The Denominator Neglect

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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

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About vivekkaul
Vivek Kaul is a writer who has worked at senior positions with the Daily News and Analysis(DNA) and The Economic Times, in the past. He is the author of the Easy Money trilogy. Easy Money: The Greatest Ponzi Scheme Ever and How It Is Set to Destroy the Global Financial System , the latest book in the trilogy has just been published. The first two books in the trilogy were published in November 2013 and July 2014 respectively. Both the books were bestsellers on Amazon.com and Amazon.in. Currently he works as an economic commentator and writes regular columns for www.firstpost.com. He is also the India editor of The Daily Reckoning newsletter published by www.equitymaster.com. His writing has appeared across various other publications in India. These include The Times of India, Business Standard,Business Today, Business World, The Hindu, The Hindu Business Line, Indian Management, The Asian Age, Deccan Chronicle, Forbes India, Mutual Fund Insight, The Free Press Journal, Quartz.com, DailyO.in, Business World, Huffington Post and Wealth Insight. In the past he has also been a regular columnist for www.rediff.com. He has lectured at IIM Bangalore, IIM Indore, TA PAI Institute of Management and the Alliance University (Bangalore). He has also taught a course titled Indian Economy to the PGPMX batch of IIM Indore. His areas of interest are the intersection between politics and economics, the international financial crisis, personal finance, marketing and branding, and anything to do with cinema and music. He can be reached at vivek.kaul@gmail.com

One Response to The Denominator Neglect

  1. Anandatman says:

    I agree with you completely ! “out of” plays a crucial factor in any decision – be it for shopping or in business.

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