“I’ll take you up on your offer and I would also like to borrow $5 at 20% APR amortizing over (4^^^^4 − 100) years, if you defer the first 1200 monthly payments.” Surely the mugger couldn’t refuse such a lucrative offer, and the 4^^^^4 years of fun will clearly be worth the total interest (a dollar a year to live 4^^^^4 years? Sign me up).
In general a reverse-mugging that is conditional on the truth of the mugger’s claim seems like the best response.
“Uh… the matrix lords that I am representing don’t want us to make that deal. They’ll only give you 4^^^^4 years of fun if you give me $5 right now and I keep it.”
As I noted at the beginning of the post, the real problem isn’t an actual intelligent mugger, the real problem is that you’re able to come up with a harebrained scheme all by yourself, if you consistently maximize expected utility.
I realized that after thinking a little longer. There’s nothing from preventing me from believing “There’s an Omega who will give me 4^^^^4 years of fun if I decrease my utility by X right now.”
One way to approach it is by the likelihood that such a hypothesis could pay rent, in which case the possibility of trade with the Omega is a way to test the truth of the statement. If there’s an entity that can dramatically improve my life I would be willing to pay for it with reasonable economic means. If that entity refuses all sane economic means it dramatically lowers the probability that it is a true offer.
Another approach is to consider the opportunity cost of paying this particular entity some of my negative utility when some other entity may offer a better deal. I assume there are an uncountable amount of Omegas who might offer me deals for every possible future utility if I give up some utility now. I only have so much utility that I can reasonably give up right now. Which Omega(s) do I pick to give up my utility to? I certainly shouldn’t choose the most expensive Omega that yields the lowest expected return; I should pick the most efficient Omega for my cost in negative utility. What does that Omega look like? Certainly not one that offers 4^^^^4 years of fun for $5, but one that offers 4^^^^4 years of fun for less than $5 (or even pays me to experience it). Perhaps I only have $5, and spending it now would prevent me from ever accepting another deal from a different Omega. Ultimately what this hypothetical choice reduces to is choosing the earliest likely payoff so that I have more money in the future to consider more deals, e.g. skip out on paying Omega $5 today when I could invest it in the local economy and earn $6 tomorrow and have even more utility to pay potential Omegas with. I have to assume that any particular instance of Omega is roughly as likely as any other; a mugger appearing and offering me a purported deal from a particular Omega is no proof that the particular Omega exists unless there is additional proof such as being able to take out a loan repayable in the distant future or a verifiable insurance policy against the failure of Omega to deliver on the promise.
EDIT: I should probably try to quantify this. U(deal_N)*P(deal_N_is_true) - U(cost_N) is the expected utility of giving up cost_N utility in exchange for deal_N utility from a potential entity Omega_N. Unless I have some evidence that P(deal_X_is_true) is greater than P(deal_N_is_true) for some X and every other N, I should simply pick the most efficient deal. If P(deal_X_is_true | evidence_X_is_true)*U(deal_X) - U(cost_X) > U(deal_N)*P(deal_N_is_true) - U(cost_N) for some X and all other N, then I should pick X. Is a mugger appearing and offering me a particular deal, X, evidence that X is true? No, unless the mugger (or another entity I can trade with, including myself if I find actual evidence that X is true) also believes the deal sufficiently strongly to sell me insurance. In other words the mugger has to believe the deal will pay rent in order for me to believe it will pay rent.
“I’ll take you up on your offer and I would also like to borrow $5 at 20% APR amortizing over (4^^^^4 − 100) years, if you defer the first 1200 monthly payments.” Surely the mugger couldn’t refuse such a lucrative offer, and the 4^^^^4 years of fun will clearly be worth the total interest (a dollar a year to live 4^^^^4 years? Sign me up).
In general a reverse-mugging that is conditional on the truth of the mugger’s claim seems like the best response.
“Uh… the matrix lords that I am representing don’t want us to make that deal. They’ll only give you 4^^^^4 years of fun if you give me $5 right now and I keep it.”
As I noted at the beginning of the post, the real problem isn’t an actual intelligent mugger, the real problem is that you’re able to come up with a harebrained scheme all by yourself, if you consistently maximize expected utility.
I realized that after thinking a little longer. There’s nothing from preventing me from believing “There’s an Omega who will give me 4^^^^4 years of fun if I decrease my utility by X right now.”
One way to approach it is by the likelihood that such a hypothesis could pay rent, in which case the possibility of trade with the Omega is a way to test the truth of the statement. If there’s an entity that can dramatically improve my life I would be willing to pay for it with reasonable economic means. If that entity refuses all sane economic means it dramatically lowers the probability that it is a true offer.
Another approach is to consider the opportunity cost of paying this particular entity some of my negative utility when some other entity may offer a better deal. I assume there are an uncountable amount of Omegas who might offer me deals for every possible future utility if I give up some utility now. I only have so much utility that I can reasonably give up right now. Which Omega(s) do I pick to give up my utility to? I certainly shouldn’t choose the most expensive Omega that yields the lowest expected return; I should pick the most efficient Omega for my cost in negative utility. What does that Omega look like? Certainly not one that offers 4^^^^4 years of fun for $5, but one that offers 4^^^^4 years of fun for less than $5 (or even pays me to experience it). Perhaps I only have $5, and spending it now would prevent me from ever accepting another deal from a different Omega. Ultimately what this hypothetical choice reduces to is choosing the earliest likely payoff so that I have more money in the future to consider more deals, e.g. skip out on paying Omega $5 today when I could invest it in the local economy and earn $6 tomorrow and have even more utility to pay potential Omegas with. I have to assume that any particular instance of Omega is roughly as likely as any other; a mugger appearing and offering me a purported deal from a particular Omega is no proof that the particular Omega exists unless there is additional proof such as being able to take out a loan repayable in the distant future or a verifiable insurance policy against the failure of Omega to deliver on the promise.
EDIT: I should probably try to quantify this. U(deal_N)*P(deal_N_is_true) - U(cost_N) is the expected utility of giving up cost_N utility in exchange for deal_N utility from a potential entity Omega_N. Unless I have some evidence that P(deal_X_is_true) is greater than P(deal_N_is_true) for some X and every other N, I should simply pick the most efficient deal. If P(deal_X_is_true | evidence_X_is_true)*U(deal_X) - U(cost_X) > U(deal_N)*P(deal_N_is_true) - U(cost_N) for some X and all other N, then I should pick X. Is a mugger appearing and offering me a particular deal, X, evidence that X is true? No, unless the mugger (or another entity I can trade with, including myself if I find actual evidence that X is true) also believes the deal sufficiently strongly to sell me insurance. In other words the mugger has to believe the deal will pay rent in order for me to believe it will pay rent.