Well, you can only predict conditional on what you write, you can’t predict unconditionally. However, once you’ve fixed what you’ll write in order to make a prediction, you can’t then change what you’ll write in response to that prediction.
Actually, it isn’t about utility in expectation. If you are the kind of person who pays you gain $9900, if you aren’t you gain $100. This is guaranteed utility, not expected utility.
The fact that it is “guaranteed” utility doesn’t make a significant difference: my analysis still applies. After you know the outcome, you can avoid paying in that case and get 10000 instead of 9900 (second intuition).
“After you know the outcome, you can avoid paying in that case and get 10000 instead of 9900 (second intuition)”—No you can’t. The only way to get 10,000 is to pay if the coin comes up the opposite way it comes up. And that’s only a 50⁄50 chance.
If the DM knows the outcome is heads, why can’t he not pay in that case and decide to pay in the other case? In other words: why can’t he adopt the policy (not pay when heads; pay when tails), which leads to 10000?
It seems you are arguing for the position that I called “the first intuition” in my post. Before knowing the outcome, the best you can do is (pay, pay), because that leads to 9900.
On the other hand, as in standard counterfactual mugging, you could be asked: “You know that, this time, the coin came up tails. What do you do?”. And here the second intuition applies: the DM can decide to not pay (in this case) and to pay when heads. Omega recognises the intent of the DM, and gives 10000.
Maybe you are not even considering the second intuition because you take for granted that the agent has to decide one policy “at the beginning” and stick to it, or, as you wrote, “pre-commit”. One of the points of the post is that it is unclear where this assumption comes from, and what it exactly means. It’s possible that my reasoning in the post was not clear, but I think that if you reread the analysis you will see the situation from both viewpoints.
I am considering the second intuiton. Acting according to it results in you receiving $0 in Counterfactual Prisoner’s Dilemma, instead of losing $100. This is because if you act updatefully when it comes up heads, you have to also act updatefully when it comes up tails. If this still doesn’t make sense, I’d encourage you to reread the post.
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!
To be honest, this thread has gone on long enough that I think we should end it here. It seems to me that you are quite confused about this whole issue, though I guess from your perspective it seems like I am the one who is confused. I considered asking a third person to try looking at this thread, but I decided it wasn’t worth calling in a favour.
I made a slight edit to my description of Counterfactual Prisoner’s Dilemma, but I don’t think this will really help you understand:
Omega, a perfect predictor, flips a coin and tell you how it came up. If if 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. 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. In this case it was heads.
Well, you can only predict conditional on what you write, you can’t predict unconditionally. However, once you’ve fixed what you’ll write in order to make a prediction, you can’t then change what you’ll write in response to that prediction.
Actually, it isn’t about utility in expectation. If you are the kind of person who pays you gain $9900, if you aren’t you gain $100. This is guaranteed utility, not expected utility.
The fact that it is “guaranteed” utility doesn’t make a significant difference: my analysis still applies. After you know the outcome, you can avoid paying in that case and get 10000 instead of 9900 (second intuition).
“After you know the outcome, you can avoid paying in that case and get 10000 instead of 9900 (second intuition)”—No you can’t. The only way to get 10,000 is to pay if the coin comes up the opposite way it comes up. And that’s only a 50⁄50 chance.
If the DM knows the outcome is heads, why can’t he not pay in that case and decide to pay in the other case? In other words: why can’t he adopt the policy (not pay when heads; pay when tails), which leads to 10000?
If you pre-commit to that strategy (heads don’t post, tails pay) it provides 10000, but it only works half the time.
If you decide that after you see the coin, not to pay in that case, then this will lead to the strategy (not pay, not pay) which provides 0.
It seems you are arguing for the position that I called “the first intuition” in my post. Before knowing the outcome, the best you can do is (pay, pay), because that leads to 9900.
On the other hand, as in standard counterfactual mugging, you could be asked: “You know that, this time, the coin came up tails. What do you do?”. And here the second intuition applies: the DM can decide to not pay (in this case) and to pay when heads. Omega recognises the intent of the DM, and gives 10000.
Maybe you are not even considering the second intuition because you take for granted that the agent has to decide one policy “at the beginning” and stick to it, or, as you wrote, “pre-commit”. One of the points of the post is that it is unclear where this assumption comes from, and what it exactly means. It’s possible that my reasoning in the post was not clear, but I think that if you reread the analysis you will see the situation from both viewpoints.
I am considering the second intuiton. Acting according to it results in you receiving $0 in Counterfactual Prisoner’s Dilemma, instead of losing $100. This is because if you act updatefully when it comes up heads, you have to also act updatefully when it comes up tails. If this still doesn’t make sense, I’d encourage you to reread the post.
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
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!
To be honest, this thread has gone on long enough that I think we should end it here. It seems to me that you are quite confused about this whole issue, though I guess from your perspective it seems like I am the one who is confused. I considered asking a third person to try looking at this thread, but I decided it wasn’t worth calling in a favour.
I made a slight edit to my description of Counterfactual Prisoner’s Dilemma, but I don’t think this will really help you understand:
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.