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Image of Alan Winters17 December 2018

L. Alan Winters CB, Professor of Economics and Director of the UK Trade Policy Observatory.

The UKTPO exists to provide independent and objective advice on the economics and law of Brexit and trade policy. The question of whether to hold a ‘second’ referendum is essentially a political one. However, how to organise such a referendum is a technical question on which economists have something to offer.

Given the divisions in the country it seems plausible to argue that any referendum should offer three alternatives:

But organising a three-way contest seems quite challenging.

For example, Professor Vernon Bogdanor suggests a two-stage referendum in which we ask first whether people want to leave and then, a week or so later, what form leave should take. Professor Meg Russell, in an excellent contribution to the Today Programme today (17th December 2018; at 2.39:50) characterised this as ‘difficult’, because how you vote in the first round is influenced by your hopes or expectations of the outcome of the second.

Professor Russell is quite correct – Professor Bogdanor’s ordering replicates the fundamental problem with the first referendum: no-one would know what ‘leave’ entailed. However, if we simply reversed the order of the questions, this problem would be avoided. Hence, on the assumption that the details of each option had been properly explained, I recommend a two-round referendum with:

  • Round 1: ”IF we leave the EU, would you prefer ‘no deal’ or ‘Mrs May’s deal’?”

Then, when the answer to this is known (say a week later),

  • Round 2 asks “Now you know how we would leave, would you prefer leaving or staying?”

The decision that would face the UK public in a referendum is sequential – the step of leaving inevitably precedes the step of implementing post-leave arrangements. Economists have long understood that the way to make optimal decisions in such circumstances is through a process known as ‘backward induction’. You start with what will be the last step of the actual process (which of the forms of ‘leave’ you prefer) and work backwards to determine whether the best of the leave options is better than remaining. So, in the first step, the UK electorate determines whether it would prefer no deal to Mrs May’s deal, and then knowing what it will get from leave, whether it wants to go down that path at all.

The opinions expressed in this blog are those of the author alone and do not necessarily represent the opinions of the University of Sussex or UK Trade Policy Observatory.

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  • Sheila Page says:

    But the decisions cannot be separated and made sequential because all voters will know that there is a second round, and that the choice then will depend on the choice in the first.

    If I l support leave under any circumstances, then, yes, I should vote for the leave option I prefer in the first round. If I support Remain, with May’s deal as a 2nd choice, but think that Remain is more likely to beat No Deal than the May deal, should I vote for No deal in the first round? As in any 2 round election, the polls would become extremely important for strategic decisions.

    There is also the problem of campaigning momentum. If the only 2 choices being discussed in the 1st, long, campaign are the 2 leave options, these will be perceived as the real options. Even Remain supporters will be campaigning for one of them. In order to decide to vote for one of them, voters will have decided that it is acceptable. How easy will it be for supporters of Remain, who may have campaigned for the winning Leave option in the first round, to abandon arguments used over perhaps 6 weeks and persuade other voters to abandon their initial choice in the week between rounds?

    • L Alan Winters says:


      Thanks for your comment.

      Both your points have some force, but neither seems overwhelming to me. The logic of the first is that remainers would be campaigning now for ‘no deal’ precisely because they think it will be rejected by Parliament. We don’t see that. I think most remainers would fear ‘no deal’ so much that they would not risk promoting it pro tem. It is true that remainers may keep a low profile in Round 1 (as they possibly are doing now with regard to the internal war in the Conservative Party), but that seems unobjectionable.

      On the second point I don’t think the position “I want to remain, but as an insurance policy prefer ‘Mrs May’s deal’ to ‘no deal’” is too complex for the electorate to understand. It would be important for everyone to understand the two-stage nature of the referendum, but again that is not beyond the vast majority of electors.


    • Keith Macdonald says:

      I do not think Remain voters would be wise to participate in the first vote – nor would it be honest to do so.

      There is no reason why Remain supporters should be silent in the campaign as I am sure lies will continue to be told and will need correcting but they should in general not make the positive case for the EU until the second campaign. Both campaigns should be a month and there needs to be much tighter control of spending, particularly on social media and outside interference. No dirty tricks.

      • John Kemp says:

        I disagree with Keith Macdonald. It is ESSENTIAL that REMAINERS do vote in the first referendum. I’m worried that some will think: “As a remainer, this doesn’t interest or apply to me. Plague on both their houses – I’m not voting!” If remain then loses the second referendum, it is important that the country as a whole will have chosen the least worst option. Ideally both votes should be on the same occasion, but it all gets very complicated, arguably TOO complicated, and there would need to be exhortation (but not compulsion) to answer all three questions
        Question 1 would be unchanged: “IF we leave the EU, should we leave with T. May’s deal, or with no deal?
        Question 2 would need to be: “If the outcome of Question 1 is to leave with the deal, would you prefer to
        Question 3 would need to be: “If the outcome of Question 1 is to leave with NO deal, would you prefer to

  • Keith Macdonald says:

    This is absolutely correct. The problems we face just are now are essentially caused by the fact that there is no agreement about what Brexit is and therefore what the 2016 vote meant beyond opening negotiations about leaving.

    The two people who chaired the winning campaign (Johnston and Gove) disagree about what the result meant so there is no hope for the rest of us.

    There are 4 relevant Brexit options. The first is what was promised in the campaign – most of the benefits of EU membership and few of the commitments. That has now disappeared along with any mandate beyond opening negotiations. It has been replaced by May’s deal, no deal or long negotiations to join the EEA (unrealistic in my view). There is no evidence any of these command majority support.

    To end this agony and get back to this country’s real problems we need clear propositions that are capable of being implemented. That means one of the two realistic Brexit options against remaining.

    There are those who say that the no deal option is too damaging to put before the British people. We need to show more confidence in our fellow citizens than that. After all the lying and fantasising of the last few years, it will be healthy to have definite and clear propositions which its supporters will have to back with evidence.

    Once we know what Brexit is actually going to look like we then need at least a month to allow proper discussion about how it compares to our current membership before we take this vital decision.

  • Peter says:

    There is a fatal flaw – remainers could be accused of gaming the system, or could game the system. As a remainer I would vote for a hard Brexit in the first poll, to discourage adoption of any leave option at all in the second poll. Further, even if I did not do this, if hard Brexit won the first round, there could be the accusation that remainers had voted for it to increase the chances of staying, given more people might prefer remain over hard Brexit than might prefer remain over soft Brexit.

    A preference vote system allows people one fewer votes than the number of choices (N), which must be ranked as 1 to N-1, where 1 is your top preference. You don’t need to put down all preferences if you do not want to, in which case your vote might not count in the end. The first choices are tallied. If one option gets a majority it wins. Otherwise you drop the option with the least votes and re-distribute first choice votes for that option according to their second preference. You carry on doing this until one option wins a majority, which might only happen once only two options are left.

    Comparing the benefits of the reverse auction in the article against a preference vote system (assuming 3 choices – hard Brexit, soft Brexit, remain), the reverse auction loses. With an alternative vote system you always get an outcome that the majority of voters support as either their first or second preference, and there is no obvious incentive to game the vote.

    For a reverse auction if all remainers voted for hard Brexit first time around and remain second time around, it could be the case that remain wins, even though soft Brexit was actually more popular. Even if no remainers voted for hard Brexit in the first round, the accusation can still be made that they did, leaving a number of people thinking they have been had. There is no way to prove otherwise, whereas with the alternative vote system all the stats are very clear.

    • L Alan Winters says:

      Peter, thanks for responding.

      You are right that this is a flaw in the argument I presented – but maybe not a fatal one. As I replied to Sheila, it is not clear that risk-averse voters would have the incentive individually to game the system in the way you suggest. To do so, they would need to be very confident about how people will vote in the second round.

      Suppose a remain voter valued of each option according to the government’s economic assessment of November: ‘no deal’ -7.7% (i.e. a 7.7% decline in GDP), ‘Mrs May’ -2.1% and remain 0%.

      And suppose she also reckoned that if the second Round were
      (A) remain vs. ‘no deal’, ‘no deal’ would have a 20% chance of prevailing, and that if it were
      (B) remain vs ‘Mrs May’, ‘Mrs May’ would have a 60% chance of prevailing.

      The expected value from vote (A) is -1.54% (= -7.7*0.2 + 0*0.8) and from (B) -1.26. That is, ‘no deal’ is so nasty that it is not worth the risk of promoting it to the second round. (And if the voter is risk-averse, she would be even more inclined not to risk it.)

      You worry that someone would try to coordinate the promotion of ‘no deal’ by remain voters, but I suspect that no remainer politician would do so because that would discredit the referendum.

      Whether the accusation that such coordination had occurred could be made to stick if it was false, is even more difficult to predict in these fractious days. However, it surely depends at least partly on the objective situation that individual voters would be very cautious about adopting the strategy.

      It is also worth noting that you were implicitly assuming the ranking above – viz. that ‘Mrs May’ would be the second choice for both remainers and ‘no dealers’. But that is not necessarily true: both Justine Greening (ex-cabinet) and Shanker Singham (Brexit cheer-leader) have declared it to be the worst of both worlds. So it is entirely possible that ‘no deal’ gets through to the second round for perfectly legitimate reasons.

      Finally, I was not seeking to compare a two round ballot with an alternative vote (AV) system, but it worth noting that the latter can have fairly unintuitive outcomes. For example, in a three way ballot, one can easily construct outcomes whereby the winning choice commands the smallest number of first and second votes from the whole electorate.

      • John Kemp says:

        For the record, I did some worked examples of why a “classic” STV vote would be unsatisfactory.

        For a start, a win on a 34:33:33 vote would be disastrous. Obviously!!!

        For this particular nuanced choice, the STV is clumsy and unsatisfactory. Suppose in the first count, remain wins 38% over the assorted brexiteers. They get in effect two votes, and the remainers are completely in their hands. Remain wins the first round, but the result is haphazard, and dependent on how the brexiteers split, we could end up staying in the EU, leaving with a deal, or leaving without a deal – consider three very possible scenarios:

        REMAIN 38; DEAL 29; NO DEAL 33.

        DEAL is eliminated, and if their second choice votes go

        REMAIN 14, NO DEAL 15, we get a total of REMAIN 52; NO DEAL 48.

        Remain scrapes home.

        Suppose the first count is the same, but DEAL splits differently:

        REMAIN 38; DEAL 29; NO DEAL 33.

        DEAL is eliminated, and their second choice votes go

        REMAIN 11, NO DEAL 18, giving a total of REMAIN 49; LEAVE WITH NO DEAL 51.
        Remain still won the first round, but we end up leaving in a disastrous no deal.

        Suppose all the brexiteers split differently, we could get

        REMAIN 38; DEAL 33; NO DEAL 29. NO DEAL is eliminated, and their second choice votes go REMAIN 0, DEAL 29, giving a total of REMAIN 38; LEAVE WITH A DEAL 62.

        BOTTOM LINE: Alan Winters’ idea is the best, maybe slightly tweaked as I’ve said elsewhere on this blog.

  • Keith says:

    I prefer Remain or Leave first – keep it simple and clear to voters will maximize attendance at the referendum. If Leave the Soft or Hard Brexit second, that way Remainers at least can vote for the soft Brexit and feel part of the leave process. Most likely remain would win in the first round anyhow. If you do the Leave alternatives first then it will appear to some that a decision has been made and the second round will have a lower attendance due to voter fatigue.

  • Peter Land says:

    Why 2 rounds? Give people two ballots on the same day. If question 1 results in acceptance in the current deal then so be it; burn the second ballots. Two rounds prolongs the agony.

    Overall this is a great idea though. Glad it got picked up by the Economist.

    • John Kemp says:

      I disagree with Keith. I very nuch think that Prof. Winters’ idea IS the answer, except that I agree with Peter Land that both votes should be on the same day on the same ballot paper (but disagree with Peter who seems to be implicitly changing the questions).

      I also think it should be a REQUIREMENT to cast both votes! Why?

      (1) It avoids an inherent problem of remainers opting out massively, but misguidedly, in the first vote. I think most remainers would strongly prefer May’s deal to no deal and if they don’t vote in the first question, they may hand a no-deal brexit to the brexiteers on a plate. What I would call inadvertent and counter-productive gaming – and which could lead to the result most remainers least want. If they don’t vote in the first question, it’s not so much dishonest, as culpably stupid! Why would any remainer want to use only one vote and as a result end up with their least favoured option, when brexiteers use both their votes?

      (2) Why would, or should, remainers opt out in this way by note voting? It’s giving up without a fight, no different (in the end result actually) from sulking.

      (3) “We don’t do compulsory voted here!” – the cry will go up. No, but the second referendum is NOT two votes, in which one can vote for either, both, or neither. It is (or could and should be, if something close to Prof. Winters’ scheme is chosen) a unique mechanism custom carefully crafted to resolve in as honest, open, and democratic way as possible, a unique non-binary problem.

      It will only work properly if people vote on both questions. And it’s not compulsory, but votes have rules. In a general election, if you vote for more than one candidate, all your votes are discounted. Tough! It’s the rule, and has not, to my knowledge, ever been seriously challenged. What’s different in principle in an election where you have to use two votes? Nothing! In both types of election you have free choices: not voting, putting the approved number of Xs on the paper, or putting other than the approved number of Xs on your paper, and thus wasting your vote. It’s a free country and you won’t go to prison for it!

      (4) It encourages the voter to READ THE QUESTION. Always a good idea, and a matter at risk in this peculiar situation.

      (5) It encourages honest and informed campaigning to have the double vote on the same day. Campaigners would campaign in parallel for Remain, May’s deal, or a No Deal brexit. How to allocate spending allowances would be tricky, as the situation has no symmetry. Maybe a ratio such as £3m for Remain, £2m for May’s deal, and £2m for the No Deal campaign.

  • Danny says:

    A two stage referendum with three options carries risks of being gamed either way, with voters having to think tactically about whether voting in round one for what they think is a less attractive option will make their preferred option more attractive to more voters in round two. However small a number of people think like that, the stakes are so high that it shouldn’t be risked if there are alternatives. And there are. There could be a single day’s voting, in which the three options: May’s deal, no deal brexit, remain, are all on the ballot and are ranked by voters, with the lowest preference eliminated and second preferences reallocated at full value. We have this system of voting for London mayors, so it’s not beyond the electorate’s understanding how to rank preferences.

  • Sheila Page says:

    I think we are in danger of over-complicating this. A few opinion polls and/or ‘indicative votes’ in Parliament could establish whether there was any substantial support for a hard Brexit. I have seen no evidence for this up to now. There are many people who think (or at least say) that there are better soft deals obtainable, but that is like saying that there are other better qualified people than those actually standing in an election. Maybe true, but elections can’t cater for that. There is the problem that the political statement could cover a wide range of outcomes, so there is a risk that the vote would be almost as much between a known and an unknown option as in 2016, so it would be reasonable to expect a clearer statement of how the government interprets it than we have had. It seems best to concentrate on how to define a simple question between two clear and feasible alternatives.

  • Jopie says:

    The alternative vote option has the obvious practical advantage of needing to organise only one vote. The suggested risk of a counter intuitive outcome (the eventual outcome being the one with the fewest first preferences) will need to be managed, but is also implicit in the backward induction model – you could argue the av option is more honest and open about it.

    As an aside, the “political” question of whether a further referendum is required can also be resolved. Run a 3-way av vote in parliament between hard brexit, soft brexit, another referendum.

    • John Kemp says:

      It’s not clear what sort of 3-way vote Jopie has in mind, but it would HAVE to be a free vote. The challenge of devising an acceptable three way choice remains in any Parliamentary vote, just as it would in a new referendum. But however it is devised, ‘another referendum’ would probably win in Parliament because the Remain majority would vote for it in the knowledge that the final decision would be going back to the people anyway and thus they would not simply be negating the 2016 referendum. The first stage of Alan’s ‘backward induction’ could easily be adopted by Parliament: remainer MPs are obviously sophisticated enough to cope with the ‘IF’ question, and IN THIS SCENARIO – i.e. as a prelude to a second referendum – most remainers and some brexiteers would vote for and give May’s deal a majority over no deal. Then we could have a second referendum on Remain vs May’s brexit deal.

  • CouponVPS says:

    There is no reason why Remain supporters should be silent in the campaign

  • […] UKTPO: Organising the ‘Second’ Referendum’ […]

  • […] There is, however, a potential problem. If Remainers believe that “remain” will defeat “no deal” in Round 2, they may game the system by voting for “no deal” in Round 1, even though they actually prefer “deal” to “no deal”. Of course, this presupposes that they have huge confidence that they know the outcome of Round 2 and/or that they do not think that “no deal” will be such a disaster. Thus, it may not be such a big problem in practice (as I explain in a recent UKTPO blog post here). […]

  • Mike says:

    As “No deal” is so unpopular in Parliament, then let our elected politicians vote it out and then re-run referendum with the other options – either May’s deal or Remain – only on the ballot paper…

    Shared responsibility…

  • My favoured format would be a three-option referendum with two rounds of simple voting. After the first round the least favoured option drops out, and then after about three weeks there is a runoff between the remaining two options. In theory this is equivalent to AV (“instantaneous runoff”), but it is simpler for voters to understand, it gives time to concentrate the mind and have further campaigning after the first round, and most importantly it incorporates more “practical democracy” – voters have to care enough about the the remaining two options to get themselves out to the polling stations. It is more trouble and more costly to organise than a single round vote, but in this case the importance of the matter is so enormous that this is a trivial consideration.

    All three campaigns would have to produce a detailed plan. Theresa May’s “deal” would have to be much more clearly defined than the present Political Declaration, either committing to a very close economic union with the EU and hence no backstop and no trade deals with other countries; or else committing to implementing the backstop and customs checks between the UK and Northern Ireland. The No deal campaign would have to say whether they were going to pay the divorce bill and have an implementation period of several years (still paying into the EU) while the UK negotiates trade deals with other countries and with the EU, or else “walk away”, go over the cliff, and in effect declare economic war on the EU.

  • It’s a really good thing someone decided to bring this topic up. Everyone should be encouraged to speak their voice.

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