Superrationality: How Decision Theory Resolves Any Dilemma

Chapter IV: Why Carl is Wrong

This is a follow-up to Chapter I, Chapter II and Chapter III.

Carl two-boxes in Newcomb’s Problem, because he believes his decision (to one-box or to two-box) has no effect on the prediction made by Omega. After all, this prediction already happened! You can’t change the past.

Carl’s view of Newcomb’s Problem

So Omega’s prediction is fixed, as Carl sees it. Now:

• if Omega predicts you will one-box, two-boxing earns $1,000 more than one-boxing
• if Omega predicts you will two-box, two-boxing earns $1,000 more than one-boxing.

So, two-boxing dominates one-boxing: it is better in every possible situation. Carl therefore two-boxes, and with that, follows Causal Decision Theory (CDT).

Where EDT recommends taking the action that is the best evidence for a good outcome, CDT says you should take the action that **causes** the best outcome.

What is causality, anyway?

A full explanation of causality goes beyond the purpose of this series, but a short introduction is still valuable.

Causality is about cause and effect. Importantly, the effect is dependent on the cause: if the cause happens, the effect is more likely to happen than if the cause doesn’t happen.

But that’s not all. Let’s look at an example.

Say we observe thousands of people. We notice that those who sneeze more often wipe their nose than those who don’t sneeze.

But observing those same people, we also notice that those who have hay fever wipe their nose more often than those without hay fever.

However, if we only look at the people who sneeze, those with hay fever don’t wipe their nose more often than those without it. The same is true if we only look at people who don’t sneeze.

So say we learn whether or not a person sneezes. Then also learning whether or not that person has hay fever provides no additional information about whether that person wipes her nose or not.

But if we learn the hay fever status of a person, then learning whether or not that person sneezes is helpful for determining whether that person wipes her nose.

How does causality come into play here? Well, wiping one’s nose is independent upon hay fever given that the person sneezes; therefore, it can’t be that hay fever is causing the nose wiping. It’s the sneezing that causes the wiping!

Smoking Lesion

In Smoking Lesion, your action — to smoke or not to smoke — has no causal effect on whether or not you get lung cancer. After all, lung cancer is independent upon smoking given the presence or absence of the genetic lesion!

The only thing — in the Smoking Lesion world — that does have a causal effect on getting lung cancer is the lesion itself, on which your action has no influence.

Carl, who follows CDT, correctly smokes in Smoking Lesion. If smoking doesn’t cause lung cancer anyway, he may as well enjoy it.

But he also two-boxes in Newcomb’s Problem, and we have already seen that’s problematic: Omega predicts Carl will two-box, and therefore Carl misses out on $1,000,000.

Newcomb’s Problem vs. Smoking Lesion

At this point, you may wonder about the exact difference between Newcomb’s Problem and Smoking Lesion.

After all, the two problems may seem basically the same: if we say not having the lesion is worth $1,000,000 (because you have a lower risk of lung cancer), and smoking is worth $1,000 to you, then Smoking Lesion looks like this:

That’s the same table as Newcomb’s Problem (except for the names):

It seems the dominant action in Smoking Lesion is to smoke, as that action always earns $1,000 more than not smoking.

Likewise, it seems the dominant action in Newcomb’s Problem is two-boxing.

So why am I saying the best actions are smoking and one-boxing?

The big difference between the two problems is in the predictive power of Omega. To fully understand this, we’ll get into a fun thought experiment in Chapter V.

For now, thanks for reading!

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