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A question popped into my mind the other day concerning the two referenda concerning the European Union issued by the UK Government.

The first took place on 5 June 1975 on whether the UK should stay in the European Community. The answer: yes

The second took place on 23 June 2016 on whether the UK should leave the European Union. The answer: yes

Concerning ages and voting statistics what proportion of those voting yes in the 1975 referendum also likely voted yes in the 2016 referendum? (i.e. did those who voted to stay in the EC also vote to leave the EU)

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    There's a litany of evidence that we grow more conservative as we age. – Denis de Bernardy Aug 24 '17 at 8:23
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    Why the vote to close? Surely a referendum counts as a political process, and two of them are twice as political. :-) – Royal Canadian Bandit Aug 24 '17 at 10:08
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Short answer: Nobody knows. Between 0% and 100% of them.

Long answer:

These referendums were conducted as secret ballots, so nobody knows how anyone voted.

Based on that uncertainty, one can only give a minimal/maximal range as an answer.

On 5th June 1975 17,378,581 people (67.23% of total votes) voted Yes for entry into the then European Community.

On 23rd June 2016 17,410,742 people (51.89% of total votes) voted Yes for leaving the European Union.

Now we do not know how old the Yes-Voters from 1975 were because of the secret casting of ballots, but some of them will have already died. Let's roughly assume their age was evenly spread between 20 and 60, so they were born between 1915 and 1955. Let's further assume they get 80 years old, so only those born after 1936 will still be alive in 2016. This means that roughly 8.2 million people of these might still have been alive in 2016.

Some of them didn't vote. Voting age population turnout was 65.38% in 2016. So maybe 5.4 million people who voted Yes in 1975 may have voted also in 2016.

These 5.4 million could have all voted for Yes in 2016 to leave the EU, they also could have all voted for No in 2016 to not leave the EU. Everything is possible. In particular, because voting is secret, you cannot say anything about likely behavior. Maybe indeed they were overwhelmingly still convinced of the EU or maybe not. This information is not available and never will be and it is probably futile to speculate about it.

By looking at results in voting areas you might get to some better bounds but you would add new uncertainty because you don't know who moved to where in between. Exit polls might also give some insights even though they are far from perfect and might suffer from their own error margin or bias.

Sources: Referendum 1975, Referendum 2016

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    70% (60% in 2014) of the current citiziens of Spain did not exist or were not adult enough to vote the constitution in 1982, we have similar life expectancies, so that could help you solve the X atleast on "how many" participated back in '75. eldiario.es/politica/… – CptEric Aug 24 '17 at 8:37
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    @CptEric My rough estimation says 49% of those living in the UK in 1975 and voting also still lived in 2016. To live and vote in 1975 you must have been at least of age then. It all gets difficult and very uncertain. – Trilarion Aug 24 '17 at 8:40
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    Here it's ~40%, slightly less given that voting age in 1982 was 21. – CptEric Aug 24 '17 at 8:58
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    I realise there are uncorrectable uncertainties all over the place in this, but it's probably worth noting exit polls uniformly show older people vote more than younger people, so your 49% is likely an upper bound. – origimbo Aug 24 '17 at 9:43
  • I like the idea behind this answer, but it ignores polling (both beforehand and exit polling) which can provide insight into who voted how (or at least, how they say they voted). It's by no means perfect, but it can help provide some constraints on the numbers. – Bobson Aug 24 '17 at 13:45
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Background

It's impossible to say for certain; the best we can do is make a rough estimate. We're interested in VIBRs: Voters in Both Referenda.

We have the following facts:

  • The UK voting age was lowered to 18 in 1970. Anyone voting in the 1975 referendum was at least 18; so was born no later than 1957; so was at least 59 years old at the time of the referendum in 2016.

  • Voters aged between 50 and 64 voted 40% Remain, 60% Leave in 2016, according to the best available polling data (which does not provide any further breakdown by age).

  • Voters aged over 65 voted 36% Remain, 64% Leave in 2016, again according to polling data.

  • The result of the 1975 referendum was 67% Remain, 33% Leave. (Quick Googling failed to locate a breakdown by age, but it seems likely the result was decisive across all age groups.)

  • Young to middle-aged voters in 1975 are still present and voting in fairly large numbers; for example, a voter who was 35 in 1975 would have been 76 in 2016.

Obviously, voters in 1975 do not exactly match up with voters aged over 59 in 2016:

  • Some voters from 1975 have died, left the UK, or did not vote in 2016;

  • Some voters from 2016, aged over 59, did not vote in 1975. Some were not eligible (for example, immigrants who arrived after 1975); others were eligible but did not cast a vote.

Conclusions

We have two groups which approximate to the VIBRs:

1) The electorate as a whole in 1975: This group voted 67% Remain.

2) Voters aged 59 or over in 2016: This group voted between 60% and 64% Leave.

Neither is exactly the same as the VIBRs, but in the absence of better data this is the closest we can get. The difference in voting results is striking, going from two-thirds Remain to almost two-thirds Leave.

Even with all of the above caveats, it seems plausible that a large majority of people in group (2) are also in group (1). If this is the case, a substantial proportion of VIBRs have changed their minds; perhaps as many as one-third or even higher.

  • "It seems reasonable to suppose neither of the above two groups has skewed voting patterns too much." This is exactly the crucial point that needs to be found out in order to make the answer valuable. You assume it doesn't matter what people voted in 1975, just the age matters. We rather need to find out if there is a correlation between 1975 and 2016. It could be that those who votes Yes in 1975 are still so convinced of it that they voted No in 2016 and I challenge you to prove that wrong. – Trilarion Aug 24 '17 at 11:26
  • I strongly disagree that we know with any valid certainty that "a net one-third of voters changed their minds". That may have or they may not have, but we do not know that. – Trilarion Aug 24 '17 at 11:26
  • @Trilarion: As I make clear, my answer is a rough estimate based on two major assumptions: (a) the chance that a 1975 voter did not vote in 2016 (for whatever reason) is independenent of which way they voted in 1975; (b) voters born after 1957 who immigrated to the UK after 1975 are neither so numerous, nor so extreme in their opinions, as to have a large impact on the percentage votes in their age group in 2016. If the assumptions are at least approximately true, we can draw some interesting conclusions. – Royal Canadian Bandit Aug 24 '17 at 11:53
  • I agree that under some assumptions one can draw conclusions, but the assumption that voting in 2016 is independent of voting in 1975 totally comes out of the blue. It's equivalent to that for every new election I basically throw a die to decide what to vote for. Since the assumption cannot be made in my opinion I also think the conclusion is not very valuable (mostly just mapping voting results from one age group then to another age group now disregarding the rest). But of course you can do it. – Trilarion Aug 24 '17 at 12:06
  • I think you've misread my comment. To put it bluntly, some of the people who voted in 1975 are dead. We can assume the chance of dying between 1975 and 2016 is not affected by how one voted in 1975. In statistical language, the events "dying between 1975 and 2016" and "voting Remain in 1975" are independent. That being the case, the number for "percentage voting Remain in 1975" is a good approximation to "percentage voting Remain in 1975, among the survivors who voted in 2016". – Royal Canadian Bandit Aug 24 '17 at 13:04

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