Poll Question Analysis

Question

Imagine you buy a lottery ticket every week, and you always select the same numbers. Then, one day, your friend convinces you to change all of the numbers.

Later that evening, you turn on the television to watch the lottery drawing. Slowly but surely, each one of your original numbers drops out of the machine!

How do you feel?

Response

This is a question I’ve asked various people, in various different ways, many times.

They usually give me a funny look before they answer.

But when they do answer, I try to remember what they said.

Although I acknowledge that my “research” is not at all scientific, anecdotal evidence tells me that there’s an interesting cognitive bias at play here. You see, most people are well aware that they would have a negative reaction to this set of events.

Facets readers have reaffirmed my belief, with only 16% selecting answer (a). For the remaining 84%, there was an even split between those who would simply be disappointed and those who would be driven to commit murder. Rest assured that we have reported the latter crowd to the authorities.

But is this negative reaction rational?

We must first acknowledge that – at the time of selecting your own numbers – the drawn lottery numbers were indeterminate.

Indeterminate is more than simply unknown. It means that the outcome had not yet been determined. The lottery numbers were random variables yet to be realized.

Now, if one were inclined to stumble into a metaphysical argument about whether future events are predetermined or random, this is where it might happen.

But let’s not go there yet.

Assuming that future events are indeed random variables, we can estimate probabilities for those events. This is rather easy to compute for a controlled system like a lottery drawing. Taking the UK National Lottery (Lotto) as an example, your odds of winning are less than 1 in 45 million (~0.00000002). In some circles, you’d be well within your rights to round that down to zero.

Now the important part: since the drawing of the lottery numbers is independent of your own selection, this probability does not change when you change your numbers! The lottery machine simply doesn’t care whether you succumbed to the malicious intent of your friend and changed your lucky numbers.

The negative reaction is irrational.

“But my numbers came up!” I hear you cry.

Perhaps they did, in this hypothetical scenario. My question described a single realization of the random variables, in a timeline where you had already switched your numbers. If you could go back and choose not to change your numbers, does that mean you would have definitely won?

“Yes!”

No. By “going back,” you essentially reset the probability to 0.00000002.

If you don’t buy this argument, you may be a proponent of predeterminism, a philosophical belief that all future events are determined in advance. This is colloquially known as fate.

If not – and you selected answer (b) or (c) – then there appears to be a contradiction here, and perhaps a powerful cognitive bias at its root.

Admittedly, I’m not even sure if this cognitive bias has a name. It’s similar to some of the biases I’ve written about in the series, but it’s not quite the same. If you know, please enlighten me.