# Cheer up and look on the bright side of life

## You'll be better off if you focus on maximising the happiness you get from good things

Trigger warning: Today, I thought I'd take a risk and include some maths equations in what is supposed to be a light Sunday read.

Don't worry, it won't be a lot of maths or even particularly difficult maths - you're not, for instance, going to require working knowledge of the Weierstrass factorisation theorem (God knows I don't have the intellectual capacity to pull that off) - but I thought I should give you a heads-up all the same.

With that out of the way, let me get to what I really want to write about, and that is the question of how much risk people should reasonably include in their lives.

To tackle that, I am first going to tell you about my father's airport habits.

My father insists on arriving at the airport a full four hours before a flight departs.

To my father, the two-hour recommended arrival time buffer is a conspiracy designed to make you miss your flight and buy another ticket. He is the kind of man who arrives two hours ahead of time to catch the out-of-town bus.

It has become such a habit for him that he once went to the airport four hours ahead of a flight, even though he was not technically getting on the flight or even dropping someone off.

He was there to pick up my brother.

Despite years of lobbying from the rest of the family, he has steadfastly held on to this practice, mainly because nobody has yet been able to come up with a convincing reason why his way is all that bad. After all, he has never missed a flight.

I was pondering my latest attempt to persuade him to delay departure when I came across arguments made some time back by the late Nobel Prize-winning economist George Stigler.

He said: "If you never miss the plane, you're spending too much time in airports."

Stigler's reasoning rests on the principle of expected value - that is, you can calculate how much happiness/sadness you will derive from some unknown event by multiplying the probability of it happening with how it will affect you if it actually happened.

The argument was fleshed out by maths professor Jordan Ellenberg using three scenarios.

Scenario 1: Arrive two hours before flight, miss the flight 2 per cent of the time.

Scenario 2: Arrive 90 minutes before flight, miss the flight 5 per cent of the time.

Scenario 3: Arrive an hour before flight, miss the flight 15 per cent of the time.

Spending time and effort to negate all risk is going to leave you unhappier than if you just accepted a small chance that things could go wrong. In other words, in the equation of life, you are likely to end up better off if you focus on maximising the happiness you get from good things instead of minimising the regret you get from the bad.

Now this is the part with the maths.

Try not to get hung up on the specific percentages. They are not meant to be strictly accurate, but just to illustrate a point.

Now let's assume, as Prof Ellenburg does, that each hour you spend in the airport deducts one point from your overall happiness. However, missing the flight is worse, so that would deduct six points from your overall happiness.

If we were to thus calculate the expected value of each scenario, we would get the following:

Scenario 1: -2 + 2 per cent × (-6) = negative 2.1 units of happiness

Scenario 2: -1.5 + 5 per cent × (-6) = negative 1.8 happy units

Scenario 3:-1 + 15per cent × (-6) = negative 1.9 happy units

Now, this maths would not be convincing to someone like my father because he can justifiably say that the amount of regret he gets from missing a flight is far greater than six units and that he goes early enough so as to reduce the likelihood of missing a flight to zero.

So let's do the sums for his case, assuming he goes four hours early, never misses a flight and would experience 100 units of anger if he didn't make the plane.

My father's scenario: -4 + 0 per cent x (-100) = negative 4 happy units

As you can see from the above equations, the most kiasu person comes off worst.

Now, don't get me wrong. I am not by any means suggesting that everyone should start showing up late at the airport or jumping off cliffs. Remember, the percentages are made up.

And despite what it looks like, I certainly did not go through this whole exercise just to once again try and convince my father to go later to the airport. (Although I'll let you know if it worked.)

The lesson I think I take away from this is that some risk can be productive.

If you play with the maths, you will always find that the optimal amount of happiness is achieved when the risk of the bad outcome is not zero.

Spending time and effort to negate all risk is going to leave you unhappier than if you just accepted a small chance that things could go wrong.

In other words, in the equation of life, you are likely to end up better off if you focus on maximising the happiness you get from good things instead of minimising the regret you get from the bad.

Or at least that's what I think this all means. I could very well be wrong.

I did consider running the argument by an economist first to reduce the chance of error, but that would be like turning up at the airport four hours before my flight.

A version of this article appeared in the print edition of The Sunday Times on July 30, 2017, with the headline 'Cheer up and look on the bright side of life'. Print Edition | Subscribe