There is a 0.001 chance that someone who did not have the disease will get it. But he can repeat the procedure.
No, that doesn’t work. It invalidates the implicit assumption you’re making that the probability that a person chooses to “forget” is independent of whether they have the disease. Ultimately, you’re “mixing” the various people who “forgot”, and a “mixing” procedure can’t change the proportion of people who have the disease.
When you take this into account, the conclusion becomes rather mundane. Some copies of you can gain the disease, while a proportional number of copies can lose it. (You might think you could get some respite by repeatedly trading off “who” has the disease, but the forgetting procedure ensures that no copy ever feels respite, as that would require remembering having the disease.)
The “repeating” will not be repeating from internal point of view of a person, as he has completely erased the memories of the first attempt. So he will do it as if it is first time.
My point still stands. Try drawing out a specific finite set of worlds and computing the probabilities. (I don’t think anything changes when the set of worlds becomes infinite, but the math becomes much harder to get right.)
The trick is to use already existing practice of meditation (or sleeping) and connect to it. Most people who go to sleep do no do it to use magic by forgetting, but it is natural to forget something during sleep. Thus, the fact that I wake up from sleeping does not provide any evidence about me having the disease.
But it is in a sense parasitic behavior, and if everyone will use magic by forgetting every time she goes to sleep, there will be almost no gain. Except that one can “exchange” one bad thing on another, but will not remember the exchange.
Not “almost no gain”. My point is that it can be quantified, and it is exactly zero expected gain under all circumstances. You can verify this by drawing out any finite set of worlds containing “mediators”, and computing the expected number of disease losses minus disease gains as:
num(people with disease)*P(person with disease meditates)*P(person with disease who meditates loses the disease) - num(people without disease)*P(person without disease meditates)*P(person without disease who meditates gains the disease)
My point is that this number is always exactly zero. If you doubt this, you should try to construct a counterexample with a finite number of worlds.
I think I understand what you say—the expected utility of the whole procedure is zero.
For example, imagine that there are 3 copies and only one has the disease. All meditate. After the procedure, the copy with disease will have 2⁄3 chances of being cured. Each of two copies without the disease are getting 1⁄3 chance of having the disease which in sum gives 2⁄3 of total utility. In that case total utility of being cured = total utility of getting the disease and the whole procedure is neutral.
However, If I already know that I have the disease, and I am not altruistic to my copies, playing such game is a wining move to me?
However, If I already know that I have the disease, and I am not altruistic to my copies, playing such game is a wining move to me?
Correct. But if you don’t have the disease, you’re probably also not altruistic to your copies, so you would choose not to participate. Leaving the copies of you with the disease isolated and unable to “trade”.
Yes, it only works if other copies are meditating for some other reason. For example, they sleep or meditate for enlightenment. And they are exploited in this situation.
But don’t the non-diseased copies not just need to generally meditate, but to do some special kind of meditation where they forget the affirmative evidence they have that they don’t have the disease?
non-disease copies do not need to perform any changes in their meditation routine in this model, assuming that they naturelly forget their disease status during meditation.
No, that doesn’t work. It invalidates the implicit assumption you’re making that the probability that a person chooses to “forget” is independent of whether they have the disease. Ultimately, you’re “mixing” the various people who “forgot”, and a “mixing” procedure can’t change the proportion of people who have the disease.
When you take this into account, the conclusion becomes rather mundane. Some copies of you can gain the disease, while a proportional number of copies can lose it. (You might think you could get some respite by repeatedly trading off “who” has the disease, but the forgetting procedure ensures that no copy ever feels respite, as that would require remembering having the disease.)
The “repeating” will not be repeating from internal point of view of a person, as he has completely erased the memories of the first attempt. So he will do it as if it is first time.
My point still stands. Try drawing out a specific finite set of worlds and computing the probabilities. (I don’t think anything changes when the set of worlds becomes infinite, but the math becomes much harder to get right.)
The trick is to use already existing practice of meditation (or sleeping) and connect to it. Most people who go to sleep do no do it to use magic by forgetting, but it is natural to forget something during sleep. Thus, the fact that I wake up from sleeping does not provide any evidence about me having the disease.
But it is in a sense parasitic behavior, and if everyone will use magic by forgetting every time she goes to sleep, there will be almost no gain. Except that one can “exchange” one bad thing on another, but will not remember the exchange.
Not “almost no gain”. My point is that it can be quantified, and it is exactly zero expected gain under all circumstances. You can verify this by drawing out any finite set of worlds containing “mediators”, and computing the expected number of disease losses minus disease gains as:
num(people with disease)*P(person with disease meditates)*P(person with disease who meditates loses the disease) - num(people without disease)*P(person without disease meditates)*P(person without disease who meditates gains the disease)
My point is that this number is always exactly zero. If you doubt this, you should try to construct a counterexample with a finite number of worlds.
I think I understand what you say—the expected utility of the whole procedure is zero.
For example, imagine that there are 3 copies and only one has the disease. All meditate. After the procedure, the copy with disease will have 2⁄3 chances of being cured. Each of two copies without the disease are getting 1⁄3 chance of having the disease which in sum gives 2⁄3 of total utility. In that case total utility of being cured = total utility of getting the disease and the whole procedure is neutral.
However, If I already know that I have the disease, and I am not altruistic to my copies, playing such game is a wining move to me?
Correct. But if you don’t have the disease, you’re probably also not altruistic to your copies, so you would choose not to participate. Leaving the copies of you with the disease isolated and unable to “trade”.
Yes, it only works if other copies are meditating for some other reason. For example, they sleep or meditate for enlightenment. And they are exploited in this situation.
Exactly.
In this scenario, why are the non-disease-having copies participating? They are not in a state of ignorance, they know they don’t have the disease.
I assume that meditation happens naturally, like sleep.
But don’t the non-diseased copies not just need to generally meditate, but to do some special kind of meditation where they forget the affirmative evidence they have that they don’t have the disease?
non-disease copies do not need to perform any changes in their meditation routine in this model, assuming that they naturelly forget their disease status during meditation.
I am not a mediator so maybe you have me beat, but it’s not immediately clear why you would assume this