Not pleasing anyone any of the time

One of the great ironies of the modern information economy is that we have more facts at our disposal than ever before, yet we are also subject to more fake news. In this environment, proponents of Brexit are able to make the most outrageous claims and brush aside objections without any regard for the facts. This is particularly annoying in the context of the phrase “will of the people” which is used to justify going ahead with a Brexit policy very much at odds with what a large slice of the electorate voted for. More importantly, the statement is statistically incorrect.

Admittedly 51.9% of those who voted did indeed favour Brexit. But this merely represents the will of those who voted: The fact that 28% of eligible voters did not even make it to the polling booth means that, by definition, the outcome cannot represent the views of all people. This is not to deny the democratic legitimacy of the vote. After all, no UK government in modern times has ever taken more than 50% of all available votes, so the process is no more undemocratic than usual. The difference is that Brexit is an irreversible process and it was therefore incumbent on the powers-that-be to make sure that sufficient checks and balances were built in to prevent it from descending into the farce we see today. This is why the  Scottish devolution referendum held in 1979 required that a threshold of 40% of all eligible voters was necessary to validate the result. Although the pro-devolution faction secured 51.6% of the popular vote, they only obtained 32% of eligible votes due to the fact that the turnout was fairly low at 63.7%. Ironically, if the turnout had been 77.5% or higher, the same final outcome would have given them victory. In 2014 the turnout was 84.6% so had people been as motivated to vote as in 1979, Scotland would long since have achieved greater independence from the UK.

A key issue of contention over the past year is whether the narrow margin of victory in the Brexit referendum is sufficient to justify the government’s gung-ho attitude. If all those eligible to vote had done so, there would be no need to have the discussion. But on a statistical basis since more than a quarter of those eligible to do so did not cast a vote, we can think of the result as representing a sample – albeit a large one – of the whole population. And as with any sample, there is an associated error. We cannot ever know how the stay-at-homes would have voted but if they had voted 55-45 in favour of Remain, the result would have gone the other way. It is thus reasonable to look more closely at the statistical evidence. 

Classical statistics suggests that a 90% confidence interval around the Leave vote share implies that they would still have swung it. But this neat little paper entititled 'What does the data of the Brexit referendum really say?, written by a couple of statisticians, uses effect size, which is a way of quantifying the magnitude of the difference between two groups without relying on sample size as in classical statistics, and this paper measures the sizes of differences between the Leave and Remain votes. The authors conclude that “a 52%-48% split represents only a spurious difference, not sufficiently different from a 50-50 split to claim a majority for either side.” They also suggest that on the basis of a 72% turnout “a minimum split required to make those claims is 69%-31%.” 

This obviously raises the question of how we should respect the result – a question posed by Simon Wren-Lewis on his blog. SWL takes the view that the lies told by the Leavers during the referendum campaign are “enough to completely discredit the referendum as an exercise in democracy.” Although he stops short of suggesting we should ignore the result, it is quite clear that many of the things which people thought they were voting for cannot possibly be achieved. For example, UK government sources suggest that EU citizens will be free to visit the UK after Brexit without having to obtain visas. Whilst this does not mean they will have the right to remain indefinitely, it is a significant watering-down of the position which many Brexit supporters thought they were voting for.

The very fact that the referendum result was insignificantly different from a 50-50 shot suggests that nobody is going to be satisfied with whatever compromise agreement is finally achieved. The UK will clearly not be able to leave the EU on the basis which many hard Brexiteers might wish but given the government’s decision to trigger Article 50 (before it lost its parliamentary majority, lest it be forgotten) it equally cannot remain an EU member. I maintain my view that for a long time to come, various elements of UK policy will be conducted on the basis of a Schrödinger’s Cat approach: Simultaneously half-in and half-out of the EU. They say you can’t please all the people all of the time. Brexit is a case of not being able to please anybody any of the time. If the current generation of politicians had a better grasp of statistics they would have known this all along.

* 22 August 2017: I subsequently amended this piece to correct a couple of errors. Thanks to those who pointed them out