COVID-19 | The simple mathematical error that can hinder the control of the pandemic

Imagine your bank offers you a deal where your money will double every three days. If you invest just US$1 today, approximately 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 US$1,048,576.

After another 30 days, you would have earned over 1 billion. And after a year, you would have more than US$1,000,000,000,000,000,000,000,000,000,000,000,000.

If your calculations fell far short of the answer, you are not alone. Many people consistently underestimate how fast a stock is rising, a mistake known as “exponential growth bias.”

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

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

In other words, this simple math error could be costing lives, meaning correcting bias should be a priority in attempts to flatten the curves and prevent 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.

On the contrary, Exponential 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, rise to three on the second day, and nine on the third day. But soon it will increase significantly

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

According to 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 on 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 up to the 64th square.

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.

Most people intuitively assume that most growth is linear.which leads her to greatly underestimate the speed of exponential increase.

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

Most savings accounts offer compound interest, meaning you accumulate additional interest on top of the interest you’ve already earned.

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

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

The education trap

Surprisingly, a higher level of education does not prevent people from making these mistakes.

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

This may be because they rely on their intuition rather than deliberative thinking, so 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 they understand exponential growth, but then fall into bias when asked to estimate things like compound interest.

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

Experiment

With the COVID-19 pandemic, researchers began to think about whether bias could also influence our understanding of infectious diseases.

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

In March, Joris Lammers of the University of Bremen in Germany and Jan Crusius and Anne Gast of 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 greatly 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: exponential growth bias had made them complacent about official advice.

Media Graphics

This is in line with other findings by Ritwik Banerjee and Priyama Majumda at the Indian Institute of Management in Bengaluru and Joydeep Bhattacharya at Iowa State University in the United States.

In their study (currently under peer review), they found that exponential growth bias may predict lower compliance with World Health Organization recommendationsincluding wearing masks, washing hands, using disinfectants and self-isolation.

Researchers speculate that some of the graphic depictions of the pace 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 numbers on the “y” (vertical) axis increase 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 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 the exponential growth bias and asked them to estimate the growth of the disease over two weeks, people greatly improved their estimates and changed their views on social distancing.

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

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

Lammers believes the exponential nature of the virus’s spread should be highlighted in coverage of the pandemic. The media “should not only report the numbers from the previous day and week, but also explain what will happen in the coming days, weeks, months, if the same accelerated growth persists,” she says.

He is confident that even a small effort to correct this bias could bring enormous benefits. In the US, where the pandemic has hit hardest, it took just a few months for the virus to infect more than five million people, she says.

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

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