> I reject one and would accept the trade, largely for the reasons described above.
The way the trade is presented this is clearly false. You have a good imagination. I have a good imagination. The worst torture that could be thought up by a perfectly imaginative being would undoubtably get to negative infinity utility.
Secondly,
> Surely one instance of this torture is less bad than two instances of slightly less gruesome torture…
This is a strong argument, but I don’t think it’s necessarily true. It seems plausible that some forms of torture could act like a clean breaking piecewise function instead of a curve.
Imagine for a moment you tried answering a code of ethics that said murder was the ultimate wrong with this argument. You can’t imagine being slightly “less dead” such that you could eventually only be “a little dead” at which other considerations outweigh. Dead is Dead! (Insert meme here).
So yeah I don’t think it necessarily applies.
*However*
Isn’t there an even simpler response to this kind of negative util? The preference charts given here have a vertical asymptote at some value p of suffering.
What about value of suffering 2p? It seems like 2p is either out of the domain of the function, which is absurd, equal to p, which is also absurd, or scales linearly with an increased coefficient. I don’t think the latter makes either conceptual sense with the idea of a “critical value” of negative utility, or mathematical sense with regards to operations involving infinities.
"The way the trade is presented this is clearly false. You have a good imagination. I have a good imagination. The worst torture that could be thought up by a perfectly imaginative being would undoubtably get to negative infinity utility."
Well, the way the trade is presented is that for any finite amount of suffering there is an associated positive experience that would outweigh, which I accept, and I think you'd accept.
"Isn’t there an even simpler response to this kind of negative util? The preference charts given here have a vertical asymptote at some value p of suffering. What about value of suffering 2p? It seems like 2p is either out of the domain of the function, which is absurd, equal to p, which is also absurd, or scales linearly with an increased coefficient. I don’t think the latter makes either conceptual sense with the idea of a “critical value” of negative utility, or mathematical sense with regards to operations involving infinities."
Well, I think that Aaron would argue that this indifference curve is just quantifying over a limited range. However, you could still say that there are other incommensurable thresholds to the right of the asymptote.
Nice response, thanks for engaging with it. I'll write a more complete response soon, but my basic thoughts are that:
1) I bite most of the bullets you list, except:
2) VNM shows that preferences have to be modeled by an *ordinal* utility function. You write that
"Well, the vnm formula shows one’s preferences will be modellable as a utility function if they meet a few basic axioms. Let’s say a papercut is -n and torture is -2 billion."
but this only shows that the torture is worse than the papercut - not that it is any particular amount worse.
Afaik there's no argument or proof that one state of the world represented by (ordinal) utility u_1 is necessarily some finite number of times better or worse than some other state of the world represented by u_2
It shows that the torture is 2 billion/n times worse. The vnm formula shows it must be cardinal, not merely ordinal. A 1/2 chance of 2 utility is just as good as 1 utility, vnm formula shows we need to have our utility modellable as a function such that if a 1/n chance of n utility = a 100% chance of 1 utility.
> I reject one and would accept the trade, largely for the reasons described above.
The way the trade is presented this is clearly false. You have a good imagination. I have a good imagination. The worst torture that could be thought up by a perfectly imaginative being would undoubtably get to negative infinity utility.
Secondly,
> Surely one instance of this torture is less bad than two instances of slightly less gruesome torture…
This is a strong argument, but I don’t think it’s necessarily true. It seems plausible that some forms of torture could act like a clean breaking piecewise function instead of a curve.
Imagine for a moment you tried answering a code of ethics that said murder was the ultimate wrong with this argument. You can’t imagine being slightly “less dead” such that you could eventually only be “a little dead” at which other considerations outweigh. Dead is Dead! (Insert meme here).
So yeah I don’t think it necessarily applies.
*However*
Isn’t there an even simpler response to this kind of negative util? The preference charts given here have a vertical asymptote at some value p of suffering.
What about value of suffering 2p? It seems like 2p is either out of the domain of the function, which is absurd, equal to p, which is also absurd, or scales linearly with an increased coefficient. I don’t think the latter makes either conceptual sense with the idea of a “critical value” of negative utility, or mathematical sense with regards to operations involving infinities.
"The way the trade is presented this is clearly false. You have a good imagination. I have a good imagination. The worst torture that could be thought up by a perfectly imaginative being would undoubtably get to negative infinity utility."
Well, the way the trade is presented is that for any finite amount of suffering there is an associated positive experience that would outweigh, which I accept, and I think you'd accept.
"Isn’t there an even simpler response to this kind of negative util? The preference charts given here have a vertical asymptote at some value p of suffering. What about value of suffering 2p? It seems like 2p is either out of the domain of the function, which is absurd, equal to p, which is also absurd, or scales linearly with an increased coefficient. I don’t think the latter makes either conceptual sense with the idea of a “critical value” of negative utility, or mathematical sense with regards to operations involving infinities."
Well, I think that Aaron would argue that this indifference curve is just quantifying over a limited range. However, you could still say that there are other incommensurable thresholds to the right of the asymptote.
Nice response, thanks for engaging with it. I'll write a more complete response soon, but my basic thoughts are that:
1) I bite most of the bullets you list, except:
2) VNM shows that preferences have to be modeled by an *ordinal* utility function. You write that
"Well, the vnm formula shows one’s preferences will be modellable as a utility function if they meet a few basic axioms. Let’s say a papercut is -n and torture is -2 billion."
but this only shows that the torture is worse than the papercut - not that it is any particular amount worse.
Afaik there's no argument or proof that one state of the world represented by (ordinal) utility u_1 is necessarily some finite number of times better or worse than some other state of the world represented by u_2
It shows that the torture is 2 billion/n times worse. The vnm formula shows it must be cardinal, not merely ordinal. A 1/2 chance of 2 utility is just as good as 1 utility, vnm formula shows we need to have our utility modellable as a function such that if a 1/n chance of n utility = a 100% chance of 1 utility.