Brexit Negotiation Outcomes using a Sankey Diagram.


With negotiations entering the final phase for the withdrawal agreement, there is immense speculation. The actual negotiations are being held in a “tunnel” and seem have been going on forever. I am reminded of a scene from an Ian Banks novel where the players have to play a valid game of Bridge, but are unable to see the cards. Banks calls this game tunnel which seems to be an apt metaphor. There is little real information leaking from the tunnel but loads of speculation.

The real sticking point seems to be the Irish Backstop – the all weather insurance policy to keep the Irish Border invisible. There seems little doubt that this will be in the final agreement but needs to be dressed in terms which are acceptable to the UK Government. It  is however not at all sure this is even possible – the Cabinet can still not come to an agreed position. There are also growing calls for the legal advice on the Brexit Deal to be published. There is every likelihood that the eventual outcome will be a humiliation for the Brexiters and tie the UK closely to the EU for many years to come – the so called BINO solution.

There have been a number of good articles this week, but two deserve special mention.

Britain’s arrogant attempts to hoodwink the EU have sacrificed all trust in the Guardian by Jonathan Lis, which finishes:

Brexit’s slow unravelling was both predictable and avoidable. Officials frequently remark that if they had trusted the UK’s motives and competence, they would have afforded the government more leeway. But instead of building bridges, the UK quickly burned them. The EU now suspects the government will do everything it can to wriggle out of the backstop, and is determined to thwart Britain’s faithlessness with a watertight withdrawal treaty. If, in the final weeks, the EU is holding our feet to the fire, it’s because we have shown it that it must.

Secondly one by Robert Shrimsley of the FT and reproduced in the Irish Times Brexit is teaching Britain its true place in the world:

Perhaps we should step back from the bloviated rhetoric. Humiliation is too strong; a national humbling is more accurate. The philosophy of Brexit was that, freed of EU constraints, the UK would take its rightful place in the world. This is indeed what is happening, but alas that place is not as the great power of their imagination. The UK’s place in the world is hardly terrible but, as Mr Johnson learnt during his brief but undistinguished term as foreign secretary, our emissaries no longer bestride summits like Castlereagh.

Sankey Diagrams

I have been trying to visualise probable outcomes and thought a Sankey Diagram might be a good metaphor. Sankey diagrams are a graphical representation where the width of a line is proportional to the value of the quantity. Sankey diagrams are named after Irish Captain Matthew Henry Phineas Riall Sankey, born in Nenagh Co Tipperary, but the earliest historical use  was by Minard, depicting Napoleon’s disastrous Russian campaign of 1812-13. Another interesting Irish dimension is that both Castlereagh and indeed the Duke of Wellington were born in Dublin.

In Minard’s Sankey diagram the French army of 422k setting out from Kowno (Kauaus Lithuania) was reduced to 10k at the end of the campaign.

Fig 1. Minard’s Sankey diagram of Napoleon’s Disastrous Russian Campaign.


Given the Irish connection and the likely disastrous Brexit deal, it seemed too good a metaphor to miss.

Brexit Sankey Diagram

The Brexit Sankey Diagram is shown in Fig. 2. There are a number of branching points, which I think are correct, but the probabilities assigned are fairly arbitrary. The first branching point is whether a deal can be agreed in Brussels which will satisfy the Cabinet. This is by no means certain as the Cabinet position on the Irish Backstop is still not agreed. Raab seems to be doing his best to scupper a deal, but according to Lord Adonis, Barnier has been advised to negotiate with Ollie Robbins and ignore Raab. The odds of an agreed deal still hang in the balance and have been set to 50:50 – in line with Barnier’s estimate.

Fig.2 Sankey diagram of Brexit outcomes.


If there is a deal, it is possible the Government may try to push this through without a Meaningful Vote (MV) in parliament. It is also likely that the deal will be terrible, but of course better than “no deal.” If there is no MV the Government will push the deal through. If there is a meaningful vote then the likelihood is set at 50:50 for accept/reject. Opinions are divided on whether this  50:50 figure is too high or too low. The overall likelihood of a deal being accepted is therefore 37.5%.

If the deal is rejected by parliament, I have set the probability to 10% that there will be a total breakdown and a “no deal” outcome. It will be too late to renegotiate another deal – we are really at the last chance saloon. There will be two options: a General Election (GE) or a People’s Vote (PV). The politics here is very strange.

A recent poll shows 86% of Labour members want a new Brexit vote and there is also growing Momentum support for a People’s Vote. Momentum is important as they are Corbyn’s Praetorian Guard. Corbyn and McDonnell however (and some of the inner circle like Len McCluskey and Seumas Milne) are very much Lexit people and believe in a socialist Utopia outside the EU. They are desperate to leave the EU and want a GE, but not a PV as the country would probably vote remain. Can the Labour membership force the Leadership to listen?

On the Tory side it is unlikely that May would go for a GE given the disaster of the 2017 campaign. One reason they might want a GE is to get the DUP off their back. The DUP are rumoured to be despised by the vast majority of the Tory party. The Backstop has been framed as a sovereignty issue. My view is that this is incorrect (as argued here) and is being used  as a tactic to try and get a full UK backstop. Having framed it in these terms however, it may well be near to impossible to get the backstop and the “Deal” through parliament. If there is complete breakdown in parliament It may well be the Tories who put a People’s Vote in place.

I have placed the PV/GE odds at 50:50. The politics is evolving rapidly however and the probability of a  PV is increasing.   More and more voices seem to being added every day with Lord Kerslake, who led the civil service between 2012 and 2014 the latest to call for a Peoples Vote. There is also the argument that a GE followed by a PV is the most democratically sound way to go. Time is short. There is absolutely no time to renegotiate another deal. “The clock is ticking” as Barnier continually says and as David Alan Green explains the UK leaves the EU by default through the “automatic process of law” at 11:00pm on the 29th March 2019. It is possible the A50 deadline could be extended by unanimous agreement of all EU27 governments. That however is only likely to happen if a PV with a remain in the EU option is on the ballot which is already set in motion.

On the other branch where no deal has been agreed, things are likely to get very chaotic. No rational government could countenance “No Deal” so it would have to go back to parliament. Parliament may break down completely. The hardliners of the ERG and the DUP want “no deal” – the ERG out of the desire of a deregulated “Singapore on Thames” and the DUP for the simple pleasure of sticking it to the Irish Government and the NI nationalist community. The probability of this is low but must be higher than in a “deal” scenario – it has been set at 20%. The PV/GE probability ratio has again been set to 50:50.

The final outcome therefore is a “Deal” at 37.5%, a GE/PV at 25.625% each (combined total 51.25%) and “No Deal” at 11.25%. These figures are of course fun and have no scientific basis whatsoever – but as stated at the outset it was an interesting exercise to think through the various scenarios.


An interesting few weeks lie ahead. My preferred scenario of a People’s Vote is looking more likely by the day. It is almost guaranteed that the “Deal” will be far worse than the EU membership we already have. A “No Deal” would be so catastrophic that no sane government or parliament should contemplate it. I am actually quite hopeful. For the first time since the Referendum result in June 2016 there seems a fighting chance of righting that historic error.




  1. Sean Danaher -

    There has been some discussion on Twitter with Jonathan Mills (@muinchille)
    Problems with the PV;
    1 – vote may not actually be to Remain

    Very true but as Dominic Grieve says at least he can accept the result with a clear conscience

    2 – will further divide and harden attitudes among people making compromise & agreement more unobtainable

    Not sure I agree here – I think the UK is stuck with this fault line for at least a generation. There has been absolutely no sign of healing and agreement. Remain majority is because older people have died (largely Leavers) and young people have become 18 and can vote (largely Remainers). Those who have not voted last time but will vote this time are largely Remainers and visa versa largely Leavers.

    There is an interesting debate as to UK instability. There is no question that the UK economy will be far worse if Leave prevails but that may not translate into more instability as Remainers seem far less emotionally angry than Leavers.

    3 – deprives the politicians of a chance to rewrite UK’s constitution unseen.
    Agree here if you have not read Anthony Barnett’s Lure of Greatness you should.

    4 – there isn’t time.

    Agree. the EU27 would have to extend the deadline which is by no means certain as it requires unanimous agreement.

  2. Samuel Johnson -

    Had no idea Sankey was Irish, though I am fan of Tufte’s work which introduced me to that brilliant diagram.

    Would be interesting to be a fly on the wall at DUP HQ when Arlene’s letter is discussed. Must be some chance of a volte face.

    Wellington may have been born in Dublin but famously (or notoriously) noted that being born in a stable didn’t make one a horse, so I don’t think we should claim him at all (slightly surprised to see him mentioned on the window at bar at the top of Guinness’s at St James’s Gate) and suspected the tourists there had no idea who he was anyway.

    1. Sean Danaher -

      Indeed re Wellington – I’m not sure if he ever said the famous horse quote but the general thrust is true

      The Duke of Wellington never did say about his Irish birth “just because you are born in a stable does not make you a horse”.

      It was said by Daniel O’Connell about him and has hung about the reputation of the Iron Duke ever since like a bad smell because it is true.

      Wellington was Irish in so far as he was born in Ireland and spent his youth in Ireland, but he was really a British aristocrat and imperialist. His allegiances were to his own class and to the British monarchy.

      He never self-identified as Irish though his family had been in Ireland for centuries. It would not have occurred to him. He saw Ireland as an integral part of the United Kingdom and a querulous one at that. He dismissed Ireland as a “nation of scoundrels”.

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