by Stephen Fisher and Alan Renwick.

It is commonly asserted by people commenting on the EU referendum that people tend to be risk averse and so vote against change. The Prime Minister appealed to people not to “roll the dice” on their children’s and grandchildren’s future. Daniel Hannan in his book Why Vote Leave accepted the idea of risk aversion in referendums, and then argued that people should see remaining in the EU as more risky than leaving.

But is it really true that people tend to vote against change in referendums? There are certainly several examples in Britain where people have rejected change, the most prominent examples include the referendums on Scottish Independence, the Alternative Vote electoral system, and, in 1975, the UK’s membership of the European Community. But it is also true that people in different parts of Britain have voted for change in referendums on numerous occasions. They voted for a Scottish Parliament (and separately to give it tax varying powers), a Welsh Assembly (and later for it to have more power), a Greater London Assembly, and the Good Friday Agreement. Setting aside referendums at the sub-regional level, the change option has won in six out of the thirteen referendums that have been held in the UK.

It maybe objected that both of the UK wide referendum results have been for the status-quo. True. So what if we cast our net further afield?

Looking at all national (by which we here mean entire-state) referendums from democracies since 1990 (but excluding Switzerland), we can consider whether the status-quo option tends to win. We find that actually the change option won a majority of the votes cast in 186 out of 268 referendums, i.e. 69% of the time.

On the other hand, that figure might be misleading. Many countries have extra thresholds for a vote for change to count as valid: either that turnout must exceed a certain minimum or that support for change must pass a minimum proportion of the eligible electorate. Once we take this into account, only 106 of the 268 referendums (40 per cent) have actually passed.

The question therefore arises of which of these measures more accurately reflects how often publics are willing to back change. The answer is probably that neither does, and that the true answer is somewhere in between. In some of the votes rendered invalid by turnout thresholds, it appears very likely that majority public opinion was thwarted. In Italy in 1999, for example, 91.5 per cent of those who voted backed the change, but the result was invalid, as turnout was just below the 50 per cent threshold, at 49.6 per cent. Indeed, the electoral roll was old at the time and contained significant numbers of people who had died (see here, p. 122), so true turnout may well have been over 50 per cent. On the other hand, it is equally clear that, in many other cases, those opposed to change saw that the best (or least effortful) way to block the proposal was just not to turn out, ensuring that the vote would be invalid.

In other words, looking across the board, we can say little more than that publics support change in somewhere between 40 and 69 per cent of referendums.

By far the commonest context in which change achieves more than 50 per cent but does not pass is when the referendum is based on a citizens’ initiative. Fully 83 out of 109 citizen-initiated referendums since 1990 won a majority of the votes cast, but only 22 of those 83 passed. After setting aside all citizen-initiated referendums, 65 per cent of the remaining 159 proposals received a majority of votes, and 52 per cent passed. Still a gap, but not so big a gap. Moreover, change was effected in just over half the referendums.

People often remark that people use referendums to vote against the government. When the Prime Minister is in favour of change just over half of referendums passed. This increases to 56 per cent if we set aside the citizen initiatives.

More pertinent to tomorrow’s referendum is what happens when a Prime Minister is against the proposed change. Our preliminary analysis suggests that only 21 of the 268 referendums fall into this category. There is just one referendum where change has been effected against the publicly stated will of a sitting Prime Minister. That was the 2011 Malta referendum on whether to permit divorce in certain circumstances after four years of separation.

So it seems that democracies are not generally against voting for change in referendums. When given the opportunity they support change more often than not. But they have only once, since 1990, done so when their prime minister has advised against. That does not bode particularly well for the Leave side in Britain’s EU referendum.

Another key question pertinent to tomorrow’s referendum is whether there is a late swing to the status quo when the final polls suggest the result will be close. Again looking at all nationwide referendums in democracies globally since 1990 we find that the status quo option tends to outperform the average of the final polls by some 3.3 percentage points across the 99 referendums where we have polls within ten days of the vote. (By final polls here we mean the average of the up to six polls that were fielded closest to the vote and no more than ten days before.)

But the 3.3 point average includes some 19 shocking cases where the polls have been more ten points out. Sometimes the polls were more than 20 points out, or even 40 points out! Sometimes it is because the referendum is just so low profile and sometimes the polls were poor quality. It is not always clear. Certainly the global experience of referendum polls does not suggest plebiscites are easy for pollsters to predict.

Setting aside the extreme cases of major polling misses, we find that the average apparent swing to the status quo following the final polls is 1.5 percentage points. Still excluding extreme failures, if we narrow our focus to the 20 cases where the average of the polls in the final ten days was between 45 per cent and 55 per cent then the apparent movement between the polls and the final result is a similar 1.7 points in favour of the status quo.

Yet the averages may not tell the whole story. If a late swing to the status quo applied consistently it should mean that the change option has to be at least at 51.7 per cent in the final polls to win. But that is not the experience. Intriguingly, as can be seen from the table below, the change option won all the referendums where the change option was between 49.1 per cent and 52.3 per cent in the average of the final polls. Change won in fully 12 out of 16 cases where the change option was between 50% and 60% on average in the final polls. Late swing to the status quo definitely cannot be relied on to save the day for Remain if Leave are ahead in the polls later today and tomorrow.

National referendums since 1990 in democracies (excluding Switzerland) where final polls put change option between 40% and 60%

Note to table: Poll average is the average of the up to six latest polls in the campaign within the final ten days.

This is work in progress. Comments welcome, especially if you think we have made coding errors. Thanks to Jack Sheldon, Roberta Damiani and Johnny Runge for data gathering.