Looking at Gustafsson, 2022′s money pumps for completeness, the precaution principles he uses just seem pretty unintuitive to me. The idea seems to be that if you’ll later face a decision situation where you can make a choice that makes you worse off but you can’t make yourself better off by getting there, you should avoid the decision situation, even if it’s entirely under your control to make a choice in that situation that won’t leave you worse off. But, you can just make that choice that won’t leave you worse off later instead of avoiding the situation altogether.
Here’s the forcing money pump:
It seems obvious to me that you can just stick with A all the way through, or switch to B, and neither would violate any of your preferences or be worse than any other option. Gustafsson is saying that would be irrational, it seems because there’s some risk you’ll make the wrong choices. Another kind of response like your policy I can imagine is that unless you have preferences otherwise (i.e. would strictly prefer another accessible option to what you have now), you just stick with the status quo, as the default. This means sticking with A all the eay though, because you’re never offered a strictly better option than it.
Another problem with the precaution principles is that they seem much less plausible when you seriously entertain incompleteness, rather than kind of treat incompleteness like equivalence. He effectively argues that at node 3, you should pick B, because otherwise at node 4, you could end up picking B-, which is worse than B, and there’s no upside. But that basically means claiming that one of the following must hold:
you’ll definitely pick B- at 4, or
B is better than any strict probabilistic mixture of A and B-.
But both are false in general. 1 is false in general because A is permissible at 4. 2 is false in general because A and B are incomparable and incomparability can be infectious (e.g. MacAskill, 2013), so B can be incomparable with a strict probabilistic mixture of A and B-. It also just seems unintuitive, because the claim is made generally, and so would have to hold no matter how low the probability assigned to B- is, as long it’s positive.
Imagine A is an apple, B is a banana and B- is a slightly worse banana, and I have no preferences between apples and bananas. It would be odd to say that a banana is better than an apple or a tiny probability of a worse banana. This would be like using the tiny risk of a worse banana with the apple to break a tie between the apple and the banana, but there’s no tie to break, because apples and bananas are incomparable.
If A and B were equivalent, then B would indeed very plausibly be better than a strict probabilistic mixture of A and B-. This would follow from Independence, or if A, B and B- are deterministic outcomes, statewise dominance. So, I suspect the intuitions supporting the precaution principles are accidentally treating incomparability like equivalence.
I think a more useful way to think of incomparability is as indeterminancy about which is better. You could consider what happens if you treat A as (possibly infinitely) better than B in one whole treatment of the tree, and consider what happens if you treat B as better than A in a separate treatment, and consider what happens if you treat them as equivalent all the way through (and extend your preference relation to be transitive and continue to satisfy stochastic dominance and independence in each case). If B were better, you’d end up at B, no money pump. If A were better, you’d end up at A, no money pump. If they were equivalent, you’d end up at either (or maybe specifically B, because of precaution), no money pump.
Looking at Gustafsson, 2022′s money pumps for completeness, the precaution principles he uses just seem pretty unintuitive to me. The idea seems to be that if you’ll later face a decision situation where you can make a choice that makes you worse off but you can’t make yourself better off by getting there, you should avoid the decision situation, even if it’s entirely under your control to make a choice in that situation that won’t leave you worse off. But, you can just make that choice that won’t leave you worse off later instead of avoiding the situation altogether.
Here’s the forcing money pump:
It seems obvious to me that you can just stick with A all the way through, or switch to B, and neither would violate any of your preferences or be worse than any other option. Gustafsson is saying that would be irrational, it seems because there’s some risk you’ll make the wrong choices. Another kind of response like your policy I can imagine is that unless you have preferences otherwise (i.e. would strictly prefer another accessible option to what you have now), you just stick with the status quo, as the default. This means sticking with A all the eay though, because you’re never offered a strictly better option than it.
Another problem with the precaution principles is that they seem much less plausible when you seriously entertain incompleteness, rather than kind of treat incompleteness like equivalence. He effectively argues that at node 3, you should pick B, because otherwise at node 4, you could end up picking B-, which is worse than B, and there’s no upside. But that basically means claiming that one of the following must hold:
you’ll definitely pick B- at 4, or
B is better than any strict probabilistic mixture of A and B-.
But both are false in general. 1 is false in general because A is permissible at 4. 2 is false in general because A and B are incomparable and incomparability can be infectious (e.g. MacAskill, 2013), so B can be incomparable with a strict probabilistic mixture of A and B-. It also just seems unintuitive, because the claim is made generally, and so would have to hold no matter how low the probability assigned to B- is, as long it’s positive.
Imagine A is an apple, B is a banana and B- is a slightly worse banana, and I have no preferences between apples and bananas. It would be odd to say that a banana is better than an apple or a tiny probability of a worse banana. This would be like using the tiny risk of a worse banana with the apple to break a tie between the apple and the banana, but there’s no tie to break, because apples and bananas are incomparable.
If A and B were equivalent, then B would indeed very plausibly be better than a strict probabilistic mixture of A and B-. This would follow from Independence, or if A, B and B- are deterministic outcomes, statewise dominance. So, I suspect the intuitions supporting the precaution principles are accidentally treating incomparability like equivalence.
I think a more useful way to think of incomparability is as indeterminancy about which is better. You could consider what happens if you treat A as (possibly infinitely) better than B in one whole treatment of the tree, and consider what happens if you treat B as better than A in a separate treatment, and consider what happens if you treat them as equivalent all the way through (and extend your preference relation to be transitive and continue to satisfy stochastic dominance and independence in each case). If B were better, you’d end up at B, no money pump. If A were better, you’d end up at A, no money pump. If they were equivalent, you’d end up at either (or maybe specifically B, because of precaution), no money pump.