Introduction

Decision theory is about how to behave rationally under conditions of uncertainty, especially if this uncertainty involves being acausally blackmailed and/or gaslit by alien superintelligent basilisks.

Decision theory has found numerous practical applications, including proving the existence of God and generating endless LessWrong comments since the beginning of time.

However, despite the apparent simplicity of "just choose the best action", no comprehensive decision theory that resolves all decision theory dilemmas has yet been formalized. This paper at long last resolves this dilemma, by introducing a new decision theory: VDT.

Decision theory problems and existing theories

Some common existing decision theories are:

Causal Decision Theory (CDT): select the action that *causes* the best outcome.
Evidential Decision Theory (EDT): select the action that you would be happiest to learn that you had taken.
Functional Decision Theory (FDT): select the action output by the function such that if you take decisions by this function you get the best outcome.

Here is a list of dilemmas in decision theory that have vexed at least one of the above decision theories:

Newcomb's problem: a superintelligent predictor, Omega, gives you two boxes. Box A is transparent and has $1000. Box B is opaque and has $1M if Omega predicts you would pick only Box B, and otherwise empty. Do you take just Box B, or Box A and Box B?
- CDT two-boxes and misses out on $999k.
Smoking lesion: people with a certain genetically-caused lesion tend to smoke and develop cancer, but smoking does not cause cancer (this thought experiment is sponsored by Philip Morris International). You enjoy smoking and don't know if you have the lesion. Should you smoke?
- EDT says you shouldn't smoke, because that's evidence you have the lesion.
Parfit's hitchhiker: you're stranded in a desert without money trying to get back to your apartment, and a telepathic taxi driver goes past, but will only save you if they predict you'll actually bring back $100 from your apartment once they've driven you home. Do you commit to paying?
- CDT decides, upon arriving in the apartment, to not pay the taxi driver, and therefore leaves you stranded.
Counterfactual mugging: another superintelligent predictor (also called Omega because there aren't very many baby name books for superintelligent predictors), flips a fair coin. If the coin la

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