I would suggest that torture has greater and greater disutility the larger the size of the society. So given a specific society of a specific size, the dust specks can never add up to more suffering than the torture; the greater the number of dust specs possible, the greater the disutility of the torture, and the torture will always add up to worse.
If you’re comparing societies of different size, it may be that the society with the dust specks has as much disutility as the society with the torture, but this is no longer a choice between dust specks and torture, it’s a choice between dust specks+A to torture+B, and it’s not so counterintuitive that I might prefer torture+B.
As for why I have such an odd utility function as “torture is worse tin a larger society”? I’m trying to derive my utility function from my preferences and this is what I come up with—I’m not choosing a utility function as a starting point.
I’m trying to derive my utility function from my preferences and this is what I come up with—I’m not choosing a utility function as a starting point.
Any utility function runs into a repugnant conclusion of one type or another. I wonder if there is a theorem to this effect, following from transitivity + continuity. Yours is no exception.
For example, in your case of disutility of torture growing larger with the size of the society, doesn’t the disutility of dust specks grow both with the number of people subjected to it and the society’s size? If not, how about the intermediate disutilities, that of a stabbed toe, a one-min long agony and up and up slowly until you get to the full-blown 50 years of torture? Where it this magic boundary between the society size-independent disutility of specks and the scaling up disutility of torture?
As I noted, I’m trying to compute my utility function from my preferences, not the other way around. So in response to that I’d refine the utility function a bit: My new utility function has two terms, the main term and an inequality term. While my original statement that torture has a term based on the size of the society is still true, it is true because increasing the size of the society and still torturing 1 person means more inequality.
doesn’t the disutility of dust specks grow both with the number of people subjected to it and the society’s size?
The extra term applies to the dust specks as well, but I don’t think this is a problem.
In the original problem, everyone gets a dust speck, so there’s no inequality term. The torture does have an inequality term and ends up always worse than the dust specks.
If you want to move towards intermediate values by increasing the main term and keeping the inequality term constant, thus increasing the dust specks to stubbed toes and the like, you’ll eventually come to some point where it exceeds the torture. But at that point they won’t be dust specks—instead you’ll decide that, for instance, many people suffering 1 day of torture will be worse than one person suffering 50 years of torture. I can live with that result.
If you want to move towards intermediate values by increasing the inequality term and keeping the main term constant, you would “clump up” the dust specks, so one person receives many dust specks worth of disutility. If you keep doing this, you might eventually exceed the torture as well—but again, at the point where you exceed the torture, you won’t have dust specks any more, you’ll have larger clumps and you’ll say that many clumps (equivalent to 1 day of torture each, for instance) can exceed one person getting 50 years. Again, I can live with that result.
If you want to move towards intermediate values by increasing the inequality term and not bothering to keep the population constant, adding more people (in a way that is otherwise neutral if you ignore the inequality term) would increase the disutility. I haven’t worked out if this requires being able to increase the disutility beyond that of torture, but as I noted above, that would be a case of dust specks+A compared to torture+B and having either of those quantities be greater wouldn’t surprise me..
This is a type of variable value principle and avoids the Repugnant Conclusion itself, but may allow for a variety of Sadistic Conclusion, since adding some tortured people can be better than adding a larger number of well-off people. However, I would argue that despite the name “Sadistic”, this should be okay: I am not claiming that adding tortured people is good, just that it is bad but less bad than the other choice. And the other choice is bad because the decrease in total utility from adding more people and increasing inequality overwhelms the increase in total utility from those new people living good lives.
I would suggest that torture has greater and greater disutility the larger the size of the society. So given a specific society of a specific size, the dust specks can never add up to more suffering than the torture; the greater the number of dust specs possible, the greater the disutility of the torture, and the torture will always add up to worse.
If you’re comparing societies of different size, it may be that the society with the dust specks has as much disutility as the society with the torture, but this is no longer a choice between dust specks and torture, it’s a choice between dust specks+A to torture+B, and it’s not so counterintuitive that I might prefer torture+B.
As for why I have such an odd utility function as “torture is worse tin a larger society”? I’m trying to derive my utility function from my preferences and this is what I come up with—I’m not choosing a utility function as a starting point.
Any utility function runs into a repugnant conclusion of one type or another. I wonder if there is a theorem to this effect, following from transitivity + continuity. Yours is no exception.
For example, in your case of disutility of torture growing larger with the size of the society, doesn’t the disutility of dust specks grow both with the number of people subjected to it and the society’s size? If not, how about the intermediate disutilities, that of a stabbed toe, a one-min long agony and up and up slowly until you get to the full-blown 50 years of torture? Where it this magic boundary between the society size-independent disutility of specks and the scaling up disutility of torture?
As I noted, I’m trying to compute my utility function from my preferences, not the other way around. So in response to that I’d refine the utility function a bit: My new utility function has two terms, the main term and an inequality term. While my original statement that torture has a term based on the size of the society is still true, it is true because increasing the size of the society and still torturing 1 person means more inequality.
The extra term applies to the dust specks as well, but I don’t think this is a problem.
In the original problem, everyone gets a dust speck, so there’s no inequality term. The torture does have an inequality term and ends up always worse than the dust specks.
If you want to move towards intermediate values by increasing the main term and keeping the inequality term constant, thus increasing the dust specks to stubbed toes and the like, you’ll eventually come to some point where it exceeds the torture. But at that point they won’t be dust specks—instead you’ll decide that, for instance, many people suffering 1 day of torture will be worse than one person suffering 50 years of torture. I can live with that result.
If you want to move towards intermediate values by increasing the inequality term and keeping the main term constant, you would “clump up” the dust specks, so one person receives many dust specks worth of disutility. If you keep doing this, you might eventually exceed the torture as well—but again, at the point where you exceed the torture, you won’t have dust specks any more, you’ll have larger clumps and you’ll say that many clumps (equivalent to 1 day of torture each, for instance) can exceed one person getting 50 years. Again, I can live with that result.
If you want to move towards intermediate values by increasing the inequality term and not bothering to keep the population constant, adding more people (in a way that is otherwise neutral if you ignore the inequality term) would increase the disutility. I haven’t worked out if this requires being able to increase the disutility beyond that of torture, but as I noted above, that would be a case of dust specks+A compared to torture+B and having either of those quantities be greater wouldn’t surprise me..
This is a type of variable value principle and avoids the Repugnant Conclusion itself, but may allow for a variety of Sadistic Conclusion, since adding some tortured people can be better than adding a larger number of well-off people. However, I would argue that despite the name “Sadistic”, this should be okay: I am not claiming that adding tortured people is good, just that it is bad but less bad than the other choice. And the other choice is bad because the decrease in total utility from adding more people and increasing inequality overwhelms the increase in total utility from those new people living good lives.