I rather think you’ve missed most, if not all, of the point of that hypothetical (and you also don’t seem to have fully read the grandparent comment to this one, judging by your question).
Perhaps we should set the grandmother/chickens example aside for now, as we’re approaching the limit of how much explaining I’m willing to do (given that the threads where I originally discussed this are quite long and answer all these questions).
and you also don’t seem to have fully read the grandparent comment to this one, judging by your question
Do you mean the a), b), c) comment? Which section did I miss?
Either way, I ask: do you prefer destroying an arbitrary amount of wealth (not yours) to any probability of your grandma dying? At least give a Yes/No.
Take a look at the other example I cited.
From some book? You know, it would be great if your arguments were contained in your comments.
As I said, there are old LW comments of mine where I explain said argument in some detail (though not quite as much detail as the source). (I even included diagrams!)
Edited to add:
Either way, I ask: do you prefer destroying an arbitrary amount of wealth (not yours) to any probability of your grandma dying? At least give a Yes/No.
What difference does it make?
If I say “yes”, then we can have the same conversation as the one about the chickens. It’s just another example of the same thing.
If I say “no”, then it’s not a relevant example at all and there’s no reason to discuss it further.
This is a totally pointless line of inquiry; this is the last I’ll say about it.
As I said, there are old LW comments of mine where I explain said argument in some detail (though not quite as much detail as the source). (I even included diagrams!)
Where? I didn’t see any such things in the LW comments I found. Are there more threads? Are you going to link to them? You’ve made a big claim, and I haven’t seen nearly enough defense for it.
What difference does it make?
Of course, the question is such that I get to feel right either way. If you say “no”, then I can deduce that you don’t understand what “wealth” is. If you say “yes”, then I can deduce that you’re a sociopath with poor understanding of cause and effect. Charitably, I could imagine that you were talking about destroying chickens in some parallel universe, where their destruction could 100% certainly not have consequences for you, but that’s a silly scenario too.
Regarding the grandma-chicken argument, having given it some thought, I think I understand it better now. I’d explain it like this. There is a utility function u, such that all of my actions maximize Eu. Suppose that u(A) = u(B) for some two choices A, B. Then I can claim that A > B, and exhibit this preference in my choices, i.e. given a choice between A and B I would always choose A. However for every B+, such that u(B+) > u(B) I would also claim B < A < B+. This does violate continuity, however because I’m still maximizing Eu, my actions can’t be called irrational, and the function u is hardly any less useful than it would be without the violation.
Finally I read your link. So the main argument is that there is a preference between different probability distributions over utility, even if expected utility is the same. This is intuitively understandable, but I find it lacking specificity.
I propose the following three step experiment. First a human chooses a distribution X from two choices (X=A or X=B). Then we randomly draw a number P from the selected distribution X, then we try to win 1$ with probability P (and 0$ otherwise, which I’ll ignore by setting u(0$)=0, because I can). Here you can plot X as a distribution over expected utility, which equals P times u(1$). The claim is that some distributions X are more preferable to others, despite what pure utility calculations say. I.e. Eu(A) > Eu(B), but a human would choose B over A and would not be irrational. Do you agree that this experiment accurately represents Dawes claim?
Naturally, I find the argument bad. The double lottery can be easily collapsed into a single lottery, the final probabilities can be easily computed (which is what Eu does). If P(win 1$ | A) = P(win 1$ | B) then you’re free to make either choice, but if P(win 1$ | A) > P(win 1$ | B) even by a hair, and you choose B, you’re being irrational. Note that the choices of 0$ and 1$ as the prizes are completely arbitrary.
I’m afraid that the moderation policy on this site does not permit me to do so effectively
Are you referring to that one moderation note? I think you’re overreacting.
I rather think you’ve missed most, if not all, of the point of that hypothetical (and you also don’t seem to have fully read the grandparent comment to this one, judging by your question).
Perhaps we should set the grandmother/chickens example aside for now, as we’re approaching the limit of how much explaining I’m willing to do (given that the threads where I originally discussed this are quite long and answer all these questions).
Take a look at the other example I cited.
Do you mean the a), b), c) comment? Which section did I miss?
Either way, I ask: do you prefer destroying an arbitrary amount of wealth (not yours) to any probability of your grandma dying? At least give a Yes/No.
From some book? You know, it would be great if your arguments were contained in your comments.
As I said, there are old LW comments of mine where I explain said argument in some detail (though not quite as much detail as the source). (I even included diagrams!)
Edited to add:
What difference does it make?
If I say “yes”, then we can have the same conversation as the one about the chickens. It’s just another example of the same thing.
If I say “no”, then it’s not a relevant example at all and there’s no reason to discuss it further.
This is a totally pointless line of inquiry; this is the last I’ll say about it.
Where? I didn’t see any such things in the LW comments I found. Are there more threads? Are you going to link to them? You’ve made a big claim, and I haven’t seen nearly enough defense for it.
Of course, the question is such that I get to feel right either way. If you say “no”, then I can deduce that you don’t understand what “wealth” is. If you say “yes”, then I can deduce that you’re a sociopath with poor understanding of cause and effect. Charitably, I could imagine that you were talking about destroying chickens in some parallel universe, where their destruction could 100% certainly not have consequences for you, but that’s a silly scenario too.
http://www.greaterwrong.com/posts/g9msGr7DDoPAwHF6D/to-what-extent-does-improved-rationality-lead-to-effective#kpMS4usW5rvyGkFgM
Regarding the grandma-chicken argument, having given it some thought, I think I understand it better now. I’d explain it like this. There is a utility function u, such that all of my actions maximize Eu. Suppose that u(A) = u(B) for some two choices A, B. Then I can claim that A > B, and exhibit this preference in my choices, i.e. given a choice between A and B I would always choose A. However for every B+, such that u(B+) > u(B) I would also claim B < A < B+. This does violate continuity, however because I’m still maximizing Eu, my actions can’t be called irrational, and the function u is hardly any less useful than it would be without the violation.
Please see https://www.lesserwrong.com/posts/3mFmDMapHWHcbn7C6/a-simple-two-axis-model-of-subjective-states-with-possible/wpT7LwqLnzJYFMveS.
Finally I read your link. So the main argument is that there is a preference between different probability distributions over utility, even if expected utility is the same. This is intuitively understandable, but I find it lacking specificity.
I propose the following three step experiment. First a human chooses a distribution X from two choices (X=A or X=B). Then we randomly draw a number P from the selected distribution X, then we try to win 1$ with probability P (and 0$ otherwise, which I’ll ignore by setting u(0$)=0, because I can). Here you can plot X as a distribution over expected utility, which equals P times u(1$). The claim is that some distributions X are more preferable to others, despite what pure utility calculations say. I.e. Eu(A) > Eu(B), but a human would choose B over A and would not be irrational. Do you agree that this experiment accurately represents Dawes claim?
Naturally, I find the argument bad. The double lottery can be easily collapsed into a single lottery, the final probabilities can be easily computed (which is what Eu does). If P(win 1$ | A) = P(win 1$ | B) then you’re free to make either choice, but if P(win 1$ | A) > P(win 1$ | B) even by a hair, and you choose B, you’re being irrational. Note that the choices of 0$ and 1$ as the prizes are completely arbitrary.
Are you referring to that one moderation note? I think you’re overreacting.
I would love to respond to your comment, and will certainly do so, but not here. Let me know what other venue you prefer.
I’m afraid not.
I think that he set the mind experiment in the Least convenient possible world. So your last hypothesis is right.