A few weeks ago, I wrote about how humans are not terribly good at assessing probabilities. Needless to say, I was not surprised when I came across this article on Politico. The article lays out five possible scenarios in which Brexit could be avoided. It also estimates the probability of each of these scenarios coming to fruition.
|"Wrong Answer, Try Again"||A current petition for a second referendum succeeds and another vote is administered.||1/15|
|"Renegotiation, Mark Two"||The successful Leave vote is really just a ploy to force the rest of the EU to the negotiating table."||1/9|
|"Parliament Flexes Sovereignty"||Parliament decides to ignore the non-binding referendum.||3/20|
|"New elections bring in pro-EU PM"||Citizens treat PM election as an unofficial re-do of the referendum, electing a PM that favors staying.||1/10|
|"Scottish backdoor"||UK negotiates associate status that keeps it as part of EU single market.||1/7|
You may or may not agree with these probabilities. Either way, there is a major problem with the article as a whole.
It concludes by saying that there is a 9/10 (90%) chance that Brexit goes ahead as planned.
If the probability of Brexit going through is 90%, then the probability of any individual event derailing it cannot be more than 10%. Three of the five event probabilities violate this condition.
However, the individual probabilities all being no more than 10% isn't enough to ensure consistency unless all the events are perfectly correlated. Perfect correlation among these five events is unlikely.
For simplicity, let's just consider two events with 10% probably of occurring. If the events are uncorrelated, the probability of at least one occurring - implying that Brexit would be reversed - is 19.0%. As correlation increases, this probability decreases. At a correlation of 0.5, the probability of at least one occurring is 14.5%. At a correlation of 0.9, the probability drops to 10.9% - certainly lower, but still in violation of the 90% Brexit estimate.
With five possible events on the table, the odds of at least one occurring is even higher at the same correlation levels.
Normally, it's hard to argue with subjective viewpoints like those presented in the Politico article. This is not one of those cases. The author(s) have either overestimated the probability of Brexit proceeding or overestimated the odds of an event disrupting Brexit (or a combination of the two).