Betting and reward arguments like this is deeply problematic in two senses:
The measurement of objective is the combined total reward to all in a purposed reference class, like the 20 “you” in the example. Usually the question would try to boost the intuition of this by saying all of them are copies of “you”. However, even if the created persons (actually doesn’t even have to be all persons, AIs or aliens will work just fine) are vastly different, it does not affect the analysis at all. Since the question is directed at you, and the evidence is your observation —that you awake in a green room—shouldn’t the bet and reward be constructed—in order to reflect the correct probability—to concern your own personal interest? Why use the alternative objective and measure the combined reward of the entire group? This takes away the first-person elements of the question, just as you have said in the post, the bet has nothing to do with “‘I’ see green.”
Since such betting arguments use the combined reward of a supposed reference class instead of using self interest, the detour is completed with an additional assertion in the spirit of “what’s best for the group must be best for me.” That is typically achieved by some anthropic assumption in the form of seeing “I” as a random sample from the group. Such intuitions runs so deep that people use the assumptions without acknowledging it. In trying to explain why “I” am “a person in green room” yet the two can have different probabilities you said “The same way a person who visited a randomly sampled room can have different probability estimate than a person who visited a predetermined room.” It subtly considers who “I” am: the person who was created in a green room, the same way as if someone randomly sampling the rooms and sees green. However intuitive that might be, it’s an assumption that’s unsubstantiated.
These two points combined effectively changes an anthropic problem regarding the first-person “I” to a perspective-less, run-of-the-mill probability problem. Yet this conversion is unsubstantiated, and to me, the root of the paradoxes.
However, even if the created persons (actually doesn’t even have to be all persons, AIs or aliens will work just fine) are vastly different, it does not affect the analysis at all.
Yes, this is the whole point. Probability theory doesn’t have any special case for anthropics. Neither it’s supposed to have one.
Since the question is directed at you, and the evidence is your observation —that you awake in a green room—shouldn’t the bet and reward be constructed—in order to reflect the correct probability—to concern your own personal interest? Why use the alternative objective and measure the combined reward of the entire group?
Probability theory should be able to lawfully deal with all kind of bets and rewards. The reason why this particular type of bet was looked into is because it apparently lead to a paradox which I wanted to resolve.
It subtly considers who “I” am: the person who was created in a green room, the same way as if someone randomly sampling the rooms and sees green.
I though this assimption wasn’t subtle at all. There are two possibilities: either “I” is a person who is always meant to see green, or “I” is a person who could either see green or red and was randomly sampled. The first case is trivial—if I was always supposed to see green then I’m not supposed to update my probability estimate and thus there is no paradox. So we focus on the other case as a more interesting one.
These two points combined effectively changes an anthropic problem regarding the first-person “I” to a perspective-less, run-of-the-mill probability problem. Yet this conversion is unsubstantiated, and to me, the root of the paradoxes.
I don’t see how it is the case. If anything it’s the opposite. Paradoxes happen when people try to treat first person perspective as somewhat more than just a set of possible outcomes and anthropics as something beyond simple probability theory. As if there is some extra rule about self-selection, as if the universe is supposed to especially care about our personal identities for some reason. Then they try to apply this rule to every other anthropic problem and get predictably silly results.
But as soon as we do not do that and just lawfully use probability theory as it is—all the apparent paradoxes resolve which this posts demonstrates. “I” is not “perspectiveless” but it corresponds to a specific set of possible outcomes thus we have a run-of-the-mill probability problem. There may be disagreements about what set of possible outcomes correctly represent first person perspective in a specific situation—usually in problems where different number of people are created in different outcomes—but this problem isn’t an example of it.
On priors, the theory that claims that anthropics is special case is more complicated and thus, less likely, than a theory that anthropics is not special in any way. Previously you appealed to the existence of anthropic paradoxes as evidence in favour of anthropic specialness. But here I’m showing that these paradoxes are not native to anthropics, that the same issues are encountered in a general case when we are sloppy with the application of probability theory or misunderstand it and as soon we are more careful, the paradox dissolves in both anthropic and non-anthropic cases. What other reasons to believe in anthropic specialness do you have? Do you feel that one example is not enough? I’m going to highlight more in the next post. Do you believe that there are anthropic paradoxes that my method can’t deal with? What kind of evidence is required to change your mind in this regard?
Betting and reward arguments like this is deeply problematic in two senses:
The measurement of objective is the combined total reward to all in a purposed reference class, like the 20 “you” in the example. Usually the question would try to boost the intuition of this by saying all of them are copies of “you”. However, even if the created persons (actually doesn’t even have to be all persons, AIs or aliens will work just fine) are vastly different, it does not affect the analysis at all. Since the question is directed at you, and the evidence is your observation —that you awake in a green room—shouldn’t the bet and reward be constructed—in order to reflect the correct probability—to concern your own personal interest? Why use the alternative objective and measure the combined reward of the entire group? This takes away the first-person elements of the question, just as you have said in the post, the bet has nothing to do with “‘I’ see green.”
Since such betting arguments use the combined reward of a supposed reference class instead of using self interest, the detour is completed with an additional assertion in the spirit of “what’s best for the group must be best for me.” That is typically achieved by some anthropic assumption in the form of seeing “I” as a random sample from the group. Such intuitions runs so deep that people use the assumptions without acknowledging it. In trying to explain why “I” am “a person in green room” yet the two can have different probabilities you said “The same way a person who visited a randomly sampled room can have different probability estimate than a person who visited a predetermined room.” It subtly considers who “I” am: the person who was created in a green room, the same way as if someone randomly sampling the rooms and sees green. However intuitive that might be, it’s an assumption that’s unsubstantiated.
These two points combined effectively changes an anthropic problem regarding the first-person “I” to a perspective-less, run-of-the-mill probability problem. Yet this conversion is unsubstantiated, and to me, the root of the paradoxes.
Yes, this is the whole point. Probability theory doesn’t have any special case for anthropics. Neither it’s supposed to have one.
Probability theory should be able to lawfully deal with all kind of bets and rewards. The reason why this particular type of bet was looked into is because it apparently lead to a paradox which I wanted to resolve.
I though this assimption wasn’t subtle at all. There are two possibilities: either “I” is a person who is always meant to see green, or “I” is a person who could either see green or red and was randomly sampled. The first case is trivial—if I was always supposed to see green then I’m not supposed to update my probability estimate and thus there is no paradox. So we focus on the other case as a more interesting one.
I don’t see how it is the case. If anything it’s the opposite. Paradoxes happen when people try to treat first person perspective as somewhat more than just a set of possible outcomes and anthropics as something beyond simple probability theory. As if there is some extra rule about self-selection, as if the universe is supposed to especially care about our personal identities for some reason. Then they try to apply this rule to every other anthropic problem and get predictably silly results.
But as soon as we do not do that and just lawfully use probability theory as it is—all the apparent paradoxes resolve which this posts demonstrates. “I” is not “perspectiveless” but it corresponds to a specific set of possible outcomes thus we have a run-of-the-mill probability problem. There may be disagreements about what set of possible outcomes correctly represent first person perspective in a specific situation—usually in problems where different number of people are created in different outcomes—but this problem isn’t an example of it.
On priors, the theory that claims that anthropics is special case is more complicated and thus, less likely, than a theory that anthropics is not special in any way. Previously you appealed to the existence of anthropic paradoxes as evidence in favour of anthropic specialness. But here I’m showing that these paradoxes are not native to anthropics, that the same issues are encountered in a general case when we are sloppy with the application of probability theory or misunderstand it and as soon we are more careful, the paradox dissolves in both anthropic and non-anthropic cases. What other reasons to believe in anthropic specialness do you have? Do you feel that one example is not enough? I’m going to highlight more in the next post. Do you believe that there are anthropic paradoxes that my method can’t deal with? What kind of evidence is required to change your mind in this regard?