In order to make a decision, we do not always need an exact probability: sometimes just knowing that a probability is less than, say, 0.5 is enough to determine the correct decision. So, even though an exact probability p may be incomputable, that doesn’t mean that the truth value of the statement “p<0.1” can not be computed (for some particular case). And that computation may be all we need.
That said, I’m not sure exactly how to interpret “A decision procedure which entails uncomputability is unacceptable.” Unacceptable to whom? Do decision procedures have to be deterministic? To be algorithms? To be recursive? To be guaranteed to terminate in a finite time. To be guaranteed to terminate in a bounded time? To be guaranteed to terminate by the deadline for making a decision?
In order to make a decision, we do not always need an exact probability: sometimes just knowing that a probability is less than, say, 0.5 is enough to determine the correct decision.
Alright, so you compute away and determine that the upper bound on Chaitin’s constant for your needed formalism is 0.01. The mugger than multiplies his offering by 100, and proceeds to mug you, no? (After all, you don’t know that the right probability isn’t 0.01 and actually some smaller number.)
That said, I’m not sure exactly how to interpret “A decision procedure which entails uncomputability is unacceptable.”
This is pretty intuitive to me—a decision procedure which cannot be computed cannot make decisions, and a decision procedure which cannot make decisions cannot do anything. I mean, do you have any reason to think that the optimal, correct, decision theory is uncomputable?
I have no idea whether we are even talking about the same problem. (Probably not, since my thinking did not arise from raking). But you do seem to be suggesting that the multiplication by 100 does not alter the upper bound on the probability. As I read the wiki article on “Pascal’s Mugging”, Robin Hanson suggests that it does. Assuming, of course, that by “his offering” you mean the amount of disutility he threatens. And the multiplication by 100 does also affect the number (in this example 0.01) which I need to know whether p is less than. Which strikes me as the real point.
This whole subject seems bizarre to me. Are we assuming that this mugger has Omega-like psy powers? Why? If not, how does my upper bound calculation and its timing have an effect on his “offer”? I seem to have walked into the middle of a conversation with no way from the context to guess what went before.
In order to make a decision, we do not always need an exact probability: sometimes just knowing that a probability is less than, say, 0.5 is enough to determine the correct decision. So, even though an exact probability p may be incomputable, that doesn’t mean that the truth value of the statement “p<0.1” can not be computed (for some particular case). And that computation may be all we need.
That said, I’m not sure exactly how to interpret “A decision procedure which entails uncomputability is unacceptable.” Unacceptable to whom? Do decision procedures have to be deterministic? To be algorithms? To be recursive? To be guaranteed to terminate in a finite time. To be guaranteed to terminate in a bounded time? To be guaranteed to terminate by the deadline for making a decision?
Alright, so you compute away and determine that the upper bound on Chaitin’s constant for your needed formalism is 0.01. The mugger than multiplies his offering by 100, and proceeds to mug you, no? (After all, you don’t know that the right probability isn’t 0.01 and actually some smaller number.)
This is pretty intuitive to me—a decision procedure which cannot be computed cannot make decisions, and a decision procedure which cannot make decisions cannot do anything. I mean, do you have any reason to think that the optimal, correct, decision theory is uncomputable?
I have no idea whether we are even talking about the same problem. (Probably not, since my thinking did not arise from raking). But you do seem to be suggesting that the multiplication by 100 does not alter the upper bound on the probability. As I read the wiki article on “Pascal’s Mugging”, Robin Hanson suggests that it does. Assuming, of course, that by “his offering” you mean the amount of disutility he threatens. And the multiplication by 100 does also affect the number (in this example 0.01) which I need to know whether p is less than. Which strikes me as the real point.
This whole subject seems bizarre to me. Are we assuming that this mugger has Omega-like psy powers? Why? If not, how does my upper bound calculation and its timing have an effect on his “offer”? I seem to have walked into the middle of a conversation with no way from the context to guess what went before.