Omega, a perfect predictor, flips a coin. If it comes up heads, Omega asks you for $100, then pays you $10,000 if it predict you would have paid if it had come up tails and you were told it was tails. If it comes up tails, Omega asks you for $100, then pays you $10,000 if it predicts you would have paid if it had come up heads and you were told it was heads.

Here there is no question, so I assume it is something like: “What do you do?” or “What is your policy?”

That formulation is analogous to standard counterfactual mugging, stated in this way:

Omega flips a coin. If it comes up heads, Omega will give you 10000 in case you would pay 100 when tails. If it comes up tails, Omega will ask you to pay 100. What do you do?

According to these two formulations, the correct answer seems to be the one corresponding to the first intuition.

Now consider instead this formulation of counterfactual PD:

Omega, a perfect predictor, tells you that it has flipped a coin, and it has come up heads. Omega asks you to pay 100 (here and now) and gives you 10000 (here and now) if you would pay in case the coin landed tails. Omega also explains that, *if* the coin had come up tails—but note that it hasn’t—Omega would tell you such and such (symmetrical situation). What do you do?

The answer of the second intuition would be: I refuse to pay here and now, and I would have paid in case the coin had come up tails. I get 10000.

And this formulation of counterfactual PD is analogous to this formulation of counterfactual mugging, where the second intuition refuses to pay.

Is your opinion that

The answer of the second intuition would be: I refuse to pay here and now, and I would have paid in case the coin had come up tails. I get 10000.

is false/not admissible/impossible? Or are you saying something else entirely? In any case, if you could motivate your opinion, whatever that is, you would help me understand. Thanks!

Ok, if you want to clarify—I’d like to—we can have a call, or discuss in other ways. I’ll contact you somewhere else.