WHICH LIE TO BELIEVE?

 

 

In WW2, RAF bomber crews had to fly 30 missions.

Like anything, the belief was that the more missions you flew the less chance you had of surviving, every mission was a step closer to getting shot down.

So, on your first mission you had a 1 in 30 chance of getting hit, on your second mission it was 2 in 30, by your 15^th mission it was 50/50, the more missions you flew the worse your odds.

Obviously, this had a depressing effect on morale and an effort was made to educate bomber crews that every time you went out your chances were exactly the same, they were always 1 out of however many planes were in the raid, they didn’t change with the number of missions.

If there were 400 planes in that raid, your odds were 1 out of 400, if there were 250 planes your odds were 1 out of 250, not one out of the number of missions you flew.

You always had the same chance as the crew of every other plane in the raid.

This lifted morale because everyone could see it made sense.

At least it seemed to make sense until I heard about the Monty Hall paradox.

This is a statisticians’ thought experiment based on the American game-show host, Monty Hall.

He shows the contestant 3 doors and says that behind one is a car, behind the other two doors are donkeys.

He asks the contestant to pick a door.

When the contestant has chosen a door, Monty Hall opens one of the two remaining doors to reveal a donkey behind that door.

He then offers the contestant the chance to stay with the door they picked or change to the other remaining door.

And here’s the part where it gets interesting (confusing but interesting).

The numbers show that most of us would stay with the door we picked, with two doors left it’s 50/50 so changing makes no difference.

But the numbers also show that we SHOULD change to stand a better chance of winning.

This feels like cognitive dissonance, what possible reason is there to change?

Well apparently, when we made our first choice we had a 1 in 3 chance of being right, if we stick with that we still have the result of that 1 in 3 choice.

But the situation has now changed, we now have a 1 in 2 chance of picking the right door.

This is why we are told we should change, to give us better odds.

We are told that we only resist changing because of the sunk-cost fallacy: the tendency to stick with what we’ve already invested in.

If we change and get the donkey we feel as if we lost the car (even though we never actually had it).

For me, this feels like the opposite of the RAF reasoning.

The Monty Hall logic feels like every time you go up the odds change according to the fact that you’ve already been up before.

Which would mean you had less chance of a safe return every time you flew.

Changing circumstances every time is more in accordance with Bayesian theory which is fashionable amongst marketing types.

Its complexity makes it attractive to strategists and academics.

So which is the best route for us to choose, the simple or the complicated?

Well, it depends which department you’re in.

When he was accused of always changing his opinion, the economist J M Keynes said:

“Of course, when facts change I change my opinion. Why sir, what do you do?”

Which justifies the more complicated way of thinking.

But, nearly 200 years earlier, when Dr Johnson had just heard a lecture on immaterialism, he was asked what he thought of it.

He gave a large stone a hefty kick and said: “I refute it thus”.

 

Because they deal in theory, marketing and strategists will choose the more complicated JM Keynes route.

Because they deal with punters, creative will choose the simpler Dr Johnson route.