Are Britain and the US Midwitocracies?

Noah Carl, "Are we ruled by midwits?"

“The first method for estimating the intelligence of a ruler,” said Machiavelli, “is to look at the men he has around him”. If we look at the men (and women) around our contemporary rulers, what do we find?

Few reasons for optimism, I’m afraid.

In 2011, the Royal Statistical Society asked 97 British MPs a simple maths question: “If you spin a coin twice, what is the probability of getting two heads?” Since the chance of getting heads on one spin is 50%, and the two spins are independent, the answer is just 50% × 50% = 25%. Not exactly quantum physics.

Shockingly, only 40% of MPs got the answer right. (Among Labour MPs, it was only 23%.) Most of those who got the answer wrong said “50%”, which is obviously incorrect when you think about it. Imagine spinning a coin 20 times and getting heads every single time. That would be extremely unlikely. So getting heads twice in a row has to be less likely than getting it once.

The fact that so few MPs got the right answer is particularly worrying in light of what else the survey found: 77% of MPs said they “generally feel confident when dealing with numbers”. So at least 1 in 3 MPs felt confident when dealing with numbers but couldn’t answer a simple math question. They were both innumerate and overconfident – a dangerous combination.

In 2021–22, the Royal Statistical Society asked another sample of 101 MPs the same question. The results were better, but only slightly: 52% of MPs gave the right answer. (In this case, there was almost no difference between Conservative and Labour MPs.)

The more recent survey asked MPs two further questions. First, “Suppose you roll a 6-sided die. The rolls are 1, 3, 4, 1, and 6. What are the mean and mode values?” I’d say this is even easier than the coin-toss question: to calculate the mean, you just have to add and divide; and to obtain the mode, you just have to notice that ‘1’ appears twice.

Remarkably though, only 64% gave the mean correctly and only 63% gave the mode correctly. Again, that’s almost 40% who couldn’t answer the most basic questions about statistics. How they interpret GDP figures, unemployment numbers, and public opinion data is anyone’s guess.

The second additional question was, “Suppose there was a diagnostic test for a virus. The false-positive rate (the proportion of people without the virus who get a positive result) is one in 1,000. You have taken the test and tested positive. What is the probability that you have the virus?” There were five response options: “99.9%”, “99%”, “1%”, “0.01%” and “Not enough information to know”.

The correct answer is “Not enough information to know”, since the probability that you have the virus depends not only on the false-positive rate of the test, but also on the false-negative rate and the prevalence of the virus in the population.

This is definitely the hardest of the three, but still only 16% of MPs got the answer right – which is actually less than if they’d answered at random. Doing worse than chance would be embarrassing in any circumstances, but the country had just been through a viral pandemic where this kind of problem came up repeatedly.

MPs weren’t even required to calculate the probability of having the virus. They just had to realise that it depends on viral prevalence, which is pretty intuitive when you think about extreme examples. If the prevalence is 1 in 10,000, most positive tests will be false-positives. But if the prevalence is 1 in 100, most positive tests will be true-positives.

The MPs did at least do better than the general public – though barely on the last question. 25% of British people got the coin toss question right; 25% gave the mean correctly; 25% gave the mode correctly; and 15% got the diagnostic test question right.

While MPs may have outsmarted the general public on these simple maths questions – an outcome that is less flattering to MPs than it is unflattering to the general public – they did worse than school children in a recent mock exam.

Eight MPs and five members of the House of Lords sat two SAT papers under strict exam conditions. The SATs – not to be confused with the American exams of the same name – are taken by 11 year olds in Britain. They assess basic knowledge in reading, writing and maths.

Past papers can be found online. Examples of some of the harder questions are shown below. As you can see, it’s pretty straightforward stuff – although you do have to answer quickly.

Left: maths questions. Right: English questions.

Incredibly, only 50% of those who took part passed the English test, and only 44% passed the math test. (You may have noticed there are no whole numbers that correspond to 50% or 44% of 13 – the number of individuals who took part. Yet these were the figures reported by the Times. So it’s possible that whoever wrote the press release wasn’t very good at maths.) By comparison, 72% of school children passed the English test, and 71% passed the maths test.

The parliamentarians’ poor performance could be partly down to them having forgotten the meaning of jargon like ‘obtuse angle’ or ‘adverbial phrase’ (though you can usually work it out from the context). And perhaps a different sample of 13 individuals would have done better. Still, performing noticeably worse than 11 year olds is quite an achievement!

Were MPs any smarter in the past? Based on the quality of parliamentary debate, you’d assume they were. But I’m not aware of any test-score data to back this up.

A less satisfactory method is to track their education levels over time. Doing so reveals two countervailing trends: while the percentage of MPs with a university degree has increased, the percentage who attended Oxford or Cambridge has decreased (amongst Conservatives).

Overall, the evidence suggests that our elected representatives could be accurately described as “midwits” – people of above-average but unremarkable intelligence. Their cognitive faculties seems to be particularly lacking when it comes to non-verbal reasoning – a domain that is increasingly important for navigating our “knowledge economy”.

Returning to the quote from Machiavelli, he was of course referring to rulers who appointed the men around them. His point was: judge a ruler’s intelligence by those whom he appoints. But in a democracy, “we the people” rule through our elected representatives. So what does it say about us that we have selected such mediocre intellects to fill that role?