What divides Leavers and Remainers? This is a question that has been asked and answered hundreds of times since the 2016 referendum.

A recent survey carried out by UCL, with fieldwork by YouGov, shows that one of the biggest divides between Leave and Remain voters was over the importance of returning sovereignty to the UK: Leave voters see this as a top priority whereas most Remain voters do not. When we asked respondents to prioritise what they mean by sovereignty, we found that Leave voters cared most about the legislative functions of government taking place at the level of the nation state, reflecting a common complaint that the EU is undemocratic and/or that its institutions are remote and unaccountable.

Remainers often find it frustrating that Leavers simultaneously complain about the lack of democracy in the EU and then refuse to engage with the bodies that make it democratic; elections to the European Parliament tend to have an embarrassingly low turnout.

But the ability to vote does not in itself make an institution feel democratic. Many Britons clearly believe that the disparate voters of Europe do not constitute a proper “demos”, ie a group of people who feel sufficiently connected to each other to engage in joint decision-making processes. Without any feeling of common connection with the rest of Europe, then the UK will always be just one nation among 28, with the constant risk of being outvoted by other countries who do not care about our interests.

Budget payments into the EU are a particular concern: the survey found that this was seen as the third most important aspect of sovereignty by Leave voters. The fact that a large proportion of the UK’s contributions come back into the country makes little difference; Leavers would argue that the same amount of regional aid and subsidies could come from national government, with British voters in control of what happened to the money.

What are the implications for Brexit? Our research has shown that out of four outcomes – Remaining, a softer Brexit, Theresa May’s withdrawal agreement and no deal – there is no option which unambiguously commands popular support. Attitudes among Leavers have hardened since 2016: 53 per cent of Leavers (and 27 per cent of all voters) favour a no-deal exit, which roughly coincides with the percentage of voters who are planning to either vote for Ukip or the Brexit Party in the European Parliamentary elections. Given that these parties already regard the withdrawal agreement as an unacceptable betrayal, it seems unlikely that many of their voters would be persuaded by an even softer Brexit. At the other end of the spectrum are those Remainers who would be very unhappy about leaving the EU at all – the size of this group is also likely to be around 25 per cent of the electorate (the current total polling numbers for all the parties explicitly backing a “people’s vote”).

Instinctively, a compromise solution such as the Common Market 2.0 proposal (where the UK stays within the EEA and the customs union) seems the most likely to end up being grudgingly accepted by most voters. While few name it as their first choice, it is most voters’ second choice. It is also arguably the least economically damaging Brexit which still fulfils the mandate of the 2016 referendum by leaving the European Union.

We found that Leavers do see intrinsic value in the fact of leaving the EU, no matter what the terms of departure – 86 per cent of Leavers preferred a softer Brexit to Remain. However, the problem remains that the biggest win of Common Market 2.0 is economic, but Leave voters care more about sovereignty, and Common Market 2.0 does not deliver any of the Leavers’ top sovereignty priorities. Its supporters argue that the UK would be subject to fewer laws and regulations and potentially pay less money into the EU budget. But these are gradualist and technocratic points, and the referendum campaign of 2016 showed how ineffective this type of argument can be against simpler messages. Common Market 2.0 does not even deliver a definitive end to the Brexit process – negotiations are likely to go on for many years.

There are strong arguments in favour of the UK remaining inside European institutions after Brexit. The seamless trading relationship which the UK enjoys with the EU simply cannot exist without a complex and enforceable set of common rules (something that is rarely put across in debates about Europe). Issues such as the governance and taxation of multi-national corporations and climate change can only be tackled by international bodies. The lack of a common “demos” does not prevent membership of European institutions being seen as a practical solution to the practical problems thrown up by a globalised world.

Meanwhile, the issues that are most relevant to Britons’ daily lives – the state of the health service, whether trains arrive on time, whether the local school is any good, the level of taxation – will continue to be determined at national level. So if it were possible to persuade Leavers that belonging to rule-making European institutions does not pose an existential threat to British sovereignty, then why not go all the way and argue to stay in the EU, when this would have the advantage of keeping the dedicated Remainers on board?

The Common Market 2.0 solution comes from an understandable desire to acknowledge and respect the result of the 2016 referendum. Undoubtedly most Leavers would be pleased and relieved at finally exiting the EU. But a softer Brexit solution risks generating a slow burn of disappointment; delivering continuity where the referendum was ultimately a vote for change. Common Market 2.0 would be an enormous bet that Leave voters would be content to live within an EU regulatory system over which Britain has far less democratic oversight than before. Over the medium-term, this is a gamble that seems unlikely to pay off.

Christabel Cooper is a professional data analyst and Christina Pagel a professor of Operational Research at University College London.

The survey was jointly funded by UCL Grand Challenges, UCL Mathematics and The UCL Clinical Operational Research Unit with valuable input from the UCL European Institute.