Among other things, schools teach Mathematics very badly, leading to a situation where most adults don’t understand the practical applications of even fifth standard Mathematics and pay for it in the process.
One such mistake that we make is known as the denominator neglect. As Thomas Gilovich and Less Ross write in The Wisest One in the Room—How You Can Benefit from Social Psychology’s Most Powerful Insights: “The effects of strategically choosing the right scale (i.e. the right denominator) can be dramatic. In one study, respondents judged a disease that kills 1,200 out of every 10,000 afflicted individuals to be more dangerous than one that’s twice as lethal, killing 24 out of every 100.”
This didn’t make any sense. The second disease was clearly more lethal given that chances were that it would kill twice the number of afflicted people than the first one would. But people still found the first disease more dangerous because the number 1,200 is much bigger than the number 24. In the process, they had totally neglected the denominator and made a blunder in arriving at the conclusion that they did.
In fact, a well-known experiment will make the point even clearer. In this experiment participants are given a choice to draw a red marble, out of two urns and win a prize. The first urn contains 10 marbles of which one is red. The second urn contains 100 marbles, of which 8 are red. It doesn’t take rocket science to figure out that the chances of drawing a red marble and in the process winning a prize are higher in case of the first urn. The probability of winning in the first case is 10 per cent and in the second case 8 per cent.
Nevertheless, as Daniel Kahneman writes in Thinking, Fast and Slow: “About 30-40% of student s[basically participants in the experiment] choose the urn with the larger number of winning marbles, rather than the urn that provides a better chance of winning…Vivid imagery contributes to denominator neglect…When I think of the small urn, I see a single red marble…When I think of the larger urn, I see eight winning marbles.”
And that is how denominator neglect works. In fact, that also explains why different ways of talking about risk vary so much. As Kahenman writes: “You read that “a vaccine that protects children from a fatal disease carries a 0.001% risk of permanent disability”. The risk appears small. Now consider another description of the same risk: “One of 100,000 vaccinated children will be permanently disabled.” The second statement does something to your mind that the first does not: it calls up the image of an individual child who is permanently disabled by the vaccine; the 99,999 safely vaccinated children have faded into the background.”
That is how things work. The larger point is that people concentrate on absolute values in most cases and don’t take the denominator into account. This also explains why people are more likely to spend in a stronger currency than a weaker one. As Gilovich and Ross write: “People are more likely to buy expensive brand-name products when they are priced in a strong currency like the British pound that results in a relatively small price tag (318 pounds for an Apple iPad with retinal display) than when priced in a weak currency like the Mexican peso that results in a relatively large price tag(6,395 pesos for the same iPad).”
This also explains why many Indians buy gadgets when they go abroad. Of course, in many cases, the goods bought abroad are actually cheaper but in many other cases they simply appear cheaper because they are priced in a much stronger currency.
And this is how our lack of understanding of middle-school maths hurts in the decisions that we make in our daily lives.
The column originally appeared in the Bangalore Mirror on September 28, 2016