October 26, 2020

# What is the exponential growth bias, the mathematical error that can favor the increase in COVID-19 cases

A simple mathematical error may explain why many people underestimate the dangers of the coronavirus and do not take social distancing, the use of masks and hand washing so seriously.

Imagine that your bank offers you a deal whereby your money will double every three days. If you invest just \$ 1 today, about how long will it take you to become a millionaire?

The precise answer is 60 days from your initial investment, when your balance would be exactly \$ 1,048,576.

After another 30 days, you would have made more than \$ 1 billion. And after a year, you would have more than \$ 1,000,000,000,000,000,000,000,000,000,000,000,000,000 dollars

If your calculations are too far from the answer, you are not alone. Many people consistently underestimate how fast a security increases, a mistake known as “exponential growth bias.”

And this is something that may have had profound consequences on people’s behavior during the COVID-19 pandemic in 2020.

A number of studies have shown that people who are susceptible to exponential growth bias are less concerned about the spread of COVID-19 and they are less likely to support measures such as social distancing, hand washing, or the use of masks.

In other words, this simple mathematical error could be costing lives, which means that correcting the bias should be a priority in attempts to flatten the curves and avoid the second waves of the pandemic around the world.

### An Indian legend

To understand the origins of this particular bias, we must first consider the different types of growth.

The best known is “linear” growth. If your garden produces three apples every day, you have six after two days, nine after three days, and so on.

Conversely, andExponential growth accelerates over time. If you have a weed in your pond that triples every day, the number of plants can be low at the beginning, going up to three on the second day, and nine on the third day. But it will soon increase significantly.

Our tendency to overlook exponential growth has been known for millennia.

According to an Indian legend, the Brahmin Sissa ibn Dahir was offered a prize for inventing an early version of chess.

The Brahmin asked that one grain of wheat be placed in the first square of the board, two for the second square, four for the third square, and so on, doubling the number of grains each time to square 64.

The king apparently laughed at the humility of ibn Dahir’s request, until his treasurers reported that it would exceed all the food in the kingdom (18,446,744,073,709,551,615 grains in total).

### Linear growth

It was only in the late 2000s that scientists began to formally study bias.

Lto most of people intuitively assumes that most growth is linear, leading her to grossly underestimate the speed of the exponential increase.

Initial studies focused primarily on the consequences for our bank balance.

Most savings accounts offer compound interest, meaning you accrue additional interest on the interest you have already earned.

This is a classic example of exponential growth and it means that even low interest rates pay off handsomely over time.

The bias also makes people more vulnerable to bad loans, in which debt increases over time.

### The education trap

Surprisingly, a higher level of education doesn’t stop people from making these mistakes.

Even science students with a math background can be vulnerable, says Daniela Sele, who researches economic decision-making at the Swiss Federal Institute of Technology in Zurich. “It helps a bit, but it doesn’t prevent bias,” he says.

This may be because they are based on their intuition rather than deliberative thinking, so that even if they have learned things like what compound interest is, they forget to apply them.

To make matters worse, most people will confidently say that they understand exponential growth, but will then fall into bias when asked to estimate things like compound interest.

As I explored in my book “The Intelligence Trap,” intelligent and educated people often have a “bias blind spot,” leading them to believe that they are less susceptible to error than others, and exponential growth bias seems fall into that blind spot.

### Experiment

With the covid-19 pandemic, researchers began to wonder if bias could also influence our understanding of infectious diseases.

According to several epidemiological studies, if there is no intervention, the number of new cases of covid-19 doubles every three to four days, which is why so many scientists advised quick closures.

In March, Joris Lammers from the University of Bremen in Germany and Jan Crusius and Anne Gast from the University of Cologne launched online surveys to ask people about the possible spread of the disease.

Their results showed that exponential growth bias was prevalent in people’s understanding of the spread of the virus, and that most of them vastly underestimated the rate of increase.

More importantly, the team found that those beliefs were directly related to participants’ opinions about 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 with official advice.

### Graphics in the media

This is consistent with other findings by Ritwik Banerjee and Priyama Majumda, at the Indian Institute of Management, Bangalore, and by Joydeep Bhattacharya, from Iowa State University, USA.

In their study (currently in peer review), they found that andExponential growth bias may predict lower compliance with World Health Organization recommendations, including the use of masks, hand washing, use of disinfectants and self-isolation.

The researchers speculate that some of the graphic representations of the rate of contagion found in the media may have been counterproductive. It is common for the number of infections to be presented on a “logarithmic scale”, in which the figures on the “y” (vertical) axis increase multiplied by 10, but in which the gap between 1 and 10 is the same as the gap between 10 and 100, or 100 and 1000.

This means that exponential growth appears more linear than it actually is, which could reinforce the exponential growth bias.

### Growth in a short time

The good news is that people’s opinions are malleable.

When Lammers and his colleagues reminded participants of exponential growth bias and asked them to estimate the growth of the disease over two weeks, people vastly improved their estimates and changed their views on social distancing.

Meanwhile, Sele has recently shown that small changes in communication can be important.

Emphasizing how little time it will take to reach a large number of cases, for example, and the time that would be gained from social distancing measures, improves people’s understanding of accelerating growth.

Lammers believes that the exponential nature of the spread of the virus should be highlighted in the coverage of the pandemic. The media “must not only report the figures for the day and the previous week, but also explain what will happen in the next days, weeks, months, if the same accelerated growth persists,” he says.

Trust that even a small effort to correct for this bias could bring huge benefits. In the US, where the pandemic has hit the hardest, it took just a few months for the virus to infect more than 5 million people, he says.

“If we had overcome the exponential growth bias and convinced everyone of this risk in March, I am sure that 99% would have taken all possible distancing measures.”

*David Robson is the author of “The Intelligence Trap: pHearing Smart People Are Foolish and How to Avoid It ”which examines the psychology of irrational thinking and the best ways to make wiser decisions.