A sideways look at economics

In September 2015, Jeremy Corbyn, a 500:1 outsider, won the leadership of the British Labour Party, Her Majesty’s Official Opposition. In May 2016, Leicester City FC won the English Premier League having been given odds of 5000:1 against at the start of the season. In June, the British referendum delivered a vote to leave the European Union, when the odds were 7:1 against at their longest. In October, the Colombian referendum on the proposed peace deal there delivered a ‘No’, against long odds. In early November, the Cubs won the World Series for the first time in over a century. And, on 8 November, the US voted for Donald Trump as President, when the polls and the bookies’ odds were pointing strongly in the opposite direction.

Surely that sequence of unlikely events cannot be unrelated? Surely there must be an underlying explanation that ties them all together? Is this, as Nasim Taleb warned, more evidence of the existence of black swans – evidence that the tails of the distribution of possible outcomes are fatter than we might previously have judged them to be?

No.

That sequence of outcomes is entirely normal. If we feel differently, it is because we are suffering from a cognitive bias known as ‘clustering illusion’, perhaps compounded by an ‘availability heuristic’. A lot of unlikely things have happened all at once, which causes us to see a pattern that is not really there; and some of those things have a strong emotional resonance – they are shocking events, and the shock causes us to overlook the welter of other, more normal events occurring alongside.

A sequence of shocking, unlikely events. That is what normally happens from time to time.

There will be years like this.

Take Leicester City. The chances that that particular club would win the EPL were very slim indeed. But the chances that some club outside the six top clubs (currently including Manchester United, Manchester City, Arsenal, Liverpool, Chelsea and Tottenham) would win were much greater – perhaps more like 20:1. Which means it should happen roughly once every 20 years. Which, it turns out, is pretty close to the mark. Back in 1995, after just three seasons of top flight football, striker Alan Shearer helped propel Blackburn Rovers to the top of the Premier League.

Something similar applies to Jeremy Corbyn, and to the Cubs. For the referenda, and the US election, these were binary outcomes in which the probability of the less likely outcome before the event was reasonably close to 0.5 – probably around 0.4 on average. That implies the probability that all three events would deliver the less likely outcome was around 6.4%. Which means we should expect that kind of sequence to occur once every 15 years or so. Do we have good grounds to believe the frequency is higher than that? Particularly if we take into account the host of other, less emotionally shocking binary events that occurred over the same period, whose results we cannot recall.

Moreover, we know from probability theory that, given enough repetitions – with a probability of 0.4, that is around 20 – the binomial distribution (the distribution of binary outcomes) tends towards a normal distribution. But when the sample size is small (in this case, 3), the binomial distribution is not close to the normal. In other words, weird things happen in short sequences fairly regularly. It’s normal.

So don’t panic – we are living in normal times. A sequence of shocking events doesn’t change that, even if it makes you feel bad. If you are feeling that way, remember the words of Van Morrison:

When it’s not always raining there’ll be days like this
When there’s no one complaining there’ll be days like this
When everything falls into place like the flick of a switch
Well my mama told me there’ll be days like this

When you don’t need to worry there’ll be days like this
When no one’s in a hurry there’ll be days like this
When you don’t get betrayed by that old Judas kiss
Oh my mama told me there’ll be days like this

When you don’t need an answer there’ll be days like this
When you don’t meet a chancer there’ll be days like this
When all the parts of the puzzle start to look like they fit
Then I must remember there’ll be days like this

When everyone is up front and they’re not playing tricks
When you don’t have no freeloaders out to get their kicks
When it’s nobody’s business the way that you wanna live
I just have to remember there’ll be days like this

When no one steps on my dreams there’ll be days like this
When people understand what I mean there’ll be days like this
When you ring out the changes of how everything is
Well my mama told me there’ll be days like this