## Saturday, 4 October 2014

### The Top Gear Coincidence Hypothesis

Top Gear are in trouble for having taken a car with an offensive number plate ('H982 FKL' - I suppose the right-hand stem of the 'H' looks like a '1') to Argentina.  The angry Argentines allege a deliberate insult.  Jeremy Clarkson proposes that it is a coincidence.  What are the probabilities that each is right?

As usual it pays to be as clear as possible about what the hypotheses and the evidence are.  I'll run with these:

Hypothesis 1: The number plate was deliberately chosen by one of the Top Gear production team to refer to the Falklands War;

Hypothesis 2: The number plate was not deliberately chosen by one of the Top Gear production team to refer to the Falklands War;

Evidence:  One of the cars taken to Argentina by Top Gear bore the number plate 'H982 FKL'

Denials and so forth are unlikely to have much information value (because of the Rice-Davies effect) so I'll forget about those.  And although we could describe the evidence differently - e.g. as 'One of the cars taken to Argentina had a number plate that could be interpreted as a reference to the Falklands War' - this would complicate matters without materially affecting the hypotheses' likelihood ratio.

So, in order of magnitude terms, what are the likelihoods here?

If the Top Gear team wanted to refer to the Falklands using a number plate, how likely would they be to choose that one?  This largely translates to: 'How many different number plates can you use to refer to the Falklands War?'  I suppose it could just about work with 'J982', 'L982', 'M982', 'N982' and other combinations such as 'GB82' or 'FW82'.  Similarly, you could come up with other combinations of the three letters that would do a similar job to 'FKL', like 'FKW', 'FLK', 'FK1' or whatever.  You might tentatively say that there are possibly 10-100 combinations that would do the job.  On the other hand, 'H982 FKL' might be the only number plate in existence along these lines.  I'd therefore say the likelihood of the evidence under hypothesis 1 is somewhere between 0.01 and 1, refinable if necessary through further research.

How likely is that number plate to have appeared under hypothesis 2, the 'coincidence' hypothesis?  This would require quite a bit of research into how number plates work, which is only slightly interesting.  Luckily City AM's Billy Ehrenberg has already had a go.  He gives it a whopping 100,000,000 to 1.  Although I don't entirely follow all of his reasoning, it's certainly not less than 1,000,000 to 1.  This gives us an evidential likelihood ratio of at least 10,000 and possibly 100,000,000 in favour of the 'conspiracy' rather than 'coincidence' hypothesis.

But what is the prior probability?  Ignoring the number plate, how probable is it that the Top Gear team decided to use number plates to refer to the Falklands War?  Given that there is a whole Wikipedia page on 'Top Gear Controversies', it cannot be reckoned terribly low.  Let's assume they intended a controversy with a probability of about 1 in 10, and, if they did, that there are perhaps 100 ways of doing it of which number plates are just one.  This would give us a prior of around 1 in 1000.

Crunching the numbers, I judge the probability of Hypothesis 1 to be above 90% and defensibly 99.999%.

#### 1 comment:

Anonymous said...

The numbers you have for hypothesis two are way out. The false assumptipn is that there are only a limited set of plates that could be interpreted as relating to the 1982 war. For example, what are the relationships of 146, 215, 649, 205 to the Falklands in 1982? The letters have a similar possibility of wide interpretation, you based your interpretation purely on FLK, how about H982 GBR, H982 ENG? I think on this basis there should be a third hypothesis, Top Gear noticed that a number plate cpould be interpreted in a way likely to cause controversy and went with the idea.