Calculus in Game and Decision Theory
Intuitive Introduction to Functional Decision Theory


"In your problem description you said you receive the letter"

True, but the problem description also specifies subjunctive dependence between the agent and the predictor. When the predictor made her prediction the letter isn't yet sent. So the agent's decision influences whether or not she gets the letter.

"This intuition is actually false for perfect predictors."

I agree (and have written extensively on the subject). But it's the prediction the agent influences, not the presence of the termite infestation.

Given that you receive the letter, paying is indeed evidence for not having termites and winning $999,000. EDT is elegant, but still can't be correct in my view. I wish it were, and have attempted to "fix" it.

My take is this. Either you have the termite infestation, or you don't.

Say you do. Then

  • being a "payer" means you never receive the letter, as both conditions are false. As you don't receive the letter, you don't actually pay, and lose the $1,000,000 in damages.
  • being a "non-payer" means you get the letter, and you don't pay. You lose $1,000,000.

Say you don't. Then

  • payer: you get the letter, pay $1,000. You lose $1,000.
  • non-payer: you don't get the letter, and don't pay $1,000. You lose nothing.

Being a payer has the same result when you do have the termites, but is worse when you don't. So overall, it's worse. Being a payer or a non-payer only influences whether or not you get the letter, and this view is more coherent with the intuition that you can't possibly influence whether or not you have a termite infestation.

XOR Blackmail is (in my view) perhaps the clearest counterexample to EDT:

An agent has been alerted to a rumor that her house has a terrible termite infestation that would cost her $1,000,000 in damages. She doesn’t know whether this rumor is true. A greedy predictor with a strong reputation for honesty learns whether or not it’s true, and drafts a letter:

 I know whether or not you have termites, and I have sent you this letter iff exactly one of the following is true: (i) the rumor is false, and you are going to pay me $1,000 upon receiving this letter; or (ii) the rumor is true, and you will not pay me upon receiving this letter.

The predictor then predicts what the agent would do upon receiving the letter, and sends the agent the letter iff exactly one of (i) or (ii) is true. Thus, the claim made by the letter is true. Assume the agent receives the letter. Should she pay up?

(Styling mine, not original.) EDT pays the $1,000 for nothing: it has absolutely no influence on whether or not the agent's house is infested with termites.

Is it necessary to be able to work during all MIRI office hours, or is it enough if my hours are partially compatible? My time difference with MIRI is 9 hours, but I could work in the evening (my time) every now and then.

Your original description doesn't specify subjunctive dependence, which is a critical component of the problem.

Heighn’s response to this argument is that this is a perfectly fine prescription.

Note that omnizoid hasn't checked with me whether this is my response, and if he had, I would have asked him to specify the problem more. In my response article, I attempt to specify the problem more, and with that particular specification, I do indeed endorse FDT's decision.

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