Newcomb's Paradox - What Would You Choose? - YouTube

In front of you there are two boxes.

Box one is transparent and contains £1,000.

Box two is opaque and contains either £1,000,000 or nothing.

You are given the following choice: either you can take what is in both boxes, or you

can take only what is in the second box.

However, before you are presented with this choice, a supercomputer which has the power

to predict your choices with an unerring accuracy adds the following catch: if the

computer predicts that you will open both boxes, then it will put nothing in box two.

If it predicts that you will choose to open only the second box, then it puts £1,000,000

in the box.

The supercomputer has carried out this test hundreds of times and has never made a wrong

prediction.

So the sequence of events are as follows: The supercomputer makes its prediction, and

based on this prediction it either puts the million pounds into box two or leaves it empty.

You then make your choice.

What do you choose?

Created by William Newcomb, and first published by Robert Nozick in 1969, the problem has

been dividing people for the last 50 years.

You might be thinking that the answer is obvious, and that there’s no actual problem here.

However, in a recent poll of over 31,000 people, 53.5% choose to open box 2, and 46.5% chose

to open both boxes.

So why are people so divided on this question?

Let’s find out.

At the heart of Newcomb’s paradox is a conflict between two principles of decision theory:

the expected utility principle, and the dominance principle.

But before we look at these, let’s look at the standard arguments for being a one-boxer

or a two-boxer.

If I decide to take what is in both boxes, then the supercomputer will have almost certainly

predicted this and will have left the second box empty, leaving me with only £1,000.

But if I decide to just take what’s in the second box, then the supercomputer will have

predicted this and put the million pounds inside, leaving me much richer.

I should therefore choose to take only what is in the second box.

But, a two-boxer will say, when you make your decision, standing in front of the boxes,

the supercomputer has already made its prediction and has therefore already placed the

million inside box two, or has left it empty.

Therefore, taking both boxes can only maximise your reward, as you would either get £1M

+ £1,000 or £0 + £1,000.

Whatever the supercomputer has predicted, you will end up with £1,000 more by choosing

both boxes.

The options and outcomes of the problem can be shown in a payoff matrix.

Here we can clearly see that taking both boxes will leave you with more money, whichever

prediction the supercomputer has made.

In decision theory, this follows the dominance principle, which states that if one strategy

is always better, no matter the circumstances, then it is rational to choose that strategy.

However, this contradicts the expected utility principle, which states that the rational

choice is the one which has the maximal expected utility, or value, to you.

We can work out the expected utility of each action by multiplying each of its mutually

exclusive outcomes by the probability of the outcome, given the action.

Let’s say, being conservative, that the supercomputer can predict the future with

a 90% accuracy.

We can then work out the expected utility of both actions like so

We can see therefore, that using the expected utility principle, the rational choice is

to choose to open only the second box.

So we have two rational but contradictory answers.

Still not sure if you are a one-boxer or a two-boxer?

Well, consider the following.

Suppose your friend is taking the experiment and chooses to open just the second box.

Before the box is opened, you are asked to place a bet on whether there will be a million

pounds inside.

Given the success of the supercomputer in correctly predicting the outcome in hundreds

of previous tests, you would surely bet that inside the box was £1,000,000.

Likewise, if your friend chose to open both boxes, wouldn’t you bet that box two is

empty?

Now suppose that the back of box two is transparent, and from where you stand, you can see what’s

inside both boxes.

Your friend taking the experiment can still only see inside box one, and the £1,000.

Assuming you want the best for your friend, you would want him to open both boxes, regardless

of what’s in box two.

If the £1,000,000 is in the box, it’s not suddenly going to disappear if he chooses

to open both.

It seems that the logical thing to do would be to open both boxes, but is that how you

would actually act if given the opportunity?

Click on the poll in the top right hand corner to make your choice, and let me know how you

voted and why, down in the comments.

Hey, thanks for watching.

Have you ever heard about the dancing plague of 1518, where over 400 people danced wildly

around the city of Strasbourg until they collapsed or died from exhaustion?

Click here to find out why.

Or if you want to watch some more paradox videos then check out this playlist here.

See you next time.