If it has done nothing else, the signals sent by Conservative ministers last week about what they think Brexit means have instigated a keen debate amongst everybody else about what in fact it should mean. Those who believe that the UK should have greater control over immigration were cheered that achieving that objective appears to be the government’s priority. Those (including, it seems, many working in the currency markets) who believe the UK needs to remain a member of the single market are concerned that ending freedom of movement means abandoning that membership.

Both sides have attempted to back their arguments with claims about what was motivating voters when they cast their ballots on June 23rd, and thus what mandate voters gave their politicians in the referendum. The Prime Minister appears to be of the view that concern about immigration was the principal motivation behind the Leave vote and that restoring UK ‘control’ over who can and cannot come here represents the ‘will of the British people’. Her critics, in contrast, suggest that nobody voted to make Britain poorer (which is what they believe would be the consequence of leaving the single market) and that the government’s negotiating stance should take cognisance of the views of the 48% who voted to Remain as well as the 52% who voted to Leave.

So which interpretation is right? Was the majority vote to Leave primarily the reflection of a wish to curb immigration, with voters little concerned about the economics of leaving? Or were many voters, and perhaps especially those voting to Remain, in fact primarily making a judgement about the economics of leaving the EU?

The answer is, in truth, not as straightforward, as either side suggests.

Academic students of voting behaviour commonly infer voters’ motivations from correlation. An issue is said to have mattered to voters if those who take one view about an issue voted one way while those who took a different view voted the other way. And by this criterion it seems clear that people’s views about the economic consequences of leaving the EU mattered more to them in deciding which way to vote than what they thought it would mean for immigration.

Consider, for example, the evidence of recently released data from the British Election Study. This study has for the last three years been interviewing on a regular basis an unusually large panel of 30,000 people. The three most recent waves of interviewing were conducted before the local and devolved elections at the beginning of May, during the EU referendum campaign in May/June and immediately after June 23rd. It is the results of this last round of interviewing that have just become available. As a result, we can now relate how people said they voted on June 23rd to their expectations, as expressed shortly before the vote took place, of what leaving the EU would entail.

The link between people’s expectations of the economic consequences of Brexit and the way in which they voted is remarkably strong. No less than 93% of those who thought that the general economic situation would be made worse by leaving the EU voted to Remain. Equally, 90% of those who thought that Britain’s economy would be better as a result of leaving the EU voted to Leave. Rarely do survey data show so sharp a divide between two sets of voters.

People’s views about the implications of Brexit for immigration also map on to the choice that they made on June 23rd. However, the link is not so strong. Just 70% of those who thought that immigration would be reduced voted to leave the EU, while the level of support for Remain amongst those who actually thought immigration would be higher if we left the EU was just 65%.

This pattern whereby the economy seems to be more important than immigration was, in fact, in evidence well before polling day. For example, the random probability internet panel survey run by NatCen between mid-May and mid-June found that 88% of those who thought that Britain’s economy would be better off as a result of Brexit intended to vote to Leave, while 90% of those who thought the economy would be worse off planned to vote to Remain.

In contrast, just 63% of those who thought that immigration would be lower if we left the EU said they would vote to Leave, while no more than 80% of those who reckoned it would either stay the same or would fall were at that point backing the Remain camp.

The same pattern is also evident in the regular polling that YouGov undertook during the referendum campaign. For example, in their final poll before polling day, as many as 95% of those who thought the economy would be worse off as a result of Brexit said that they would vote to Remain, while only 75% of those who anticipated that immigration would be lower wanted to Leave.

So, it would seem that the position is straightforward. While voters may in part have been sending a message about immigration, they were more obviously voting on the basis of which option they thought would be better economically – and thus it is on getting the best economic deal out of Brexit that the government should now be focusing.

However, this classic academic approach to assessing voters’ motivations is, on its own at least, potentially misleading. We also need to look at the distribution of expectations, that is, at how many people actually thought the economy would get better or worse as a result of Brexit, and at how many reckoned immigration would increase or fall.

On the economy voters were divided, albeit somewhat unevenly, about what they thought the consequences of leaving would be. According to the pre-referendum wave of the British Election Study, while rather more thought that the economy would get worse (35%) than reckoned it would get better (23%), as many as 42% either felt things would be much the same, or said they did not know what would happen. The equivalent figures in NatCen’s panel were 37% worse, 27% better, and 30% no difference/don’t know respectively, while YouGov’s final referendum poll scored it, 40%, 23% and 37%.

In contrast, while voters were far from unanimous in their view of what would happen to immigration if we left the EU, consistently well over half reckoned that it would fall if we did so. According to the British Election Study, as many as 55% felt it would be lower (and just 9% reckoned it would be higher), while the NatCen panel found that as many as 60% were of that opinion (6% thought it would be higher), and YouGov, 53 % (3%).

In short, many more people were convinced that immigration would fall if Britain left the EU than reckoned the economy would suffer as a result. If immigration had been the only issue at stake in the referendum for voters, the UK would have voted by a wider margin to Leave than in the event it actually did. It only appears to be the less important issue in an academic analysis because a significant minority of those who thought that immigration would fall following Brexit voted to Remain nevertheless.

So, any suggestion that many voters were not sending a message about immigration on June 23rd seems wide of the mark. Rather, even many of the 48% who voted to Remain seemingly accepted that Brexit would help bring immigration down – and thus might well now be content if that were to happen. But for some voters at least, the perceived economic risks of leaving the EU were more important than any wish they might have had to see immigration reduced. At the same time, few of those who did vote to Leave were expecting to be poorer as a result. That is why, at the end of the day, the government will find itself under pressure to deliver on the economics of Brexit as well as on its implications for immigration.