The pitfalls of 50-50 thinking

Back in university, in one of India’s most reputed technological institutions, one of my batch mates posed a conundrum. He looked at his ceiling fan and claimed – that fan has two states: it can fall down or stay fixed to the ceiling. Therefore, the probability that it falls down is 1 in 2, or 50%.

His question sent the hostel into a tizzy. Now everybody in the hostel, including him, knew that this conclusion was wrong. Given our institute was located in the sultry Indian west coast, we all used ceiling fans nearly every day and hadn’t once read the headline “Whirling fan decapitates hapless student” in the local newspaper. If anything, there was often a fight among roommates to sleep right under the ceiling fan, where its circulation (and the risk of decapitation) was highest.

But we weren’t able to put our fingers on why his reasoning was wrong. We did not realize immediately that you can only divide equally probable outcomes by total number of outcomes to find an event’s probability – such as the toss of a fair coin. With a fair coin, the likelihood of heads is one out of two equally likely outcomes. If the coin were loaded, this calculation (one in two) would not hold even if it still had only two sides. A fan anchored to the ceiling had only two outcomes, but one was far more loaded than the other. It represented a skewed distribution. And as opposed to ‘normal’ distributions, we do not understand skewed distributions intuitively.

I point out this anecdote to demonstrate how our brains are susceptible to 50-50 thinking. That is, in the face of two outcomes, we are prone to quickly jump to the conclusion that they are, more or less, equally likely. This systematic error in thinking had some of the best technical minds in the country pause and think about how secure their ceiling fan was. Indeed, Daniel Kahneman and Amos Tversky have demonstrated how students from MIT, Harvard and Princeton are just as likely to make systematic errors in thinking as anybody else does.

Whenever distributions skew one way or another, our intuition lets us down. We continue to hold televised debates with a 50-50 division (for and against) even for issues such as climate change, where more than 97% of the scientific community agrees that we have meddled with the climate. With interviews, we continue to make “hire” or “no-hire” decisions, despite knowing that an employee who makes 10% better decisions can produce outputs that are more than 10x better in the long run.

As Nassim Taleb bemoans, the world underestimates the effect of skewness, asymmetry and eccentricity. Our our minds always try and break the world into shades of black or white, good or bad and right or wrong. In the process, they can often prevent us from making the best decisions.

Inspiration: Fooled by Randomness – Nassim Taleb

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