“Limited aggregation” allows you to say that two people suffering is worse than one and make some tradeoffs between numbers and severity without very small changes in welfare aggregating across separate individuals to outweigh large changes. “Limited aggregation” is a term in the literature, and I think it usually requires giving up the independence of irrelevant alternatives.
Almost all social welfare functions that satisfy the independence of irrelevant alternatives allow small changes to outweigh large changes. That includes non-additive but aggregative social welfare functions. See Spears and Budolfson:
It’s obvious that utilitarianism does this. Consider also maximin. Maximin requires you to focus entirely on the worst off individual (or individuals, if there are ties). This might seem good because it means preventing the worst states, but it also means even preferring to prevent a tiny harm to the worst off (or a worse off) over bringing someone down to their level of welfare. E.g., one extra pin prick to someone being tortured anyway outweighs the (only very slightly less bad) torture of someone who wouldn’t have otherwise been tortured. More continuous versions of maximin, like moderate tradeoff view/rank-discounted utilitarianism, have the same implications in some cases, which will depend on the numbers involved.
Limited aggregation allows you to make some intuitive tradeoffs without extreme prioritization like maximin or allowing tiny harms to aggregate outweigh large harms.
On the other hand, there are views that reject the independence of irrelevant alternatives but don’t allow any aggregation at all, and require you to minimize the greatest individual loss in welfare (not maximize the worst off state or maximize the welfare of the worst off individual, like maximin). This doesn’t allow enough tradeoffs either, in my view. Scanlon the contractualist and Tom Regan the deontological animal rights theorist endorsed such a principle, as “the greater burden principle” and “the harm principle”, respectively. Maybe also the animal advocate Richard Ryder, with his “painism”, unless that is just a form of maximin.
Thanks, Michael. This is what I’ve been looking for. I’ll check out your links. I tend to agree with Ryder, although I don’t know how thorough his framework is. Thanks again. PS: Hey Michael, those links were interesting. Do you have a good link to go into more about “limited aggregation”? Thanks, -Matthew Michael
Sorry I didn’t see this until now.
“Limited aggregation” allows you to say that two people suffering is worse than one and make some tradeoffs between numbers and severity without very small changes in welfare aggregating across separate individuals to outweigh large changes. “Limited aggregation” is a term in the literature, and I think it usually requires giving up the independence of irrelevant alternatives.
Almost all social welfare functions that satisfy the independence of irrelevant alternatives allow small changes to outweigh large changes. That includes non-additive but aggregative social welfare functions. See Spears and Budolfson:
https://philpapers.org/rec/BUDWTR
http://www.stafforini.com/docs/Spears & Budolfson—Repugnant conclusions.pdf
It’s obvious that utilitarianism does this. Consider also maximin. Maximin requires you to focus entirely on the worst off individual (or individuals, if there are ties). This might seem good because it means preventing the worst states, but it also means even preferring to prevent a tiny harm to the worst off (or a worse off) over bringing someone down to their level of welfare. E.g., one extra pin prick to someone being tortured anyway outweighs the (only very slightly less bad) torture of someone who wouldn’t have otherwise been tortured. More continuous versions of maximin, like moderate tradeoff view/rank-discounted utilitarianism, have the same implications in some cases, which will depend on the numbers involved.
Limited aggregation allows you to make some intuitive tradeoffs without extreme prioritization like maximin or allowing tiny harms to aggregate outweigh large harms.
On the other hand, there are views that reject the independence of irrelevant alternatives but don’t allow any aggregation at all, and require you to minimize the greatest individual loss in welfare (not maximize the worst off state or maximize the welfare of the worst off individual, like maximin). This doesn’t allow enough tradeoffs either, in my view. Scanlon the contractualist and Tom Regan the deontological animal rights theorist endorsed such a principle, as “the greater burden principle” and “the harm principle”, respectively. Maybe also the animal advocate Richard Ryder, with his “painism”, unless that is just a form of maximin.
Thanks, Michael. This is what I’ve been looking for. I’ll check out your links.
I tend to agree with Ryder, although I don’t know how thorough his framework is.
Thanks again.
PS: Hey Michael, those links were interesting. Do you have a good link to go into more about “limited aggregation”?
Thanks,
-Matthew Michael