Let’s start with the outside view. The first fact to note is that PM David Cameron has promised to hold a referendum on the UK’s membership in the EU (a.k.a. Brexit) before the end of 2017. (Both the Economist and the BBC have impeccable overviews.) How likely is it that Cameron will follow through on his promise? Pretty likely, I think. I’d be willing to make about a 100-to-1 bet in favor but not much lower, so let’s say there’s a 99% chance that there referendum will be held by the end of 2017. For the moment, I’m going to ignore this possibility, but I’ll factor it back into the mix later. And I think it’s safe to assume that the date for the vote would have to be announced no later than the end of September 2017. It’s now (roughly) half of the way through February, so in order for Britain to set a date for the Brexit vote before the end of 2017, it has to do so in the remaining 19.5 months. Assuming that the date on which the Brexit vote is set is randomly determined, the probability of that Britain will set a date prior to May 1, 2016 is 1.0-(17/19.5) = 0.128. Why? Per the above, I’m assuming that our probability space is made up of the following discrete outcomes:
- Britain announces the vote in February 2016 = Pr(0.5/19.5)
- Britain announces the vote in March 2016 = Pr(1.0/19.5)
- Britain announces the vote in April 2016 = Pr(1.0/19.5)
- Britain announces the vote in May 2016 = Pr(1.0/19.5)
- Britain announces the vote in September 2017 = Pr(1.0/19.5)
So 1 (i.e., the entire probability space) = (0.5/19.5)+(1.0/19.5)+…(1.0/19.5) (i.e., the probability that the announcement will be made in any given month). Another way to put the matter (which will be useful below) is in the following way:
- Britain announces the vote in 2016 = Pr(10.5/19.5)
- Britain announces the vote in 2017 = Pr(9.0/19.5)
From here, it’s just a matter of separating the probability that the announcement will be made in (the remainder of February), March, or April of 2016 (=2.5/19.5 = 12.8%).
But let’s complicate matters a bit. Cameron has said a number of things that suggest he strongly favors having the vote in 2016. For example, he recently said
I believe that 2016 will be the year we achieve something really vital, fundamentally changing the UK’s relationship with the EU and finally addressing the concerns of the British people about our membership.
Some other political leaders in Britain have also expressed a preference for having (or at least a willingness to have) the vote in 2016. That suggests that strongly weighting the probability that the date will be set in 2016. I’ll incorporate this fact in my model (rather crudely) as a 3-to-1 bet that the vote will be announced in 2016 as follows:
- Britain announces the vote in 2016 = Pr(15.5/19.5)
- Britain announces the vote in 2017 = Pr(4.0/19.5)
Hence, the probability of that the Brexit vote will be announced in a randomly determined month in 2016 = (15.5/19.5)/12 = 7.0%. The exceptions are January (probability = 0 since all of that month is in the past) and February (probability = 3.5% since half of that month is in the past). On these assumptions, it follows that the probability that the vote will be announced before May 1, 2016 is 7% + 7% + 3.5% = 17.5%. This number should decrease by 17.5/75 (= about .233) every day as we approach May 1, so that it will be (17.5 – (3.26))% on March 1, and so on. Finally, let’s return to the the very small possibility that Cameron will back out on his promise to hold the Brexit vote. I rated that as about a 100-to-1 shot. So today the outside view should be that there will be a 17.325% (17.5 x 0.99) chance that the Brexit vote will be announced before May 1. And it means that on March 1, there will be a 14.098% ((17.5 – (3.26)) x 0.99) chance that the Brexit vote will be announced before May 1.
So much for the outside view, but what about the inside view? Cameron has signaled that he’d like the referendum to be held on June 23. However, ongoing negotiations with Brussel looks to make it impossible for him to announce this date until after the European Council summit on 18/19 February, or perhaps as late as 22/23 February. Moreover, some think that Cameron has good reason to want the Brexit vote sooner rather than later.
Mr Cameron’s chances of victory improve the sooner he holds it. He does not want another terror attack or more refugee chaos to turn the referendum into a vote on immigration.
Others mutter that British public opinion has already turned against EU membership[8 and 9 and 10] and that Cameron’s best hope for keeping the UK in the the EU is to stall. And there’s a lot of uncertainty in the currency market about how a Bexit vote would go down. (Ideal speculation: It seems to me – I lived in the UK for 4 years during the 2000s but am no expert about its politics – that nativism among Tory voters has gotten out of the control of conservative leadership in the UK in much the same way that nativism among Republican voters has gotten out of the control of conservative leadership in the U.S.A. Brexit in the U.K., and Trumpism is the U.S.A. But, to repeat, this is just ideal speculation.) At any rate, the inside view is harder to estimate because of the qualitative (rather than quantitative) nature of the data. But I think about an 88% probability of announcing the Brexit vote before May 1 is right.
Where are we then?
- Outside View: 17.325%
- Inside View: 88.0%
So do we go with the outside view or the inside view? The obvious response is the we don’t have to chose between the two; we can synthesize the view points. Yet that’s damn hard, given the lack of isomorphism between the kinds of data I’ve got in front of me (and the squirrely way I came up with the inside estimate. A unweighted average of the two numbers is 52.66%. But at the moment, I have a lot more confidence in the inside view, that confidence might change a lot after Cameron’s negotiations with the EU conclude, so I’ll need to keep an eye on that. But until then I favor a weighted average of the inside and outside views, placing 3 times as much weight on the inside view. That means I’m forecasting 70.33% probability that Britain will set a date for a referendum on EU membership before May 1. However, I’ll need to rethink this as soon as the EU negotiations are concluded.