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.

        • PAD

          Kings College..partnered by Common Purpose.
          mm.Says it all.

          • Martin Cahn

            Just because one Dept does international leadership training has no bearing on the work of the unit in King’s College responsible for this analysis. If you approach data with this cynicism you will never learn anything. In any case it appears that Common Purpose is placing King’s College students in Kuala Lumpur, hardly in the EU.,..

          • PAD

            Kings College no doubt gets its legitimacy from somewhere….unlike Common Purpose.

        • Bunny-Gee

          David Cameron and others in the government repeatedly stated the referendum was binding. It was also WRITTEN in their propaganda leaflet (which cost us £9m) that it would be binding. If that doesn’t make it binding, I’m a banana.

          • Martin Cahn

            The material advising about the legal status says it is advisory and the act authorising it says nothing about it imposing an obligation, which it would have said for a constitutional issue like this. Cameron’s comment is a promise binding on him ethically ( but not legally). But not on his successor. In effect it is about as legally binding as the £350 million. Why are you not protesting about that? Maybe you are indeed a banana (curved?).

      • Alan Smart

        It makes the difference that ypu can only claim what actually occured leave can claim to be the will of 37.5% of the electorate, not that it is the will of the people. There is absolutely no evidence to support that statement.

        • Bunny-Gee

          And if Remain had won then it would have been “the will of [a lower percentage] of the electorate, not that is (sic) the will of the people”. So, your point is, exactly? A question based upon your own elaborations, not mine, but reasonable elaborations which extrapolate in the Leave vote’s favour you will, doubtless, concur..

  • 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.

          • Alan Smart

            You havent actually said what the remain campaign lied about.0

          • Robin

            Did you not read the booklet sent out by the government to every household?

            How about…’More than 3 million jobs in Britain are linked to exports to the European Union.’

            The original number came from a paper developed by the pro-EU Britain in Europe group in 2000 – 15 years ago. The Remain campaign has claimed it does not use the figure, but here it is, in the booklet! The economist who wrote it, Dr Martin Weale, dismissed it as “pure Goebbels” and added: “In many years of academic research, I cannot recall such a willful distortion of the facts” in relation to how the number has been used since.

            Or how about….’EU cooperation makes it easier to keep criminals and terrorists out of the UK.’

            The EU’s own border agency Frontex has warned that lack of coherent migration policy across the 28 member-state bloc has led to “a risk that some persons representing a security threat to the EU may be taking advantage of this situation… there is clearly a risk that persons representing a security threat maybe entering the EU”. As the UK is part of the EU that means that persons representing a security threat, such as terrorists, could also be entering the UK.

            Let me know if you want more!

          • Alan Smart

            Robin you are making an eroneous supposition. All of these things are becoming facts now, not scares. The timing was admittedly wrong but nonetheless the predictions are coming true.

          • John Davis

            We haven’t actually left yet and the £ took a big hit pushing inflation and prices up, we are all already worse off, after Brexit that will multiply, but you carry on with your la la land delusions.

          • John Davis

            A recent study by the IFS says after Brexit we will be £15B a year worse off.

      • John Davis

        Care to name any? Economy will bit hit – it is. We will lose NHS staff – we have.

    • Bunny-Gee

      Even with everyman and his dog on your side and despite the Remain side’s constant and consistent deceptions, you lost. Get over it. I’m LOVING it. 🙂

      • John Davis

        Loving being the reason inflation is up, we are bottom of the G7 for economic growth, race hate is up, the NHS are losing staff due to the vote……… who actually won? Certainly not the UK? The UK lost.

  • 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!

      • Alan Smart

        Speculation which as time passes appear to be coming true. I repeat you havent actually stated what lies were told by remain.

  • 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 !

      • Averyius

        Whats with the 15 years? Why not 5 or 10 or 20? I have the absolute right to vote on things going on in my country of origin and where my family still are no matter how long I have lived in another part of the EU or anywhere else. That is the whole point, there is n´t supposed to be any difference between all EU citizens in that respect. The two world wars were due to perceived differences and the rivalry and distrust that a united Europe would work against. This is the idea started by Woodrow Wilson with the League of Nations and later by Richard von Coudenhove-Kalergi and the Pan European movement which was supported by many famous people like Albert Einstein, Sigmund Freud, Thomas mann, Otto von Hapsburg and many more. https://en.wikipedia.org/wiki/Richard_von_Coudenhove-Kalergi
        My Grandfather was a Bugle Major in the Kings Royal Rifle Corp and was bayoneted by German soldier in WW1. He died decades later as a result of his wounds because of the inadequate medical treatments of the time. I best friend here in Vienna is German and he is like a brother to me! My ex-wife is Austrian and my daughter was born here.

        No common culture and history? Maybe you should study European languages, history, archaeology and anthropology like me. So Britannia was not part of the Roman Empire was it? So therefore most English vocabulary is not clearly Latin in origin? The British peoples did not wander into north west Europe thousands of years ago? There is no link to the rest of the Celtic people in Europe? There was no migration of German tribes into what is now England? No Viking influence? Where did the Angles and Saxons come from and why is the other half of modern day English actually a mixture of old Norse, German and French with some other languages as well? The list of things which are clearly of the same origin and which have influenced one another over centuries is endless. The Royal family of the UK ARE GERMAN!!!!

        So what is evil with a federal state? But it is not written anywhere that that is what the EU currently wants? I think the British would still have fish and chips and be the best at making it as well as all the other countries keeping their unique regional traditions and specialities. I would welcome a federal sate. So the USA for example is evil and does not work? Eh! There are so many differences between parts of the USA in dialects, languages and ethnicity. Funny how it works but somehow a federal Europe cannot or would not? I certainly do not regard my many “foreign” (E.U.) friends as being evil and certainly not my daughter who is Austrian and born here in Vienna. Only a dictatorship is evil. A person has to have a grander picture which you do not seem to grasp. i have mentioned past historic and pre-historic commonalities and relationships between today´s UK and other European peoples but equally one must look ahead into the future. For example how do you deal with a Russian invasion of Europe which could happen if you have a patchwork of totally independent countries? Is there a guarantee that the USA would definitely help? Nope! I don´t think so. In fact they are sick fed up with not being able to talk to a single united Europe and having to play big brother coming to our rescue. Think about the European Space Agency and future projects like the colonisation of Mars. Only a united Europe can work together to achieve great things and protect the environment etc.

        The EU as an evil empire? Have a look in the internet just how evil the British Empire was and the atrocities committed by us! Funny my parents, grandmother and teachers conveniently forget to ever mention such things and always portrayed us as being the good guys.
        Please look up on the internet the many websites which explain how the EU works. https://www.google.at/search?q=how+the+eu+works+pdf&oq=How+the+EU+works&aqs=chrome.2.69i57j69i65j0l4.22913j0j7&sourceid=chrome&ie=UTF-8. You will see it is perfectly democratic. The politicians you elect in the UK are members of the council of ministers and parliament. You and all EU citizens can vote for the members of parliament. Parliament is gaining in it´s powers and influence. https://www.theguardian.com/commentisfree/2013/may/20/eu-democratic-deficit
        The UK government in London has thousands more un-elected civil servants than the EU which is what the European commissioners are. They make suggested policies. The council and parliament may or may not agree and pass them.

        Only a dictatorship can be seen as evil and the EU and future United states of Europe is not and will not be a dictatorship. https://uploads.disquscdn.com/images/7def603f00b55397ef05a1e064ab28527d383336f8139027aa426105b4b35aeb.png

        Insulting the “British” people eh? Who are they? Maybe the equally large or even greater number of non EU citizens, non white Christian people ( Christianity is something we also have in common with other EU citizens such as the Polish who saved Europe from becoming a muhammadan world ruled by the Turks back in 1683 right here in Vienna!) from the other side of the planet who have been flooding in for decades? No I only insult my enemies. It is a kind of closed system when a small group of people just sit in the same place and discuss things and do things only there and amongst themselves.

        I certainly hope freedom of travel does continue without very pesky passport controls and someone checking my luggage every inch of the way as well as paying with the same coin as it once was throughout the Roman Empire. I love being able to just cycle down to Bratislava or drive to Italy or Germany without interference. And I do not want to maybe now have to go back to the stressful system of applying and paying for a residence and work permit every year.

        It was very short sighted of anyone back in 1973 when the UK did indeed vote for EEC membership not to think it would eventually evolve further. I was only 14 and my school friends and I were in favour of it and we certainly hoped it would bring about a United States of Europe. I do not think the EU has outgrown it´s usefulness. The World and Europe is evolving and the EU, Pan Europe or whatever it may be called in future is just starting to get going! Like Arnie said in Terminator “I´ll be back!”. I mean by that, that the UK will be back asking to re join. Mark my words!

    • 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!

  • Sam Carruthers

    I voted leave from a backpackers Australia (the other side of the world). Many other backpackers moaned at the result but couldn’t be bothered to vote. That’s their fault and goes to show that the fact of the matter is they just didn’t care enough. So you can hardly put them in the Remain box anyway. If they actually cared they would have read more about it and likely would have turned to voting Leave.

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