an artifact of scale

David Spiegelhalter and Anthony Masters:

We tried this strategy [telling people about the incorrect interpretation before they catch it in the wild] back in June 2021 when Public Health England first published data showing that, among older people who had recently died with Covid-19, most had been vaccinated. We wrote an article pointing out that this did not mean the vaccine was ineffective – just that it was imperfect – and that the great majority of people had been vaccinated: in essence, a small proportion of a large number can be bigger than a larger proportion of a small number. Another useful analogy is with seatbelts: most people who die in car accidents are wearing seatbelts, but this does not mean that seatbelts are not effective – it’s just that nearly everyone wears one and they are not perfect.

The response to our “pre-bunking” was not encouraging. The Twitter link to our article included only its title, Why most people who now die with Covid in England have had a vaccination, and not the subhead, Don’t think of this as a bad sign, it’s exactly what’s expected from an effective but imperfect jab. As such, it was mistakenly interpreted as an anti-vaccination article (or worse) and circulated online. This, in turn, led to critical comments suggesting that we had encouraged vaccine scepticism and even an extraordinary tweet saying we (and the paper’s editors) were “genocidal” and should be “hunted down and destroyed”. We made light of this, saying this seemed a bit harsh, but we had had worse referees’ reports.

Morals of this story: People only read the headlines — at most — and no matter what opinion a public person has, someone on Twitter will demand his or her death.

Also — and I think this is largely a matter of scale, with which I have been so concerned for a while now — it is virtually impossible to get people to understand that “a small proportion of a large number can be bigger than a larger proportion of a small number.” Long numbers rocket the mind.