Sunday, March 28, 2010

On the Mathematics behind Indecisiveness

Using statistics to make decisions is a good idea, but you should make sure you understand exactly what’s going on first. Think of this, for example.

Imagine I was holding two identical envelopes. One contains twice as much money as the other, but there is no way of telling which is which. I give you one of them, and you have the option to take the other one instead or keep the envelope you have. Which is the best option to choose?

The maths is pretty simple. Say you are holding envelope A, which contains an amount x. Envelope B thus contains either 2x with a probability of 50%, or 0.5x with a probability of 50%. The expected value is simply the mean of the probability space, which is 1.25x. This is more than the contents of the envelope in your hand. The maths therefore says you should switch envelopes. The problem is, I now give you the option to switch back. The maths doesn’t change, and so you should switch back. In fact, you should never settle for what you have, and always change your mind.

The moral of the story? There’s no point in being indecisive. I’ll always have more than you.

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