What if everyone had voted in the EU referendum?


Britain’s vote to leave the European Union (EU) has prompted a great deal of speculation about whether the outcome really does represent the will of the entire electorate. Citizens and commentators have asserted that the result may well have been different had various groups of potential voters gone to the polls in greater numbers. If only more_____ (fill in your choice of young people, ethnic minorities, Londoners, Scots, university graduates, etc.) had voted, then Remain would have won. At least that’s the argument.

But why restrict this discussion about increased turnout to specific groups? Let’s dare to be democratic—what would have happened if all eligible voters had exercised their franchise by casting a vote in the referendum? Would Britain have voted for Brexit or would the country instead have opted to remain in the EU?

To answer this question, we need to put our ‘nerd hats’ on for a moment and use data gathered in our Essex Continuous Monitoring EU referendum survey. As we already know, at the referendum Leave won 51.89 per cent of the vote and Remain won 48.11 per cent. The Electoral Commission reports that the overall turnout was 72.21 percent. These figures imply that 34.73 per cent of the entire electorate voted to Remain. But what about the people who did not go to the polls?

A question in our post-referendum survey asked those who did not vote how they would have voted had they gone to the polls. It turns out that 39.1 per cent would have voted Remain. Given that the Electoral Commission’s records indicate that 27.79 per cent actually did not turn out, this would have given an additional 10.87 percentage points to Remain (27.79 x .391).

But the story does not end there. Another 32.2 per cent of the respondents in our survey who did not vote said, after the referendum, they ‘did not know’ how they would have voted had they have gone to their local polling station. This amounts to 8.95 per cent of the entire electorate (27.79 x .322). To determine how these people would have voted, we use a question in the pre-referendum survey (conducted on June 19th and 20th—just a few days before the event) which asked them how they were going to vote. Of those who ‘didn’t know’, 53.1 per cent reported after the referendum survey that they opted for Remain.

Using this number to estimate how many of the 8.95 per cent of the electorate would have voted Remain suggests 4.75 per cent (8.95 x .531) would have done so. Now, if we combine these calculations (34.73+10.87+4.75) then we are left with the finding that if everybody had voted at the referendum then 50.35 per cent would have voted Remain, a narrow win but still a different result from that which emerged in reality.

Remainers, however, should not get too excited. This figure is still not conclusive evidence that Remain has majority support across the electorate as a whole. Rather, the 50.35% result is only an estimate of Remain’s strength and one that fails to account for the uncertainty in the survey data which are drawn from a sample of eligible voters. As always, it is important to respect sampling uncertainty in survey data.

To do so, we compute a standard 95 per cent confidence interval or an ‘uncertainty boundary’ which tells us how varied the results would have to be in order to be 95 per cent sure that the actual outcome would be inside the boundary. Our calculations suggest that Remain’s strength in the electorate would have varied from 48.65 per cent to 52.05 per cent. So, even if everyone had gone to the polls Remain could still have lost.

How likely would a Remain loss have been? Although we cannot be certain what would have happened if everyone had voted, we can gain additional insights into the likelihood of a Remain victory. Imagine conducting many (one million!) referendums with a random component distributed about a mean of 50.35 per cent with a standard deviation of 0.85 per cent (a measure of how variable our survey estimates were of Remain’s strength). Assuming a normal or ‘Bell shaped’ distribution for these contests, the one million simulated referendum results are shown in Figure 1. Remain’s total is greater than Leave’s in 66.03 per cent of these contests and, Leave wins 33.97 per cent of them. So, had everyone voted then the odds of a Remain victory would have been substantial but not overwhelming (1.94 to one).


Of course, UK voters did not have one million chances to vote to stay in the EU.  They had one, and a majority of those who cast a ballot opted to leave.  While Brexit likely does not reflect the sentiment of the entire electorate the result of the referendum reflects how democracy works. This is a longstanding constitutional principle and it was honored on June 23rd.  If you don’t participate, your voice is not heard.

This discussion of what ‘might have been’ has led some disappointed Remainers (and political movements) to demand a second EU referendum. Some MPs have called for Parliament to exert its constitutional power and reject the result entirely. Still others have suggested that Prime Minister May and her Government should ‘slow walk’ exit negotiations with the EU, by failing to invoke Article 50 of the Lisbon Treaty and so subvert the Brexit decision with bureaucratic inertia. The success of these efforts remains to be seen and their democratic bona fides are sure to be challenged.

Written by Harold Clarke, School of Economic, Political and Policy Sciences University of Texas at Dallas. Professor Matthew Goodwin, senior fellow UK in a Changing Europe and Paul Whiteley, Department of Government University of Essex. This piece was co published with The Conversation.

The views expressed in this analysis post are those of the authors and not necessarily those of the UK in a Changing Europe initiative.

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  • hughsansom

    A critical (and unanswered) question in this essay: Was the post-referendum survey taken after it was clear that the vote had “Remain” had lost? In other words, was the post-referendum survey taken after eligible but non-voting Britons had had a chance to reconsider in light of events?

    • Robin

      Totally irrelevant. Whoever didn’t vote, did NOT vote. We can speculate from now till doomsday on what might have been the result if little old ladies with cross bred King Carles/Cavalier spaniels had not been allowed to vote or babies that were teething had been allowed to vote. There was a clear and definite rule….any person domiciled in the UK over the age of 18 could vote. Those expats living in an EU country who were domiciled in the UK and chose to keep their nationality and were over 18 could also vote provided they had not been out of the UK for more than 15 years. Those that did not vote were assumed to be either not bothered or couldn’t care less. No in betweens, either you did or you didn’t. If you couldn’t make it ON THE DAY through illness that is just tough luck. If you weren’t going to be able to make it and knew before hand, you could elect a proxy or do any of the following: a) Go into an advance voting place where you will be given a declaration form to complete and your voting papers; or b) Complete and post an application for special declaration voting papers to your Returning Officer. They will send your voting papers and declaration; or c) Apply for voting papers by fax, e-mail or telephone from your Returning Officer. That is final. No more if’s and but’s. No speculating. Done, full stop!

  • Martin Cahn

    I made a rough back of the envelope estimate to answer the same question looking at the relationship of age to voting intentions and turnout a week before you published this and have only just found your analysis, so my estimate is completely independent of yours.

    I basically looked at the ONS estimates from Census data corrected for 2015, and the rough turnout by age and vote for remain by age (both available from publicly available polls – Ashcroft and YouGov) and then tried to produce a number voting by age and number non voting by age. I used the data for the proportion of foreign workers by age quoted by Rowntree (from ONS) and assumed that this applied to all non-voters by age (although of course foreign workers include some who are Commonwealth citizens and have the vote). This gave me figures for numbers voting by age and numbers non-voting. I simply guessed that the number of foreigners in the over 65s was 2% of the total – I suspect that this was a bit low, but number of workers obviously doesn’t give that figure. I then assumed that non-voters would vote the same way as their age group and looked at the result. I came to a proportion of, believe it or not, 50.3% Remain and 49.7% Leave. So, in a circular argument I admit, I can say that your data seem to confirm my assumption that non-voting people in a particular age group would vote in the same way as their peers who did vote, and my data seem to confirm the validity of your results.

    I have been commenting my results, and simply say that this suggests that the opinion in the electorate is 50:50 (although your analysis suggests that it is, indeed, more likely to slightly favour Remain), and that in an advisory referendum this is a valid factor to take into account when considering the way forward after the result.

    In addition, of course, it is clear from the trends that a majority of those who did not have the opportunity to vote, e.g. under 18s, EU citizens resident in Britain, would have voted Remain. So while the referendum result was a small majority (which would not have been sufficient in most EU countries to affect a constitutional matter), the balance of opinion in UK residents is clearly in favour of Remain.

    Whether MPs will wish to ignore their constitutional duty to do the best for all constituents whether or not they voted for them or could vote remains to be seen if invoking article 50 is put to Parliament.

    • Robin

      You wasted a lot of time on speculating about your figures. 38% of the voting electorate did not vote. Full stop. Whether they wish they had done so, or speculating about which way they would have voted or if under 18’s had been able to vote etc, etc, is totally irrelevant. In a sentence…they did NOT vote and no amount of speculation with figures will alter that fact. It really is that simple. Got it?

      • Martin Cahn

        This was written ages ago now but the conclusion was confirmed by Kings College. My main point was that this referendum was advisory and it seems absurd to leave when it is clear that there is hardly a simple majority in favour. In the end it has resulted in the capture of government by a far right clique representing a small minority of the electorate and triggered a wave of xenophobia. That should send you into a state of panic.

  • Graham

    I think some of the more fundamental questions that should be asked are those regarding the legality of the outcome, especially in the light of the fraudulent claims expressed by the leave campaign, they were outrageous lies and certainly affected the outcome.
    When was a political party allowed to tell such blatant lies and the press allowed to print such outlandish stories? I thought the press were bound by enforceable standards? Those elected representatives are surely breaking Parliamentary rules? Doesn’t anybody have any integrity anymore?

    • Mark Adams

      A bit late on this but what about all the Remain lies, which have proven to be false?

      • walkinthepark77

        What were the remain lies?

        • Robin

          Where would you like us to start? Get hold of the booklet that was circulated by Cameron’s government at a cost of £9 million of taxpayers money and look through it and point to all the things that have happened that they said would happen….there’s not many because most were lies – your word, not mine. I prefer speculation and conjecture from both sides. No one could actually lie because no one could tell what would happen in either case. It is a 2 door syndrome, where we will NEVER know what would have happened if we had gone through the other door. We can speculate, but we will never know!

          • Martin Cahn

            Most of the predicted impacts are coming true – as most economists had predicted over a period of time. The main prediction was a reduction of expected GDP over a period of 10 years or more of up to 10%. The way financial and car firms are now planning to leave the UK that seems accurate.

  • TLCh

    Totally with Graham on this. The Brexit campaign was purely propaganda not based on information or even solidly researched predictions. Plus, who knows how many of the Leave voters regretted their decision once they got a better idea of the potential consequences after the event.

    • Cecilia Killman

      I have only heard of an increase in people wishing they had chosen Leave .. These are Remain voters who say they are now glad to be coming out of the EU. This referendum has brought much information to light about the corrupt European Union which otherwise we would not have known about. We understand far more than some Remainers gave Leave voters credit for. It was so much easier to pick up on the Liberals very insulting statement that Leavers did not understand what they were voting for when indeed, we wonder if Remain voters knew why they wanted to stay. I never saw such a bad show of poor losers in my whole life in any democracy and I have lived many more years than some of you. One of the man reaon or th chge t Lee is the mass immigration which countries cannot cope with and which is changing the face, raditions and laws of our country. The law is not fair anymore and it took time to realise that even our laws have been, and still are, ruled by the EU. I could go on and on but I guess I answered. I along with many have had remain voters saying they voted remain but were glad we were leaving the EU

    • Robin

      See my reply above to walkinthepark77. Pure speculation on everyone’s part….both Leave and Remain. I can point out several things the Remain side campaigned on that were purely speculative. None of the leave voters I have spoken too say they would change their vote either, so again it is pure speculation that any of them would change their mind or regret their decision. I do know one person who voted to remain saying they would change their vote, but neither can be representative of the majority, so why even raise the question? Let me put it into clear concise English for everyone…Politicians voted to give the people a referendum on leaving or remaining a member of the EU. The result was around 52% in favour of leaving and around 48% for remaining. What part of that does a lot of people not seem to understand? Those people who didn’t vote at all, those who now say they would change their minds etc. is completely irrelevant. That’s what a referendum or an election or voting for something is all about. You vote, you get a result, you abide by the result. Simple!

  • Averyius

    Austrian citizens living abroad may vote by post in Austrian presidential and parliamentary elections, as well as referendums, for an unlimited time after leaving Austria. They must enrol on a dedicated foreign voters’ register and must renew their registration every ten years.[4]
    I live in Austria and am still a British citizen. I was not allowed to vote in any referendum in the UK which effects my status in Austria. I have heard and read so much about bi-lateral agreements between the UK and Austria. There should be an EU law which deals with all EU citizens equally. Why is it then that an Austrian citizen can always vote from outside Austria in any elections and referenda and a British citizen can not? This is not fair and not reciprocal. The over 1 million British citizens living in the EU should have had the right to vote in the EU referendum. One person talks about wisdom as you get older. What about the wisdom gained by travelling and living abroad and seeing a bigger picture and losing the narrow inbred thinking that comes from only living in your own back yard and among your own people and culture and speaking only one language and hearing only that point of view? The EU is a good and progressive idea. We share a common basic culture and history and should go on helping one another and understanding one another and avoid any more armed conflicts which result from distrust and rivalry and feelings of elitism.

    • Ruth Jackson

      British citizens living abroad Were allowed to vote, ..but only if they had lived abroad for LESS than 15 years! If they chose not to that was their right. And what utter clap trap about broadening your horizons…the EU isn’t progressive in the sense you refer to…its main aim is a “federation of the people’s” soverignty is an evil they want rid of ..we don’t share a common basic culture nor history..each country has its own culture and history..we have always helped one another (2 world wars ring any bells) and have an understanding yet stood as individual countries for many many years. You have just also insulted the British people with your “inbred” comment, that’s a narrow minded view if very there was one! As for travel..well that will continue ..sorry to say that you have a very blinkered ideal about the EU as it is now…it was never voted for or elected by anyone..it evolved in the 90s ..it is no longer fit for purpose !

    • Robin

      I agree that there SHOULD be many things. The plain and simple truth is that there are some things that are OK for some people whilst at the same time there are some things that aren’t with others. This is not an ideal world for those who want everything their way. We can petition, protest and campaign, but like Lincoln said, you can never please all of the people all of the time and what suits one person will always annoy another!

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