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Lots of people seem to be calling for a second referendum on the United Kingdom's status as members of the European Union.

The Labour Party policy is to renegotiate a deal with the European Union and then put that back to the public against a Remain Option.

However this to me seems very unfair to people who genuinely voted to leave at any cost. (I voted Remain but don't think it is right to just ignore the result)

If there were to be another referendum I can only see two 'fair' options. Either:

  • To Leave with a deal, or without a deal (Either way the Leave vote from the 1st referendum is respected)
  • To Leave with a deal, without a deal or remain. (If people have genuinely changed their minds then they can show it here, but if they haven't and they hate the deal then they can still vote to leave)

My question here is would it be possible to organise a referendum like the second one, where there are more than two options on the ballot paper?

If this is possible, how would the votes be counted? A simple most-votes wins could end up with more people voting to Leave in some form, but the single remain option ultimately getting more votes.

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    Are you more interested in the legal issues, or the challenges of making a fair 3 choice referendum?
    – divibisan
    Nov 7, 2019 at 17:59
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    The important thing, in the view of many Liberal Democrats, is that the public should have the chance to approve or disapprove the deal they are actually going to get, rather than the fantasy one they were offered in 2016. Such referendums are foreign to the UK system - and have led to a situation where there is general disagreement as to what people voted for. (that's assuming that the vote was valid in any case and not heavily purchased by Russian influence). But if a deal can be agreed with the EU, then put to a confirmatory ballot, that would ensure clarity as to what was on the table.
    – WS2
    Nov 7, 2019 at 18:32
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    Justine Greening, at a very early stage proposed a three-choice referendum, with transferable vote. The problem is that there is a large political body who do not want the public to play any further part whatever, presumably in case it produces the wrong result. An awful lot of concern has been expressed for fishing fleets. However it is worth remembering that the UK's computer games industry is worth five times as much as fishing. We do need to keep these issues in proportion.
    – WS2
    Nov 8, 2019 at 9:43
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    The goal of those who want another referendum is to cancel Brexit. So the choices they want to present are typically a) Remain, b) leave with a deal, c) leave without a deal. Since the leave vote is then split in two, remain comes through the middle and wins.
    – Valorum
    Nov 8, 2019 at 16:59
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    Valorum - let's hope so!
    – Michael Harvey
    Nov 8, 2019 at 21:23

8 Answers 8

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There's one problem with any referendum with more than two options: Arrow's Impossibility Theorem. This states that if you have three or more options, then the following cannot be simultaneously satisfied:

  • If every voter prefers alternative X over alternative Y, then the group prefers X over Y.
  • If every voter's preference between X and Y remains unchanged, then the group's preference between X and Y will also remain unchanged (even if voters' preferences between other pairs like X and Z, Y and Z, or Z and W change).
  • There is no "dictator": no single voter possesses the power to always determine the group's preference.

Given that, a referendum with three options is inherently risky. There's no guarantee the referendum results are what the country wants.

Concrete example: suppose the three options are "Leave with deal", "Leave without deal", and "Remain", and the results are 35% Leave with deal, 20% Leave without deal, and 45% Remain. If you were the Prime Minister of the UK, what do you do now? Technically, Remain had the most votes, but you can't know if the 20% that voted for leaving without a deal would have preferred leaving with a deal compared to remaining. If you Remain now, you could very well be doing something the country does not want.

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    It is not perfect, but the question is whether it is better or worse than the alternatives.
    – Patricia Shanahan
    Nov 8, 2019 at 15:05
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    "There's no guarantee the referendum results are what the country wants." if we have to be pedantic, there is no guarantee that the result from two options are what a country wants. Even if there is a single option, there is no guarantee it represents that, as well. The reason is that it represents the people who voted and even then only a percentage of them. Assuming 75% of the people who vote in a referendum choose option 1, that's still not "the country" if there was 50% turnout. That is what 37.5% of the population said they want.
    – VLAZ
    Nov 8, 2019 at 15:57
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    Technically, the paradox in Arrow's theorem arises from the mere presence of three alternatives. Conflating two of the answers (leave-with-deal and leave-with-no-deal) into one does not resolve the issue. So there is nothing inherently worse in having a referendum with three choices rather than one with two choices; simply, neither method works (in the sense of the theorem).
    – Federico Poloni
    Nov 8, 2019 at 16:47
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    xkcd.com/2225
    – leftaroundabout
    Nov 8, 2019 at 16:48
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    FPTP is not the only voting system that the referendum could use.
    – Richard Ward
    Nov 9, 2019 at 9:25
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I can't speak to legal issues with UK referrendums (though my understanding is that Parliamentary Sovereignty means that pretty much anything is possible if Parliament agrees to it), but the "fairness" issues would be significant. There are many ways to set up such a poll, but every option is going to influence the result in different ways.

One possible way to do what you want (have a second referendum without fully ignoring the results of the first) fairly, without using exotic voting systems, is with two linked referendums:

  1. Should the Withdrawal deal negotiated by Johnson with the EU be enacted?

  2. If the Withdrawal deal is not enacted (ie, question 1 is rejected), should the UK leave the EU with no deal, or remain in the EU?

This plan has a few pros:

  • It respects the original referrendum result and negotiations by giving priority to "the deal".
  • Since there are never more than 2 options, it doesn't split the vote for either leave or remain.
  • The winning outcome will be supported by a majority of voters. In a multiple option system, it is possible that the winning outcome will only be supported by a plurality.
  • There are no complicated systems that might confuse voters
  • It fully resolves the Brexit situation, since all possible outcomes are full plans that could be implemented. There is no option that is ambiguous about the outcome.

And a few cons:

  • It does give an advantage to leaving with a deal, since that choice has priority
  • There is the possibility that tactical voting could result in a non-ideal outcome. For example, Remain voters might reject Question 1 to get the chance of voting Remain on Question 2, but then end up stuck with no-deal
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    If a two-question referendum was used, I think a much better phrasing would be 1) Leave/Remain?, 2) If leave, Deal or No Deal? It's a more natural grouping and means fewer people are going to be put in a difficult position with the first question. I suspect that most (admittedly not all) people who vote leave would prefer either deal or no deal to remain, but there are a significant number of people who would rank the choices as 1) Remain 2) Deal 3) No Deal, which makes your question 1 hard.
    – Princess Ada
    Nov 8, 2019 at 9:39
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    @Valorum I don't understand why people insist that a second referendum would be anti-democratic since it's literally more democracy. People voted for leave as an abstract concept. Based on that, the government made a plan to leave. It only seems right to give the people the right to affirm or reject the final plan, now that they know what it is. Public opinion can change due to changing circumstances. It makes no sense to privilege the will of the people of 2016 over the people of 2019, especially when we now know that Leave means something different than it did in 2016
    – divibisan
    Nov 8, 2019 at 17:20
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    @Valorum This isn't the place to argue this, but people have never voted on either Johnson's deal or a no-deal Brexit. There was a slim majority in favor of some kind of Brexit, but, clearly, Parliament has failed to decide on what that means. So, why not put the actual plan back to voters and let them decide what kind of Brexit they actually want, rather than just letting it rattle around in Parliament for longer?
    – divibisan
    Nov 8, 2019 at 17:51
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    @Valorum, does voting in general elections every few years dissuade the public from voting because it invalidates the result of the previous general election? And if you listened to Farage just before the referendum, he was quite clear that if Leave lost by a narrow margin then he would want another referendum.
    – Peter Taylor
    Nov 8, 2019 at 18:12
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    @Valorum such a scenario would raise concerns true, but it is not analogous to the Brexit situation. Parliment has spent the last 3 years on little else but trying to match the promises of the leave campaigns to the reality of negotiating with the EU. They haven't refused to act because they don't like the result of the referendum, they have refused to actually leave because they don't like the results of the negotiation. Much more like the situation with Israel's hung Parliment than your analogy. Israel went to the polls again, do UK voters not deserve the same?
    – Jontia
    Nov 8, 2019 at 20:37
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There are now three feasible options: Remain, Deal, and No-Deal, where "Deal" is the actual deal, not an ideal but unavailable one.

There are people who would put those options in each of the six possible orders of preference. Any way of putting the question as separate choices with no more than two options will give some people problems.

For example, what should a voter do if presented with a Yes/No on their second choice, to be followed by a second vote between their first and third choices if "No" wins? If they vote "Yes" they give up any chance of getting their first choice. If they vote "No" they preserve a chance of their first choice at a risk of their third choice, which they may consider disastrous.

The voting system should let each voter express their preferences. One possibility is to use Instant-runoff voting.

Taking the example in the question, people who want to leave under some conditions would choose the orders {Deal, No-Deal, Remain} or {No-Deal, Deal, Remain}. Suppose they are the majority. Even if the first round eliminated one of Deal and No-Deal, the second round would pick the surviving leave option over Remain.

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  • This third season of brexit could be a nail bitter: tvseriesfinale.com/wp-content/uploads/2018/03/…
    – SurpriseDog
    Nov 7, 2019 at 23:11
  • Instant runoff voting would seem to be the fairest way of allowing people to show thier views. But the worry could be that if people dont read the ballot paper correctly they could end up voting for only one option.
    – PandaPops
    Nov 8, 2019 at 10:35
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    @PandaPops Given only 3 options, and therefore 6 possible orders, the ballot could be presented showing all 6 orders, and an instruction to pick one.
    – Patricia Shanahan
    Nov 8, 2019 at 14:11
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    The key problem is that no party is willing to support all three options. In the current climate the Conservatives would only offer a choice between Johnson's Deal/NoDeal. Labour would only offer (ToBeNegociated) Deal vs Remain, because both believe the 3rd option is disastrous.
    – Jontia
    Nov 8, 2019 at 15:21
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    Which leads to the obligatory (and appropriately timed) XKCD
    – MT0
    Nov 8, 2019 at 21:42
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No, because whichever party is leading the country after the next general election believes at least one of those three options is entirely unacceptable and will not allow it a place on referendum ballot.

Conservatives Responding to a petition to revoke article 50 that received 6 million signatures the Government said;

Revoking Article 50, and thereby remaining in the European Union, would undermine both our democracy and the trust that millions of voters have placed in Government.

While this was May's government rather than Johnson's there is no indication that this position has done anything except harden under the new leader. See the famous "Dead in a Ditch" saga. This indicates they would not allow a Remain option on any new referendum, which they are also opposed to.

Labour/LibDems/SNP/Green Have all repeatedly called no-deal "Disastrous" or worse. None of these parties would accept a referendum with no-deal as an option having worked so hard to prevent it.

Realistically this means any 2nd referendum can only be between the most recently negotiated deal (which ever party has does this post the GE) and Remain. As a Conservative Government will not offer a referendum and would prefer to leave without an agreement assuming they can avoid a Benn Act II situation.

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  • Interesting. This would kindof mean that there would be a sequential two-step vote like divibisan suggested, but instead of two questions on the same ballot, it's choosing a government which would then offer two of the three options in a referendum as the second step. (Assuming there is a 2nd, anyway)
    – Bobson
    Nov 8, 2019 at 16:14
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    @Bobson sort of, but I can't stress how much of a bad idea this is. Using a GE as a proxy for a single issue is perhaps the most terrible idea I can imagine as a way to govern a country. Especially when everyone will argue that this wasn't the case, either now in the case of Labour who are keen to stress their non-brexit related policies, or later as the Conservatives will stress their mandate to implement whatever else is eventually in their manifesto, no matter how much they focus on Getting Brexit Done during the campaign.
    – Jontia
    Nov 8, 2019 at 16:43
  • No argument from me on that front.
    – Bobson
    Nov 8, 2019 at 17:24
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There's no practical reason why not. In the past few decades there have been cases of the UK and other countries having multiple-option referendums.

The 1997 Scottish devolution referendum had a format with one question asking about whether Scotland should have a devolved government and a second question asking if a devolved government should be able to vary tax rates. Andorra had a three-option referendum on voting system reform in 1982, as did Slovenia in 1996. On a less important issue, the 2015-16 New Zealand flag referendum was a two-stage process, with people voting between 5 new flags in the first stage and then in the second stage voting whether to keep the old or adopt the new. The 2012 Puerto Rican status referendum also had two stages, asking if people accepted the current status and then another question with multiple options for Puerto Rico's future.

Hence it's clear that modern democracies can have multiple option referendums in a wide range of formats if the government wants to do so (although political factors will of course influence what they choose).

For more, see e.g.:

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I believe that it is a fallacy to group "Leave with the deal negotiated" with "Leave without a deal" into a common leave option.

They are, in effect, two very separate courses of action resulting in very different relations with the EU and the rest of the world. Those two, or remain, are also the only options actually on the table.

So the most fair option (given that one believes that a second referendum is fair at all) is to present three separate options:

I wish that the UK shall:

 - Remain in the european union and withdraw its article 50 request.
 - Leave the european union in accordance with the deal negotiated between the british government and the rest of the EU.
 - Leave the european union and reject the deal negotiated between the british government and the rest of the EU.

The single alternative that recieves the most votes should then be considered as the will of the people.

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    The single alternative that recieves the most votes should then be considered as the will of the people. This is an obviously unviable approach, given it directly causes the "leave" vote to split without splitting the "remain" vote. It would be a political impossibility to hold the referendum in this configuration; it would have no legitimacy amongst Leavers and, frankly, even many Remainers would question the motives of the draftee. Some form of transferable vote system would be necessary for the referendum to hold any legitimacy.
    – Dan Scally
    Nov 8, 2019 at 8:09
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    Not to mention that if the population is split roughly into thirds, then two out of three people will be unhappy with the result. That would be hard to sell as the "will of the people".
    – Bobson
    Nov 8, 2019 at 13:10
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    @DanScally Unviable as it seems, it reflects the truth. That this is not a simple yes/no question but a three way choice where a vote for “a” can neither be taken as an implicit vote for either “b” or “c”. “Leave with deal given” and “Leave without deal” are NOT merely flavors of “leave” but very different paths.
    – Guran
    Nov 8, 2019 at 13:53
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    @Guran It's not too technical for Ireland and Northern Ireland...
    – frodoskywalker
    Nov 8, 2019 at 20:24
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    @Guran The idea of transferable voting being "too technical" is completely without merit; such systems are used across the world. The reason they're not used in UK General Elections is simply that the parties most likely to get into power under the current system (Tories and Labour) oppose any reform bitterly, as they're the most likely to suffer if the voting system is changed. Currently people are forced to vote tactically against the party they like least rather than for the party they actually want; transferable voting would fix that issue.
    – Dan Scally
    Nov 9, 2019 at 8:00
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The fairest way would be: Question 1: Should the U.K. remain in the EU, or leave the EU. Question 2: If the majority is for leaving the EU, should the U.K. leave with the negotiated deal, or without a deal?

The first referendum was presented as a decision between “remain” or “leave with the best deal imaginable”. We know now that “best deal imaginable” is not going to happen, therefore “remain or leave” has to be asked again.

This also means that if the U.K. leaves, everyone has their vote counted whether there is a deal or not.

PS. Jontia: Yes, that sounds reasonable. So someone could vote “Between remain and leave with a deal, I pick leave. Between remain and leave without a deal, I pick remain”.

PS. PandaPops: Are you afraid the people could vote against “the will of the people”? Only choices “leave with a rubbish deal” or “even worse, leave with no deal”? Both choices were not part of the original referendum. And the referendum would be in 2020. Two elections since the last referendum. Surely after two elections, with a changed electorate, with an electorate that is much better informed about the realities of leaving, it is high time to ask the same question - remain or leave - a second time.

PS. smithkm: The choices in this referendum are different. There is a clear order. If someone wants to remain, 99% that their second choice is not "leave without deal". And vice versa, if someone wants to leave without a deal, 99% that their second choice is not remain. Only the ones in the middle preferring "leave with deal" would be divided between "remain" and "leave without deal" as their second choice.

About the Schulze system, read here: https://democracychronicles.org/schulze-questioning-a-popular-ranked-voting-system/ It is quite likely (very likely actually) that many people would vote strategically to get the outcome they prefer. Well, it's complicated enough that many people would try to vote strategically for their preferred outcome and get it wrong.

And if you follow my suggestion, where the first vote is "leave or remain", there is just no way to vote in a tactical way. You either want to leave or you want to remain, so that's what you have to vote for.

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  • I disagree that this is the fairest way. I think it would be fairer to ask 1. If the UK does leave, do you want to leave with Deal or No Deal. 2. Do you want to leave with the result of Question 1 or do you want to Remain. Only this way round do you actually know what's on offer before having to make choices.
    – Jontia
    Nov 8, 2019 at 16:45
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    You could argue that question 1 has already been put to the electorate (in 2016), and that only Question 2 is the only question left to ask.
    – PandaPops
    Nov 8, 2019 at 16:47
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    Using chained questions distorts the result and encourages tactical voting no matter which questions you ask in what order. If you have three options, you really need a preferential voting system to handle it. Schultze, Ranked Pairs, IRV, Borda, etc. I think Schultze is best but any of them would do at least a decent job.
    – smithkm
    Nov 8, 2019 at 19:37
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Because of Arrow's impossibility theorem using a ranked voting system would not be a good idea. It would be better to have a referendum with two questions:

  1. Are you OK with leaving the EU without a deal? (Yes/No)
  2. Are you OK with leaving the EU with Johnson's deal? (Yes/No)

The results can be interpreted as follows:

  • If one of the options gets more “yes” votes than “no” votes, the problem is settled.
  • If both options get more “yes” votes than “no” votes, the problem is settled, too – the option with more votes wins.
  • If both options get more “no” votes than “yes” votes, we have a “conditional revoke”: the A50 notification is revoked, but with the assurance (which can be made into law) that it will be invoked again whenever there is a majority for leaving the EU with any specific deal. This means that the result of the 2016 referendum is respected.

Such an arrangement has quite a few advantages:

  • It's not a ranked voting system, so Arrow's impossibility theorem is not applicable
  • There is a specific course of actions for all outcomes
  • Leavers cannot claim the 2016 referendum result is not respected
  • It would be acceptable for Remainers, because the “conditional revoke” arrangement would most likely mean staying in the EU for the foreseeable future: if both Johnson's deal and no deal are rejected, it's unlikely any specific deal would get majority support anytime soon
  • If needed, more questions could be added without making the system more complicated, e.g.:
    1. Are you OK with leaving the EU with Labour's deal? (Yes/No)
    2. Are you OK with leaving the EU with May's deal? (Yes/No)
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    Because Arrow's theorem is a special case of Gibbard's theorem, this doesn't really get around it.
    – Peter Taylor
    Nov 10, 2019 at 8:15
  • Of course Leavers can claim the 2016 referendum was not respected. They'll do that no matter what.
    – Jontia
    Nov 15, 2019 at 15:59
  • @Jontia In the case of a referendum with an option to Remain, the argument would go like: “It is not fair to repeat a referendum on Remain just because some people don't like the result of the previous referendum, where the majority of voters were against Remain”. But this argument wouldn't work against my proposal, which guarantees that the 2016 referendum will be respected: as soon as the public agrees on the terms of leaving the EU, the UK will leave. If you claim it can be argued it wouldn't respect the 2016 referendum, show me the line of reasoning.
    – michau
    Nov 16, 2019 at 21:15
  • Under option 3 the UK would not leave the EU. Plenty of 'Leave just Leave' people would argue that the 2016 referendum had has been ignored then because they don't care about anything else just Leave now.
    – Jontia
    Nov 17, 2019 at 7:44
  • And of course, actually leaving the EU can be presented as a betrayal of Brexit, which is a fairly clear synonym for not respecting the referendum. telegraph.co.uk/politics/2019/03/30/…
    – Jontia
    Nov 17, 2019 at 9:31

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