far behind England's

  6. The retention of Barnett in the current Fiscal Framework (as recommended by the Smith Commission) means this tendency to converge per capita spending is "baked in" to the current system

  7. This is a problem if one believes that spending should be based on need rather than judged to be "fair" simply if  public spending per head converges across the four nations


1. The Barnett Formula (used to calculate the Block Grant) was designed to cause convergence of per capita spending between the four nations of the UK, an effect known colloquially as the "Barnett Squeeze"

There's an excellent House of Commons Briefing Paper which describes how the Barnett Formula works which explains:
The majority of the devolved administrations’ spending is funded by grants from the UK Government – the block grant being the largest. Since the late 1970s the non-statutory Barnett formula has determined annual changes in the block grant. The formula doesn’t determine the total amount of the block grant, just the yearly change.
When there is a change in funding for comparable services in England, the Barnett formula aims to give each country the same pounds-per-person change in funding. In general, if a service is devolved it is considered to be comparable. 
When a change is made to a UK Government department’s budget (normally at a spending review) the Barnett formula takes the budget change, considers how comparable the services provided by the department are to those provided by the devolved administration, and applies a population proportion, as shown below. This calculation is carried out for all UK departments and the results are added to the devolved administrations’ block grants2.

[Change to UK gov department’s budget]
[Comparability percentage]3
[Appropriate population proportion]

Note 2: These amounts are generally referred to as "Barnett Consequentials"
Note 3: The “comparability percentage” is a function of how much of those budgets are devolved, as shown by this handy table:
This needn't distract us when it comes to understanding the fundamental dynamics of the Barnett Formula, but is often a source of heated negotiation in practice (e.g. whether spending on the Olympics or HS2 are deemed "comparable" for the purposes of calculating these Barnett Consequentials). As the Briefing Paper explains: “Each programme area, or service, is given a comparability of either 100% or 0%. A service is 0% comparable if: other arrangements are in place to determine each devolved administration’s share of a budget; expenditure is incurred on behalf of the UK as a whole by the UK department; or, the service is deemed unique at a UK level, such as the Channel Tunnel Rail link.”

Obviously if more spending powers are devolved the comparability percentage goes up, but if we're considering the underlying dynamics of the Barnett Formula it makes sense to consider an area where this doesn't change (if you like, think of a fully devolved area like Education where the comparability percentage is simply 100%).

For most departments (where spend is devolved to all four nations) the "Appropriate population proportion" for Scotland is simply [Scottish population] / [English population]. To understand the Barnett Squeeze let's first consider what happens if this proportion doesn't change (i.e. English and Scottish population growth rates are the same).

We can run the numbers with a simple spreadsheet using actual English population figures and covering the 38 year period since the Barnett Formulas was introduced in 1978. Over that period rUK has seen average annual public spending increasing at about 5.3% pa (a combination of inflation and real growth) so we'll use that assumption for this illustrative department's spending growth in England. Our last assumption is that this is a department where in 1978 Scottish  spend per head was 20% higher than England.

The snapshot of the spreadsheet below shows how the mechanics work: key modelling assumptions are in yellow and the "answer" - the amount by which Spending per head in Scotland exceeds that in England - is in green.

So under these realistic assumptions: if the starting point for the Block Grant in 1978 was a 20.0% higher spend per capita in Scotland than England, after 38 years the application of Barnett would have now reduced that to being only 2.8% higher (if Scotland's population grew at the same rate as England's and there was no "Formula bypass" or other Barnett exceptions5")

Note 4: This makes intuitive sense: 5.3% cumulated over 38 years is more than a 7-fold increase, so by 2015 over 80% of the Block Grant has been determined by the Block Grant Adjustments which are on the same per capita basis, less than 20% is at accounted for by the "base" at the 20% higher rate.
Note 5: as the House of Commons Briefing Paper explains: "The majority of changes in the devolved administrations’ DELs are determined by the Barnett formula. However, there are some items in DEL for which the population based Barnett formula is not appropriate. DEL items outside of Barnett, often known as non-assigned items, are ring-fenced and specific to their particular spending priority. Such items, including depreciation, are determined separately between the devolved administration and UK Government. The population-based approach of the Barnett formula is not appropriate for determining changes in AME grants, because of their demand-led nature, so these are determined periodically between the devolved administration and UK Government." and "Although the Barnett formula represents normal procedure, changes to the block grant can be made outside it - a process often referred to as ‘formula bypass’"

2. The fact that Scottish population growth has been slower than English population growth has to some extent dampened the expected Barnett Squeeze - but it's still happening

Now we have this simple model, it's easy to see what happens if instead of assuming Scotland's Population grows at the same rate as England's, we use the actual population figures6.

The effect of applying the actual (relatively slower) population growth in Scotland is to significantly slow the Barnett Squeeze: instead of the spend/capita premium being reduced from 20.0% to 2.8%, our model now shows it still at 9.3% in 20167.

Note 6: the proportion actually used is the prior-year population proportion, as this is the only data available when the calculations are made in real life
Note 7: this is less easy to intuit than one might expect. The "base" part of the block grant remains static in absolute terms so becomes significantly higher relative to England on a per capita basis - the same effect applies to prior years' Block Grant Adjustments which will have been calculated on a relatively higher proportion. In addition, the fact that prior-year proportions are necessarily used means there is an addition "built in" squeeze dampening affect as long as the Scottish population proportion is declining.

3. In the years from 1978 to 1992 the formula was applied "incorrectly" in a way which was materially to Scotland's advantage

There's an extraordinary throw-away line in the House of Commons Briefing Paper (page 11) which reads (highlighting mine):
".. if population proportions are not regularly updated convergence can be affected. For instance until 1992, the 1976 population estimates were used for the Barnett formula. During this time Scotland’s population was falling relative to England’s, which would have worked against the Barnett squeeze." 
We've got the model so it's easy to scale what effect this would have. To improve modelling accuracy I've applied a nominal spending growth rate of 7.6% pa until 1992 and 5.0% subsequently (reflecting actual growth rates in UK spending over those periods) and then looked at what the 20% premium would reduce to if Barnett were "correctly" applied vs. if 1976 proportions were used until 1992 (as actually happened).

"Correctly" applied the Barnett Squeeze would have reduced the 20% premium to 11.1% by 1992 (note the differential growth assumptions now used over the two periods has reduced the 2016 premium to 8.7%)

As actually applied, the premium only reduced to 13.3% by 1992 (and the 8.7% in 2016 has improved to 9.5%)

So this failure to update the population proportions between 1978 and 1992 benefited Scotland's Block Grant amount by about 2.2% - a significant impact and one which is still implicitly reflected in our Block Grant today (albeit now diluted to just a 0.8% impact).

Pause for a moment: I want you to imagine the howls of grievance we'd hear if failure to apply the Barnett Formula as agreed had resulted in a 2.2% detriment to the Block Grant instead of a 2.2% benefit. OK, now carry on.

If you're struggling to get your head around this, you're not alone. That House of Common's Briefing Paper is at best confusing when it states "During this time Scotland’s population was falling relative to England’s, which would have worked against the Barnett squeeze". The implication that updating the population proportions would have accelerated the Barnett squeeze is wrong: the correct Block Grant Adjustment would have required a lower population proportion to be applied than that actually used, reducing the Block Grant adjustment and accelerating the Barnett squeeze8.

Note 8: the error in the briefing paper is perhaps understandable. If the population proportion had remained the same the squeeze would have been greater, but by keeping the population proportion the same in the calculation that doesn't offset the fact that the actual population figure (the denominator in the per capita calculation) does relatively decline

4. In pure spend per head terms, Scotland has benefited from the fact that Social Protection has remained predominantly reserved (and therefore continues to be allocated based on need rather than subject to the Barnett Squeeze)

Because Social Protection is broken out as a category in Scottish Government GERS figures back to 1998, we can use our model to see what (in purely arithmetic terms) would have happened if in 1999 we'd devolved Social Protection (SP) spend and used the Barnett Formula to calculate Scotland's SP Budget (given what we know actually happened to SP spend in rUK). We can of course compare that to what happened to the actual, predominantly reserved Scottish SP spend per GERS.

What we can see is that on average over this 17 year period Scotland has received £54/capita more Social Protection spending than if it had been simply devolved and subject to the Barnett Formula9. Multiply that figure by Scotland's population and you get a £288m average annual benefit.

To put that figure in the context of a standard SNP grievance: their decision to centralise Police Scotland and incur VAT costs us just £25m pa.

Note 9: of course had this been money from the Block Grant adjusted by Barnett then the Scottish Government would be free to spend the money elsewhere instead

There's a lot going on behind these figures and I've had to hide some columns for display purposes. The graph below simply charts the "Barnett Effect" (the last row of the spreadsheet above), where the bar below the line means the alternative of using the Barnett formula would have led to less per capita spending in Scotland

In the early 2000s the benefit of retaining Social Protection as a reserved department allocating funds UK-wide based on need (vs. our notional alternative of devolving in 1992) was often greater than £100/capita. The fact that the gap closed in recent years is presumably something to do with Westminster policies that shifted Social Protection spending in a way which negatively impacted Scotland more than rUK ... or it could be to do with the dynamics of decelerating growth in cash spend and the relative population growth figures ... but to be honest I think I've reached the limit of my capacity to try and unravel the figures at this point.

5. Wales has suffered a worse Barnett squeeze than Scotland due to the fact that its population growth has not lagged as far behind England's

Applying the Welsh population figures to our model shows how a 20% per capita spending premium in 1978 would have reduced to a 7.4% premium in 1992 (cf Scotland's 13.3%) and 6.0% by 2016 (cf Scotland's 9.5%).

If we look at the relative population growth trends this finding is not surprising: Wales was exposed to a fairly "pure" Barnett Squeeze until the early 1990s as its population growth  pretty much matched England's

6. The retention of Barnett in the current Fiscal Framework (as recommended by the Smith Commission) means this intention to converge per capita spending is to some extent "baked in" to the system

The current Fiscal Framework is designed to satisfy the Smith Commission recommendations, in particular clause 95 (1) which states that "...the block grant from the UK government to Scotland will continue to be determined by the Barnett Formula". 

Devolved revenue raising powers adds a layer of complexity to this debate because the Block Grant (calculated using Barnett) is reduced by an amount to adjust for revenue devolved. The nature of that Block Grant Adjustment (BGA) was the source of much debate during the Fiscal Framework negotiations, in particular how one indexes the BGA in future years to satisfy (and interpret) the Smith Commission requirement of "no detriment".

As the IFS highlighted at the time: " it is impossible to design a block grant adjustment system that satisfies the spirit of the ‘no detriment from the decision to devolve’ principle at the same time as fully achieving the ‘taxpayer fairness’ principle: at least while the Barnett Formula remains in place"

7. This is a problem if one believes that spending should be based on need rather than judged to be "fair" simply if spend per head converges across the four nations

I'd hazard a guess that most voters in the UK buy into the principle of pooling & sharing resources: we spend money on public services based on need, we don't just aim to spend the same amount per person.

Aside: There is an alternative view which is that the constituent nations of the UK should "stand on their own feet" and be fully fiscally autonomous. As this blog has previously explained in detail (> Full Fiscal Autonomy For Dummies) that way madness lies. From a Scottish perspective that could only make sense when oil was generating upwards of £9bn pa of tax revenues - without those oil revenues Scotland would have to find that £9bn pa from some combination of tax rises or spending cuts to be fully fiscally autonomous and satisfy the fiscal constraints that would come with currency sharing. There's a reason we don't hear the SNP calling for Full Fiscal Autonomy anymore.

As an example: need based allocation would make more sense than equalising spend per capita where population densities differ significantly. It costs more to get basic services to people the more geographically dispersed they are - and the four nations clearly have very different population densities

Scotland's population is 6x more dispersed than England's - is it "fair" to expect the same per capita amount to be spent on Transport or Education?

The demographic challenges differ by nation as well with different proportions of the population economically productive versus those dependent on the state. This is crudely measured by the percentage of the population who are of working age (a measure on which Wales fares particularly badly)

There are of course many other factors to consider when it comes to defining need (healthy life expectancy, unemployment rates, areas of deprivation, etc.) but this blog-post is already too long to start exploring them further.

What we can say is that the arguments for a needs based spending allocation formula seem pretty compelling: as the House of Commons Briefing Paper points out, pretty much everybody who has looked at this question has reached the same conclusion
The change in population is the only consideration of ‘need’ in the Barnett formula. However, the cost of providing public services is influenced by a range of other factors including, but not limited to, characteristics of the population, deprivation and population density.
There have been frequent calls for the Barnett formula to take greater account of need, or to be replaced with a needs-based formula. In 2010 the Holtham Commission, which considered funding for devolved government in Wales, recommended that a need-based formula should determine the block grant. After considering devolution in Scotland, the Calman Commission recommended in 2009 that the block grant should be justified by an assessment of need. Lords Committees in 2009 and 2015 recommended replacing the Barnett formula with a needs-based formula. Similar recommendations were put forward by the House of Commons Justice Committee in 2009 and by other Parliamentary committees in the past.
There's an interesting point to be made here relating to "more powers". 

We've shown above that if (say) Social Protection were devolved and subject to Barnett, it would become subject to the Barnett Squeeze. Unless our population were to decline in absolute terms, the act of devolving spending in an area where we currently experience a higher per capita spend than England would inevitably see a decline in the premium given to spend in Scotland (irrespective of actual need). Were Scotland's population growth to accelerate (or the UK's decline) that squeeze would accelerate. Why would anybody in Scotland think that a good idea?

Of course one could argue that the best way to deliver Social Protection based on need is to apply the same policies nationwide and have the same criteria and needs assessments in place irrespective of which constituent UK nation you happen to live in.

Those continually complaining about spending powers that remain reserved to Westminster should maybe take a moment to consider: fairness may best be delivered by keeping spending areas like Social Protection (or Work & Pensions as defined in the departmental allocation table above) largely reserved.

Personally I'd argue against any further devolution of either spending or revenue raising powers until these fundamental issues related to the Barnett Formula are addressed.

Wednesday, 2 August 2017

How Brexit Affected SNP GE Vote Share

A very quick and dirty blog, but I saw this analysis today [A Tale of Two Referendums - the 2017 Election in Scotland] and I couldn't keep my hands off it.

The analysis looks at four cohorts based on indyref and EUref vote (Yes/Remain, Yes/Leave, No/Remain and No/Leave) and tracks how General Election voting moved between 2015 and 2017 within those cohorts. I recommend reading it.

The analysis is excellent and clear but the "visual thinker" in me wanted to see the four cohorts shown in correct relative scale so I did this crude bit of image manipulation (and a few simple sums based on SNP share of those cohorts in 2015 and 2017).

 It may be too much in one picture and I've had to estimate share of cohort figures from the printed graphs but the numbers are good enough to tell the story (working down the cohorts above):

  • The SNP lost share in all cohorts
  • The SNP saw a 2% total vote share decline among Yes/Remain voters (who largely switched to Labour)
  • The biggest source of loss for the SNP was Yes/Leave voters who were responsible for a 5% total vote share decline for them
  • The SNP of course hoped to pick up No/Remain voters - but in fact they lost another 1% total vote share through this cohort, with those No voters who'd lent their votes to the SNP in 2015 largely switching to the Lib Dems
  • No/Leave voters largely switched to the Conservatives - and the few No/Leave voters who had lent their votes to the SNP in 2015 largely switched to Labour, losing the SNP another 1% of total vote share.