But the probability of those rare things will be super low. It’s not obvious that they’ll change the EV as much as nearer term impacts. … All this theorizing might be unnecessary if our actual expectations follow a different pattern.
Yes, if the profiles are not funnel-shaped then this whole thing is moot. I argue that they are funnel-shaped, at least for many utility functions currently in use (e.g. utility functions that are linear in QALYs) I’m afraid my argument isn’t up yet—it’s in the appendix, sorry—but it will be up in a few days!
Are we? Expected utility is still a thing. Some actions have greater expected utility than others even if the probability distribution has huge mass across both positive and negative possibilities. If infinite utility is a problem then it’s already a problem regardless of any funnel or oscillating type distribution of outcomes.
If the profiles are funnel-shaped, expected utility is not a thing. The shape of your action profiles depends on your probability function and your utility function. Yes, infinitely valuable outcomes are a problem—but I’m arguing that even if you ignore infinitely valuable outcomes, there’s still a big problem having to do with infinitely many possible finite outcomes, and moreover even if you only consider finitely many outcomes of finite value, if the profiles are funnel-shaped then what you end up doing will be highly arbitrary, determined mostly by whatever is happening at the place where you happened to draw the cutoff.
Another way of describing this phenomenon is that we are simply seizing the low hanging fruit, and hard intellectual progress isn’t even needed.
That’s what I’d like to think, and that’s what I do think. But this argument challenges that; this argument says that the low-hanging fruit metaphor is inappropriate here: there is no lowest-hanging fruit or anything close; there is an infinite series of fruit hanging lower and lower, such that for any fruit you pick, if only you had thought about it a little longer you would have found an even lower-hanging fruit that would have been so much easier to pick that it would easily justify the cost in extra thinking time needed to identify it… moreover, you never really “pick” these fruit, in that the fruit are gambles, not outcomes; they aren’t actually what you want, they are just tickets that have some chance of getting what you want. And the lower the fruit, the lower the chance...
>The shape of your action profiles depends on your probability function
Are you saying that there is no expected utility just because people have different expectations?
>and your utility function
Well, of course. That doesn’t mean there is no expected utility! It’s just different for different agents.
>I’m arguing that even if you ignore infinitely valuable outcomes, there’s still a big problem having to do with infinitely many possible finite outcomes,
That in itself is not a problem, imagine a uniform distribution from 0 to 1.
>if the profiles are funnel-shaped then what you end up doing will be highly arbitrary, determined mostly by whatever is happening at the place where you happened to draw the cutoff.
If you do something arbitrary like drawing a cutoff, then of course how you do it will have arbitrary results. I think the lesson here is not to draw cutoffs in the first place.
>That’s what I’d like to think, and that’s what I do think. But this argument challenges that; this argument says that the low-hanging fruit metaphor is inappropriate here: there is no lowest-hanging fruit or anything close; there is an infinite series of fruit hanging lower and lower, such that for any fruit you pick, if only you had thought about it a little longer you would have found an even lower-hanging fruit that would have been so much easier to pick that it would easily justify the cost in extra thinking time needed to identify it… moreover, you never really “pick” these fruit, in that the fruit are gambles, not outcomes; they aren’t actually what you want, they are just tickets that have some chance of getting what you want. And the lower the fruit, the lower the chance...
There must be a lowest hanging fruit out of any finite set of possible actions, as long as “better intervention than” follows basic decision theoretic properties which come automatically if they have expected utility values.
Also, remember the conservation of expected evidence. When we think about the long run effects of a given intervention, we are updating our prior to go either up or down, not predictably making it seem more attractive.
Yes, if the profiles are not funnel-shaped then this whole thing is moot. I argue that they are funnel-shaped, at least for many utility functions currently in use (e.g. utility functions that are linear in QALYs) I’m afraid my argument isn’t up yet—it’s in the appendix, sorry—but it will be up in a few days!
If the profiles are funnel-shaped, expected utility is not a thing. The shape of your action profiles depends on your probability function and your utility function. Yes, infinitely valuable outcomes are a problem—but I’m arguing that even if you ignore infinitely valuable outcomes, there’s still a big problem having to do with infinitely many possible finite outcomes, and moreover even if you only consider finitely many outcomes of finite value, if the profiles are funnel-shaped then what you end up doing will be highly arbitrary, determined mostly by whatever is happening at the place where you happened to draw the cutoff.
That’s what I’d like to think, and that’s what I do think. But this argument challenges that; this argument says that the low-hanging fruit metaphor is inappropriate here: there is no lowest-hanging fruit or anything close; there is an infinite series of fruit hanging lower and lower, such that for any fruit you pick, if only you had thought about it a little longer you would have found an even lower-hanging fruit that would have been so much easier to pick that it would easily justify the cost in extra thinking time needed to identify it… moreover, you never really “pick” these fruit, in that the fruit are gambles, not outcomes; they aren’t actually what you want, they are just tickets that have some chance of getting what you want. And the lower the fruit, the lower the chance...
>The shape of your action profiles depends on your probability function
Are you saying that there is no expected utility just because people have different expectations?
>and your utility function
Well, of course. That doesn’t mean there is no expected utility! It’s just different for different agents.
>I’m arguing that even if you ignore infinitely valuable outcomes, there’s still a big problem having to do with infinitely many possible finite outcomes,
That in itself is not a problem, imagine a uniform distribution from 0 to 1.
>if the profiles are funnel-shaped then what you end up doing will be highly arbitrary, determined mostly by whatever is happening at the place where you happened to draw the cutoff.
If you do something arbitrary like drawing a cutoff, then of course how you do it will have arbitrary results. I think the lesson here is not to draw cutoffs in the first place.
>That’s what I’d like to think, and that’s what I do think. But this argument challenges that; this argument says that the low-hanging fruit metaphor is inappropriate here: there is no lowest-hanging fruit or anything close; there is an infinite series of fruit hanging lower and lower, such that for any fruit you pick, if only you had thought about it a little longer you would have found an even lower-hanging fruit that would have been so much easier to pick that it would easily justify the cost in extra thinking time needed to identify it… moreover, you never really “pick” these fruit, in that the fruit are gambles, not outcomes; they aren’t actually what you want, they are just tickets that have some chance of getting what you want. And the lower the fruit, the lower the chance...
There must be a lowest hanging fruit out of any finite set of possible actions, as long as “better intervention than” follows basic decision theoretic properties which come automatically if they have expected utility values.
Also, remember the conservation of expected evidence. When we think about the long run effects of a given intervention, we are updating our prior to go either up or down, not predictably making it seem more attractive.