Numbers, Spitfires and 100000 tests

I’ve previously explored a number of ways in humans struggle to think with numbers.

Only recently, I revisited the early work of Kahneman and Tversky which demonstrated that doctors and other healthcare professionals are pretty much as bad as their patients at calculating outcomes from probabilities. Not very reassuring in these difficult times when we do what to know what the scale of risks and likely outcomes are.

The explanation of this apparent weakness is not that no humans can think with numbers or that humans do this no better than other species. It’s just that mathematics and calculation are perhaps best understood as artefacts of our cultures that help us think better – just as a stick or a piece of grass might help other Great Apes entice a juicy termite out of a log.

Sure we have greater innate abilities – or capabilities, maybe – than our cousins but not all humans use them. Think about those other cultures which have no use for the detailed enumeration we enjoy. For example, the Pirahã tribe of the Amazon use a “one-two-many” system of counting and struggle when forced to think about larger numbers. Interestingly US infants at least are the same until taught to count beyond 3….

The current explanation of this natural innumeracy is that we all think in shorthands – heuristics – rather than details. The “familiar” one, the “bigger” one, the “one the other boys want” or “one that comes to mind”: all of these are heuristics.

Anchoring is the result of this same underlying cognitive apparatus and it seriously messes with our ability to “do the math(s)”

Anchoring occurs when an individual (or group) are overly dependent and fixated on a feature or a quality or characteristic so that their later thinking is skewed. Dan Ariely has a great game to show this here

But it’s not just individuals that can get anchored in this way. Many of my European chums have commented on how the UK seems to be anchored (read: obsessed) on a time when we were world leaders – whether it’s the Blitz (actually a time of rising crime) or VE Day (the 75th anniversary is to be celebrated with a new national holiday this Friday).

Spitfire bunting. What. The. Actual?

The English do the same with the 1966 World Cup (did anyone tell you England won that time?). It’s a fixed point to measure our expectations and disappointments against. A memory of what our natural national position should be…if only those other countries and their referees and their….etc etc

Because that’s what happens when your thinking is anchored – everything that follows feels a little – or a lot – worse.

And that’s not a good way to do rational thinking, let alone calculation.

Even, the desire to “get our country back” is perhaps best understood as the product of anchoring: returning us to a time when we were top dog.

Back to the numbers

When anchoring and numbers are combined it can result in all kinds of thinking error: when you notice that that investment of yours has dropped from its peak value, do you hold – waiting for it to return to its supposedly natural level? Or do you cut and run in panic and anger on the basis that things are falling apart – “hell is open and all the devils are here”?

Neither is a good response. Neither is a rational calculated choice.

But then humans don’t do that very well, as we’ve said.

So when a government minister plants a stake in the ground and promises 100,000 COVID tests per day (when he was only able to point to 4-5000 as a running rate) it serves a number of purposes:

• yes, it says to his team, this is the target – this is where we want to be by when.
• yes, it says to the media and the public, this is how serious I am about this…grrrrrrr
• but it also anchors our thinking so that 73000 tests – the actual number achieved – would seem a failure.
• And the fact the target hit (or not) is the thing we remember (it’s mostly too much hard work to dig around in the debate over whether he should count at-home tests mailed out that day but not returned so we go with a tribal shorthand here – cheat or hero)
• It’s the 100000 number we remember – no matter whether that’s an appropriate number for the task in hand; no matter whether that’s a sustainable volume or where it’s delivered or to whom
• 100000 is undoubtedly a much bigger number than 4-5000 (but I won’t ask you to tell me how much bigger)

Now you might think – as many smart people do – that you’re not affected in this way; that you are not subject to such sloppy “emotional” thinking. Well, happily the academic research suggests otherwise: a number of studies go further than Kahneman and Tversky and suggest that for example, experts are no better at predicting the future than others and are just as easily swayed by biases various (Tetlock) or that an expert’s mood (Englich) will just as likely strengthen or weaken an anchoring effect as is the case for us muggles.

Just be careful with anchoring those numbers: whether you’re a politician, a journo or just a reader. Don’t fall for their siren call.

If you want to know more, the ineffable Tim Harford has another very good piece on HMG numberwanging on his show #MoreOrLess here