I should have specified EV maximization with an unbounded social welfare function, although the argument applies somewhat more generally; I’ve edited this into my top comment.
Looking at Slider’s reply to the comment I linked, assuming that’s the one you meant (or did you have another in mind?):
Slider probably misunderstood Christiano about truncation, because Christiano meant that you’d truncate the second lottery at a point that depends on the outcome of the first lottery. For any actual value outcome X of the original St. Petersburg’s lottery, half St. Pesterburg can be truncated at some point and still have a finite expected value greater than X. (EDIT: However, I guess the sure-thing principle isn’t relevant here with conditional truncation, since we aren’t comparing only two fixed options anymore.)
I don’t understand what Slider meant in the second paragraph, and I think it’s probably missing the point.
The third paragraph misses the point: once the outcome is decided for the first St. Petersburg lottery, it has finite value, and half St. Petersburg still has infinite expected value, which is greater than a finite value.
Yes, I should have thought more about Slider’s reply before posting, I take back my agreement. Still, I don’t find dutch booking convincing in Christiano’s case.
The reason to reject a theory based on dutch booking is that there is no logical choice to commit to, in this case to maximize EV. I don’t think this applies to the Paul Christiano case, because the second lottery does not have higher EV than the first. Yes, once you play the first lottery and find out that it has a finite value the second one will have higher EV, but until then the first one has higher EV (in an infinite way) and you should choose it.
But again I think there can be reasonable disagreement about this, I just think equating dutch booking for the person-affecting view and for the total utilitarianism view is misleading. These are substantially different philosophical claims.
Yes, once you play the first lottery and find out that it has a finite value the second one will have higher EV, but until then the first one has higher EV (in an infinite way) and you should choose it.
I think a similar argument can apply to person-affecting views and the OP’s Dutch book argument:
Yes, starting with World 1, once you make trade 1 to get World 2 and find out that trade 2 to World 3 is available, trade 1 will have negative value, but until then trade 1 has positive value and you should choose it.
I agree that you can give different weights to different Dutch book/money pump arguments. I do think that if you commit 100% to complete preferences over all probability distributions over outcomes and invulnerability to Dutch books/money pumps, then expected utility maximization over each individual decision with an unbounded utility function is ruled out.
As you mention, one way to avoid this St. Petersburg Dutch book/money pump is to just commit to sticking with A, if A>B ex ante, and regardless of the actual outcome of A (+ some other conditions, e.g. A and B both have finite value under all outcomes, and A has infinite expected value), but switching to C under certain other conditions.
You may have similar commitment moves for person-affecting views, although you might find them all less satisfying. You could commit to refusing one of the 3 types of trades in the OP, or doing so under specific conditions, or just never completing the last step in any Dutch book, even if you’d know you’d want to. I think those with person-affecting views should usually refuse moves like trade 1, if they think they’re not too unlikely to make moves like trade 2 after, but this is messier, and depends on your distributions over what options will become available in the future depending on your decisions. The above commitments for St. Petersburg-like lotteries don’t depend on what options will be available in the future or your distributions over them.
I should have specified EV maximization with an unbounded social welfare function, although the argument applies somewhat more generally; I’ve edited this into my top comment.
Looking at Slider’s reply to the comment I linked, assuming that’s the one you meant (or did you have another in mind?):
Slider probably misunderstood Christiano about truncation, because Christiano meant that you’d truncate the second lottery at a point that depends on the outcome of the first lottery. For any actual value outcome X of the original St. Petersburg’s lottery, half St. Pesterburg can be truncated at some point and still have a finite expected value greater than X. (EDIT: However, I guess the sure-thing principle isn’t relevant here with conditional truncation, since we aren’t comparing only two fixed options anymore.)
I don’t understand what Slider meant in the second paragraph, and I think it’s probably missing the point.
The third paragraph misses the point: once the outcome is decided for the first St. Petersburg lottery, it has finite value, and half St. Petersburg still has infinite expected value, which is greater than a finite value.
Yes, I should have thought more about Slider’s reply before posting, I take back my agreement. Still, I don’t find dutch booking convincing in Christiano’s case.
The reason to reject a theory based on dutch booking is that there is no logical choice to commit to, in this case to maximize EV. I don’t think this applies to the Paul Christiano case, because the second lottery does not have higher EV than the first. Yes, once you play the first lottery and find out that it has a finite value the second one will have higher EV, but until then the first one has higher EV (in an infinite way) and you should choose it.
But again I think there can be reasonable disagreement about this, I just think equating dutch booking for the person-affecting view and for the total utilitarianism view is misleading. These are substantially different philosophical claims.
I think a similar argument can apply to person-affecting views and the OP’s Dutch book argument:
I agree that you can give different weights to different Dutch book/money pump arguments. I do think that if you commit 100% to complete preferences over all probability distributions over outcomes and invulnerability to Dutch books/money pumps, then expected utility maximization over each individual decision with an unbounded utility function is ruled out.
As you mention, one way to avoid this St. Petersburg Dutch book/money pump is to just commit to sticking with A, if A>B ex ante, and regardless of the actual outcome of A (+ some other conditions, e.g. A and B both have finite value under all outcomes, and A has infinite expected value), but switching to C under certain other conditions.
You may have similar commitment moves for person-affecting views, although you might find them all less satisfying. You could commit to refusing one of the 3 types of trades in the OP, or doing so under specific conditions, or just never completing the last step in any Dutch book, even if you’d know you’d want to. I think those with person-affecting views should usually refuse moves like trade 1, if they think they’re not too unlikely to make moves like trade 2 after, but this is messier, and depends on your distributions over what options will become available in the future depending on your decisions. The above commitments for St. Petersburg-like lotteries don’t depend on what options will be available in the future or your distributions over them.