A Newcomblike dilemma that pries apart the recommendations of EDT and CDT/FDT. Also known as XOR Blackmail (albeit I (EY) would object to this because it isn't what's normally understood as "blackmail").

Suppose that an excellent Predictor, greedy for cash, known to be absolutely honest, sends to the owner of an apartment complex the following letter:

> Exactly one of the following statements is true: You will pay me $1000, XOR your building already has a terrible termite infestation (I didn't put it there).

Since a terrible termite infestation would cost $1,000,000 to control, an evidential decision theorist will reason, "It is better to pay $1000; this is better news about whether I have a termite infestation." They pay the $1000.

But this makes the Predictor's statement be true! So the Predictor can go around sending letters like this to all the EDT agents in town who can afford the $1000, after checking to make sure they don't actually have a termite infestation.

Conversely a CDT or FDT agent will reason that, if they get a letter like this, they must already have a termite infestation, which will be unaffected by whether they pay (CDT) / by whether people like them predictably pay (FDT). So the Predictor won't send them letters if they have no termites, because they won't pay, and because the contents would be false. CDT/FDT agents only see these letters if the Predictor, acting perhaps to increase its credibility with EDT agents, sends them to some CDT/FDT agents who *do* have termites -- and then the result of this general policy and disposition, from an FDT perspective, is to get a valuable free warning from the Predictor about their termite infestation.

Termite dilemma

Termite dilemma