Decision Theory

Everywhere below where a Predictor is mentioned, assume that their predictions are made by scanning your brain to create a highly accurate simulation of you and then observing what this simulation does.

All the below scenarios are one-shot games. Your action now will not influence the future decision problems you end up in.

Newcomb’s Problem
Two boxes: A and B. B contains $1,000. A contains $1,000,000 if the Predictor thinks you will take just A, and $0 otherwise. Do you take just A or both A and B?

Transparent Newcomb, Full Box
Newcomb problem, but you can see that box A contains $1,000,000. Do you take just A or both A and B?

Transparent Newcomb, Empty Box
Newcomb problem, but you can see that box A contains nothing. Do you take just A or both A and B?

Newcomb with Precommitment
Newcomb’s problem, but you have the ability to irrevocably resolve to take just A in advance of the Predictor’s prediction (which will still be just as good if you do precommit). Should you precommit?

Take Opaque First
Newcomb’s problem, but you have already taken A and it has been removed from the room. Should you now also take B or leave it behind?

Smoking Lesion
Some people have a lesion that causes cancer as well as a strong desire to smoke. Smoking doesn’t cause cancer and you enjoy it. Do you smoke?

Smoking Lesion, Unconscious Inclination
Some people have a lesion that causes cancer as well as a strong unconscious inclination to smoke. Smoking doesn’t cause cancer and you enjoy it. Do you smoke?

Smoking and Appletinis
Drinking a third appletini is the kind of act much more typical of people with addictive personalities, who tend to become smokers. I’d like to drink a third appletini, but I really don’t want to be a smoker. Should I order the appletini?

Expensive Hospital
You just got into an accident which gave you amnesia. You need to choose to be treated at either a cheap hospital or an expensive one. The quality of treatment in the two is the same, but you know that billionaires, due to unconscious habit will be biased towards using the expensive one. Which do you choose?

Rocket Heels and Robots
The world contains robots and humans, and you don’t know which you are. Robots rescue people whenever possible and have rockets in their heels that activate whenever necessary. Your friend falls down a mine shaft and will die soon without robotic assistance. Should you jump in after them?

Death in Damascus
If you and Death are in the same city tomorrow, you die. Death is a perfect predictor, and will come where he predicts you will be. You can stay in Damascus or pay $1000 to flee to Aleppo. Do you stay or flee?

Psychopath Button
If you press a button, all psychopaths will be killed. Only a psychopath would press such a button. Do you press the button?

Parfit’s Hitchhiker
You are stranded in the desert, running out of water, and soon to die. A Predictor will drive you to town only if they predict you will pay them $1000 once you get there. You have been brought into town. Do you pay?

XOR Blackmail
An honest predictor sends you this letter: “I sent this letter because I predicted that you have termites iff you won’t send me $100. Send me $100.” Do you send the money?

Twin Prisoner’s Dilemma
You are in a prisoner’s dilemma with a twin of yourself. Do you cooperate or defect?

Predictor Extortion
A Predictor approaches you and threatens to torture you unless you hand over $100. They only approached you because they predicted beforehand that you would hand over the $100. Do you pay up?

Counterfactual Mugging
Predictor flips coin which lands heads, and approaches you and asks you for $100. If the coin had landed tails, it would have tortured you if it predicted you wouldn’t give the $100. Do you give?

Newcomb’s Soda
You have 50% credence that you were given Soda 1, and 50% that you were given Soda 2. Those that had Soda 1 have a strong unconscious inclination to choose chocolate ice cream and will be given $1,000,000. Those that had Soda 2 have a strong unconscious inclination to choose vanilla ice cream and are given nothing. If you choose vanilla ice cream, you get $1000. Do you choose chocolate or vanilla ice cream?

Meta-Newcomb Problem
Two boxes: A and B. A contains $1,000. Box B will contain either nothing or $1,000,000. What B will contain is (or will be) determined by a Predictor just as in the standard Newcomb problem. Half of the time, the Predictor makes his move before you by predicting what you’ll do. The other half, the Predictor makes his move after you by observing what you do. There is a Metapredictor, who has an excellent track record of predicting Predictor’s choices as well as your own. The Metapredictor informs you that either (1) you choose A and B and Predictor will make his move after you make your choice, or else (2) you choose only B, and Predictor has already made his choice. Do you take only B or both A and B?