Exponential growth bias: The numerical error behind Covid-19

“Compound interest is the eighth wonder of the world. He who understands it, earns it; he who doesn’t, pays it”, is a quote famously attributed to Albert Einstein. Indeed, many in the investing world including the legendary Warren Buffett swear by the concept of compounding. The mere mortals that we are at Marcellus don’t hide our allegiance to the concept either – we quite unimaginatively call our flagship strategy ‘Consistent Compounders’. But the magic of compounding extends its benefits (or pitfalls in the absence of appreciation for the same) beyond the world of money. In this piece for the BBC Future, David Robson, the author of ‘The Intelligence Trap: Why Smart People Do Dumb Things’ discusses why simply a better appreciation for the concept of compounding can improve people’s behaviour during the pandemic and control the damage from Covid-19. Given the spread of the virus attains an exponential curve as the infected infect even more people and so on, he highlights the concept of ‘Exponential bias’ – a quite common lack of appreciation for such compounded growth amongst people irrespective of levels of education. Robson goes on to refer to studies which have shown a significant improvement in behaviour when it comes to wearing masks, washing hands and maintaining social distancing, when people are made aware of this.
“In March, Joris Lammers at the University of Bremen in Germany joined forces with Jan Crusius and Anne Gast at the University of Cologne to roll out online surveys questioning people about the potential spread of the disease. Their results showed that the exponential growth bias was prevalent in people’s understanding of the virus’s spread, with most people vastly underestimating the rate of increase. More importantly, the team found that those beliefs were directly linked to the participants’ views on the best ways to contain the spread. The worse their estimates, the less likely they were to understand the need for social distancing: the exponential growth bias had made them complacent about the official advice.
This chimes with other findings by Ritwik Banerjee and Priyama Majumda at the Indian Institute of Management in Bangalore, and Joydeep Bhattacharya at Iowa State University. In their study (currently under peer-review), they found susceptibility to the exponential growth bias can predict reduced compliance with the World Health Organization’s recommendations – including mask wearing, handwashing, the use of sanitisers and self-isolation.
The researchers speculate that some of the graphical representations found in the media may have been counter-productive. It’s common for the number of infections to be presented on a “logarithmic scale”, in which the figures on the y-axis increase by a power of 10 (so the gap between 1 and 10 is the same as the gap between 10 and 100, or 100 and 1000).
While this makes it easier to plot different regions with low and high growth rates, it means that exponential growth looks more linear than it really is, which could reinforce the exponential growth bias. “To expect people to use the logarithmic scale to extrapolate the growth path of a disease is to demand a very high level of cognitive ability,” the authors told me in an email. In their view, simple numerical tables may actually be more powerful.
The good news is that people’s views are malleable. When Lammers and colleagues reminded the participants of the exponential growth bias, and asked them to calculate the growth in regular steps over a two week period, people hugely improved their estimates of the disease’s spread – and this, in turn, changed their views on social distancing. Sele, meanwhile, has recently shown that small changes in framing can matter. Emphasising the short amount of time that it will take to reach a large number of cases, for instance – and the time that would be gained by social distancing measures – improves people’s understanding of accelerating growth, rather than simply stating the percentage increase each day.
Lammers believes that the exponential nature of the virus needs to be made more salient in coverage of the pandemic. “I think this study shows how media and government should report on a pandemic in such a situation. Not only report the numbers of today and growth over the past week, but also explain what will happen in the next days, week, month, if the same accelerating growth persists,” he says.
He is confident that even a small effort to correct this bias could bring huge benefits. In the US, where the pandemic has hit hardest, it took only a few months for the virus to infect more than five million people, he says. “If we could have overcome the exponential growth bias and had convinced all Americans of this risk back in March, I am sure 99% would have embraced all possible distancing measures.””