Brexit’s deep roots in confusion on democracy and statistics

In the last few days before we went to press the possibility of a second referendum on leaving the EU began to look a possibility, albeit still an unlikely one. Until then, UK politicians of all persuasions
had treated the first vote as sacrosanct — a democratic expression of preference that could not be
gainsaid. As Thomas Colignatus1 points out, this reverence overlooked the fact that there was little, if any, useful information in the first vote.

Let us look beyond Brexit and determine some deeper implications for conventional thinking. Namely, the UK seems quite confused on democracy and statistics, with a big problem in the vocabulary.

UK democracy has two formal instruments to get information about voter preferences for collective decision making, namely the House of Commons, using district representation (DR), and the occasional referendum. Currently we see that both the Referendum of 2016 and the General Election of 2017 fail to provide adequate information on voter preferences. The situation can be seen as chaotic. The debate continues while the very lack of proper information is neglected. Instead it is better to stop the debate and to concentrate on the real problem: why doesn’t the UK model of democracy generate the required information about voter preferences ?

To start with: What does the UK electorate really want w.r.t. Brexit or Bremain ? The answer is: we don’t know. The 2016 Referendum Question concerned the legal issue of Leave or Remain. The policy options were left to the polls. The very Referendum Question fails the criteria for a decent statistical enquiry. I am surprised that the Royal Statistical Society (RSS) did not protest. The question of Leave or Remain is a binary legal issue but the true issue are the policy options. It took some time to analyse this, but with the help of Anthony Wells of I managed to dissect this, in an earlier Newsletter (177, October 2017). Some 17 percent of voters ranked Remain between different options for Leave, which implies a grand game of guessing what to vote for strategically. The Referendum failed in the expression of preferences.

The political parties in the House of Commons are split on both direction and options as well. It is rather damning for a claimed democracy that its two formal instruments do not result in clarity on this basic issue. Remarkably, politicians across the board agree that the electorate would have voted to leave and that this would constitute an expression of the 'popular will' that must be respected at all costs. This however fails to recognise that the Referendum Question precisely did not generate the required information for policy decisions. The politicians look for a policy conditional on the outcome of the Referendum, but the outcome of the Referendum was conditional on guessing the policy. There is far too little awareness that the policy issue better is reconsidered when more details of the exit attain clarity.

The instructive question is why the UK had the referendum in the first place. Holland since 1917 has a system of equal proportional representation (EPR) for the Dutch House of Commons so that referenda are not required. The UK system of DR lacks such proportionality, and this invites the idea as if referenda might be used to get a degree of proportionality. This however neglects the importance of bargaining between the EPR representatives. Bargaining cannot be done by voters each in a voting booth, but requires the elaborate process between their representatives.

Within political science there is the branch on 'electoral systems'. This branch enhances the current state of confusion by using the same word “election” while its meaning for DR or EPR is quite opposite. In EPR all votes for candidates indeed go to their representative of choice. In Holland two per cent of votes are wasted on tiny parties that don’t make it and that remain unrepresented. The Dutch don’t think that these voters would be represented by another party. In DR there is no such proper election but rather a contest. The district winner is supposed to represent the district but many voters explicitly did not vote for this person to be their representative. In the UK more than 50 per cent of the votes go to candidates who don’t make it. There is no effort to collect those votes into seats, and thus those votes are discarded and not just wasted.The UK is locked in confusion by its vocabulary and disinformative statistics on electoral outcomes.

My suggestion is that the UK switches to EPR, say adopt the Dutch system of open lists (in which you may always vote for a regional candidate though people don’t tend to do so), has proper elections, and then let the new House of Commons discuss the relation with the EU again. It is not unlikely that the EU would allow the UK the time for such a fundamental reconsideration on both its democracy and Brexit.

It remains to be seen whether the UK would want to switch from DR to EPR, but the first step would be to provide the public with proper information. For the latter reason, I took the last year to deconstruct this information and vocabulary on democracy and statistics. Below references contain my findings. The main paper is (2018a). My diagnosis is that 'political science on electoral systems' still is no science but is locked in tradition and the humanities.

1.Colignatus is the name in science of Thomas Cool, econometrician and teacher of mathematics, Scheveningen, Holland.

(2017a), 'Voting theory and the Brexit referendum question', RES Newsletter, Issue 177, April, pp. 14-16,
(2017b), 'Great Britain's June 2017 preferences on Brexit options', RES Newsletter, Issue 177, October,
(2017c), 'Dealing with Denial: Cause and Cure of Brexit',
(2018a), 'One woman, one vote. Though not in the USA, UK and France',
(2018b), 'Comparing votes and seats with cosine, sine and sign, with attention for the slope and enhanced sensitivity to inequality / disproportionality',
(2018c), 'An overview of the elementary statistics of correlation, R-Squared, cosine, sine, Xur, Yur, and regression through the origin, with application to votes and seats for parliament'”,
(2018d), 'An overview of the elementary statistics of correlation, R-Squared, cosine, sine, Xur, Yur, and regression through the origin, with application to votes and seats for parliament (sheets)', Presentation at the annual meeting of Dutch and Flemish political science, Leiden June 7-8,
(2018e), 'The solution to Arrow's difficulty in social choice (sheets)', Second presentation at the annual meeting of Dutch and Flemish political science, Leiden June 7-8,

From issue no.182, July 2018, pp.18-19

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