The Earache Dilemma: The Answer

In the last blog I talked about how probability favours not insuring your domestic goods.  Then I presented the following moral dilemma:

500 million people are about to experience a quite discomforting but not too serious earache for the next hour.  However if one innocent person is killed the 500 million won't have to go through with the earache for an hour. Should we kill the innocent person or let the 500 million people go through with the earache?

Unsurprisingly, everybody who emailed with an answer said we should spare the one innocent life for the sake of 500 million earaches.  That’s because, presumably, people want to minimise suffering, but yet at the same time they thought that the death of one innocent person was worse than 500 million earaches.  Fair enough, but this only goes to show that humans are weirdly inconsistent.  Here’s why.

I asked this same question at a housewarming party recently to a group of about 20 people, and the fairly unanimous consensus was, again, that we should spare the innocent life.  But out of about 20 people it turns out that at least half of them insure their domestic goods, and about half of that group gave a peculiar answer to the following question;

Would you choose a certain earache for an hour or a 1 in 500 million chance of being the innocent person of dying?

Roughly 50% of people would choose the certain earache for an hour – which is barmy.  I take it that they are having trouble envisaging just how much 500 million is – I should imagine when they try to picture 500 million they are imagining their numbered ball in a large unlucky dip bag with a few hundred other numbered balls.  No, it’s 500 million – but the mind cannot picture just how large 500 million is!!!!

How do I know that most rational people would rather have a 1 in 500 million chance of being the innocent person of dying than a certain earache?  It’s not just because the probability is so heavily in their favour of surviving; it’s because in everyday life humans have multiple opportunities to buy all kinds of safety devices for their modes of travel, for their DIY, for their mowing the lawn, for climbing ladders, or whatever, each with a much less than 1 in 500 million chance of death or serious injury, and they prefer to take the chance. That’s how I know. 

When considered with proper rationality, the observation of people’s general day to day behaviour shows that most people would not pay one pound coin to avoid a 1 in 500 million chance of death, but most people would pay a pound coin to get rid of an earache that was going to go on for another hour.

This is why the insurance issue is relevant – we choose an optimal deal because probability is hugely in our favour.  We should do the same with the earache conundrum, because as I’ve shown – given that most people would not pay one pound coin to avoid a 1 in 500 million chance of death, but most people would pay a pound coin to get rid of an earache that was going to go on for another hour – this means that most people think an earache for an hour is worse that a 1 in 500 million chance of death. 

Yet when the question is stated in the following way:

500 million people are about to experience a quite discomforting but not too serious earache for the next hour.  However if one innocent person is killed the 500 million won't have to go through with the earache for an hour. Should we kill the innocent person or let the 500 million people go through with the earache?

We find we are agreed that 500 million should suffer the earache, yet if one of us was the 1 in 500 million, we’d choose to be in that unlucky dip bag rather than having the earache.  It’s a funny old world!