Thanks for writing this up! I agree that this result is interesting, but I find it unpersuasive as a normative argument. Why should morality be based on group decision-making principles? Why should I care about VNM rationality of the group?
Also, you suggest that this result lends support to common EA beliefs. I’m not so sure about that. First, it leads to preference utilitarianism, not hedonic utilitarianism. Second, EAs tend to value animals and future people, but they would arguably not count as part of the “group” in this framework(?). Third, I’m not sure what this tells you about the creation or non-creation of possible beings (cf. the asymmetry in population ethics).
Finally, it’s worth pointing out that you could also start with different assumptions and get very different results. For instance, rather than demanding that the group is VNM rational, one could consider rational individuals in a group who bargain over what to do, and then look at bargaining solutions. And it turns out that the utilitarian approach of adding up utilities is *not* a bargaining solution, because it violates Pareto-optimality in some cases. Does that “disprove” total utilitarianism?
(Using e.g. the Nash bargaining solution with many participants probably leads to some form of prioritarianism or egalitarianism, because you’d have to ensure that everyone benefits.)
I have a strongly negative bias against any attempt to ground normative theories in abstract mathematical theories, such as game theory and decision theory. The way I see it, the two central claims of utilitarianism are the axiological claim (well-being is what matters) and the maximizing claim (we should maximize what matters ie. well-being). This argument provides no reason to ground our axiology in well-being, and also provides no reason that we should be maximizers.
In general, there is a significant difference between normative claims, like total utilitarianism, and factual claims, like “As a group, VNM rational agents will do X.”
And it turns out that the utilitarian approach of adding up utilities is *not* a bargaining solution, because it violates Pareto-optimality in some cases. Does that “disprove” total utilitarianism?
I’m not sure this is right. As soon as you maximize a weighted sum with non-negative coefficients your solution will be weakly Pareto optimal. As soon as all coefficients are strictly positive, it will be strongly Pareto optimal. The axioms mentioned above don’t imply non-negative coefficients, so theoretically they are also satisfied by “anti-utilitarianism” which counts everyone’s utility negatively. But one can add stronger Pareto axioms to force all coefficients to be strictly positive.
The problem with the utilitarian Bargaining solution is that it is not independent of affine transformations of utility functions. Just summing up utility functions is underspecified, one also needs to choose a scaling for the utility functions. A second criterion that might not be satisfied by the utilitarian solution (depending on the scaling chosen) is individual rationality, which means that everyone will be better off given the bargaining solution than some disagreement outcome.
Also, you suggest that this result lends support to common EA beliefs.
Hmm, I wasn’t trying to suggest that, but I might have accidentally implied something. I would be curious what you are pointing to?
First, it leads to preference utilitarianism, not hedonic utilitarianism
I used preferences about restaurants as an example because that seemed like something people can relate to easily, but that’s just an example. The theorem is compatible with hedonic utilitarianism. (In that case, the theorem would just prove that the group’s utility function is the sum of each individual’s happiness.)
Second, EAs tend to value animals and future people, but they would arguably not count as part of the “group” in this framework(?).
I don’t think that this theorem says much about who you aggregate. It’s just simply stating that if you aggregate some group of persons in a certain way, then that aggregation must take the form of addition.
Third, I’m not sure what this tells you about the creation or non-creation of possible beings (cf. the asymmetry in population ethics).
In that case, it would IMO be better to change “total utilitarianism” to “utilitarianism” in the article. Utilitarianism is different from other forms of consequentialism in that it uses thoroughgoing aggregation. Isn’t that what Harsanyi’s theorem mainly shows? It doesn’t really add any intuitions about population ethics. Mentioning the repugnant conclusion in this context feels premature.
In that case, it would IMO be better to change “total utilitarianism” to “utilitarianism” in the article. Utilitarianism is different from other forms of consequentialism in that it uses thoroughgoing aggregation. Isn’t that what Harsanyi’s theorem mainly shows?
Hmm, it does show that it’s a linear addition of utilities (as opposed to, say, the sum of their logarithms). So I think it’s stronger than saying just “thoroughgoing aggregation”.
I’m not very familiar with the terminology here, but I remember that in this paper, Alastair Norcross used the term “thoroughgoing aggregation” for what seems to be linear addition of utilities in particular. That’s what I had in mind anyway, so I’m not sure I believe anything different form you. The reason I commented above was because I don’t understand the choice of “total utilitarianism” instead of just “utilitarianism.” Doesn’t every form of utilitarianism use linear addition of utilities in a case where population size remains fixed? But only total utilitarianism implies the repugnant conclusion. Your conclusion section IMO suggests that Harsanyi’s theorem (which takes a case where population size is indeed fixed) does something to help motivate total utilitarianism over other forms of utilitarianism, such as prior-existence utilitarianism, negative utilitarianism or average utilitarianism. You already acknowledged in your reply further above to that it doesn’t do much of that. That’s why I suggested rephrasing your conclusion section. Alternatively, you could also explain in what ways you might think the utilitarian alternatives to total utilitarianism are contrived somehow or not in line with Harsanyi’s assumptions. And probably I’m missing something about how you think about all of this, because the rest of the article seemed really excellent and clear to me. I just find the conclusion section really jarring.
Alastair Norcross used the term “thoroughgoing aggregation” for what seems to be linear addition of utilities in particular
Ah, my mistake – I had heard this definition before, which seems slightly different.
I just find the conclusion section really jarring.
Thanks for the suggestion – always tricky to figure out what a “straightforward” consequence is in philosophy.
I changed it to this – curious if you still find it jarring?
Total utilitarianism is a fairly controversial position. The above example where (1,1)=(2,0) can be extended to show that utilitarianism is extremely demanding, potentially requiring extreme sacrifices and inequality.
It is therefore interesting that it is the only decision procedure which does not violate one of these seemingly reasonable assumptions.
Ah, my mistake – I had heard this definition before, which seems slightly different.
Probably I was wrong here. After reading this abstract, I realize that the way Norcross wrote about it is compatible with a weaker claim that linear aggregation of utility too. I think I just assumed that he must mean linear aggregation of utility, because everything else would seem weirdly arbitrary. :)
I changed it to this – curious if you still find it jarring?
Less so! The “total” still indicates the same conclusion I thought would be jumping the gun a bit, but if that’s your takeaway it’s certainly fine to leave it. Personally I would just write “utilitarianism” instead of “total utilitarianism.”
I used preferences about restaurants as an example because that seemed like something people can relate to easily, but that’s just an example. The theorem is compatible with hedonic utilitarianism. (In that case, the theorem would just prove that the group’s utility function is the sum of each individual’s happiness.)
In this case, I think it’s harder to argue that we should care about ex ante expected individual hedonistic utility and for the 1st and 3rd axioms, because we had rationality based on preferences and something like Pareto to support these axioms before, but we could now just be concerned with the distribution of hedonistic utility in the universe, which leaves room for prioritarianism and egalitarianism. I think the only “non-paternalistic” and possibly objective way to aggregate hedonistic utility within an individual (over their life and/or over uncertainty) would be to start from individual preferences/attitudes/desires but just ignore concerns not about hedonism and non-hedonistic preferences, i.e. an externalist account of hedonism. Roger Crisp defends internalism in “Hedonism Reconsidered”, and defines the two terms this way:
Two types of theory of enjoyment are outlined-internalism, according to which enjoyment has some special ’feeling tone’, and externalism, according to which enjoyment is any kind of experience to which we take some special attitude, such as that of desire.
Otherwise, I don’t think there’s any reason to believe there’s an objective common cardinal scale for suffering and pleasure, even if there were a scale for suffering and a separate scale for pleasure. Suffering and pleasure don’t use exactly the same parts of the brain, and suffering isn’t just an “opposite” pattern to pleasure. Relying on mixed states, observing judgements when both suffering and pleasure are happening at the same time might seem promising, but these judgements happen at a higher level and probably wouldn’t be consistent between people, e.g. you could have two people with exactly the same suffering and pleasure subsystems, but with different aggregating systems.
Why should morality be based on group decision-making principles? Why should I care about VNM rationality of the group?
It doesn’t have to be the group, it can be an impartial observer with their own social welfare function, as long as it is increasing with individual expected utility, i.e. satisfies ex ante Pareto. Actually, that’s how it was originally stated.
EDIT: woops, condition 2 is weaker than ex ante Pareto; it’s just vNM rationality with respect to outcomes for social/ethical preferences/views. It’s condition 3 that connects individual vNM utility and social/ethical vNM utility.
Why should morality be based on group decision-making principles? Why should I care about VNM rationality of the group?
I’ve retracted my previous reply. The original 2nd condition is different from ex ante Pareto; it’s just vNM rationality with respect to outcomes for social/ethical preferences/views and it says nothing about the relationship between individual preferences and social/ethical ones. It’s condition 3 that connects individual vNM utility and social/ethical vNM utility.
Thanks for writing this up! I agree that this result is interesting, but I find it unpersuasive as a normative argument. Why should morality be based on group decision-making principles? Why should I care about VNM rationality of the group?
Also, you suggest that this result lends support to common EA beliefs. I’m not so sure about that. First, it leads to preference utilitarianism, not hedonic utilitarianism. Second, EAs tend to value animals and future people, but they would arguably not count as part of the “group” in this framework(?). Third, I’m not sure what this tells you about the creation or non-creation of possible beings (cf. the asymmetry in population ethics).
Finally, it’s worth pointing out that you could also start with different assumptions and get very different results. For instance, rather than demanding that the group is VNM rational, one could consider rational individuals in a group who bargain over what to do, and then look at bargaining solutions. And it turns out that the utilitarian approach of adding up utilities is *not* a bargaining solution, because it violates Pareto-optimality in some cases. Does that “disprove” total utilitarianism?
(Using e.g. the Nash bargaining solution with many participants probably leads to some form of prioritarianism or egalitarianism, because you’d have to ensure that everyone benefits.)
+1
I have a strongly negative bias against any attempt to ground normative theories in abstract mathematical theories, such as game theory and decision theory. The way I see it, the two central claims of utilitarianism are the axiological claim (well-being is what matters) and the maximizing claim (we should maximize what matters ie. well-being). This argument provides no reason to ground our axiology in well-being, and also provides no reason that we should be maximizers.
In general, there is a significant difference between normative claims, like total utilitarianism, and factual claims, like “As a group, VNM rational agents will do X.”
I’m not sure this is right. As soon as you maximize a weighted sum with non-negative coefficients your solution will be weakly Pareto optimal. As soon as all coefficients are strictly positive, it will be strongly Pareto optimal. The axioms mentioned above don’t imply non-negative coefficients, so theoretically they are also satisfied by “anti-utilitarianism” which counts everyone’s utility negatively. But one can add stronger Pareto axioms to force all coefficients to be strictly positive.
The problem with the utilitarian Bargaining solution is that it is not independent of affine transformations of utility functions. Just summing up utility functions is underspecified, one also needs to choose a scaling for the utility functions. A second criterion that might not be satisfied by the utilitarian solution (depending on the scaling chosen) is individual rationality, which means that everyone will be better off given the bargaining solution than some disagreement outcome.
You’re right; I meant to refer to the violation of individual rationality. Thanks!
Thanks for the comment!
Hmm, I wasn’t trying to suggest that, but I might have accidentally implied something. I would be curious what you are pointing to?
I used preferences about restaurants as an example because that seemed like something people can relate to easily, but that’s just an example. The theorem is compatible with hedonic utilitarianism. (In that case, the theorem would just prove that the group’s utility function is the sum of each individual’s happiness.)
I don’t think that this theorem says much about who you aggregate. It’s just simply stating that if you aggregate some group of persons in a certain way, then that aggregation must take the form of addition.
I agree it doesn’t say much, see e.g. Michael’s comment.
In that case, it would IMO be better to change “total utilitarianism” to “utilitarianism” in the article. Utilitarianism is different from other forms of consequentialism in that it uses thoroughgoing aggregation. Isn’t that what Harsanyi’s theorem mainly shows? It doesn’t really add any intuitions about population ethics. Mentioning the repugnant conclusion in this context feels premature.
Hmm, it does show that it’s a linear addition of utilities (as opposed to, say, the sum of their logarithms). So I think it’s stronger than saying just “thoroughgoing aggregation”.
I’m not very familiar with the terminology here, but I remember that in this paper, Alastair Norcross used the term “thoroughgoing aggregation” for what seems to be linear addition of utilities in particular. That’s what I had in mind anyway, so I’m not sure I believe anything different form you. The reason I commented above was because I don’t understand the choice of “total utilitarianism” instead of just “utilitarianism.” Doesn’t every form of utilitarianism use linear addition of utilities in a case where population size remains fixed? But only total utilitarianism implies the repugnant conclusion. Your conclusion section IMO suggests that Harsanyi’s theorem (which takes a case where population size is indeed fixed) does something to help motivate total utilitarianism over other forms of utilitarianism, such as prior-existence utilitarianism, negative utilitarianism or average utilitarianism. You already acknowledged in your reply further above to that it doesn’t do much of that. That’s why I suggested rephrasing your conclusion section. Alternatively, you could also explain in what ways you might think the utilitarian alternatives to total utilitarianism are contrived somehow or not in line with Harsanyi’s assumptions. And probably I’m missing something about how you think about all of this, because the rest of the article seemed really excellent and clear to me. I just find the conclusion section really jarring.
Ah, my mistake – I had heard this definition before, which seems slightly different.
Thanks for the suggestion – always tricky to figure out what a “straightforward” consequence is in philosophy.
I changed it to this – curious if you still find it jarring?
Probably I was wrong here. After reading this abstract, I realize that the way Norcross wrote about it is compatible with a weaker claim that linear aggregation of utility too. I think I just assumed that he must mean linear aggregation of utility, because everything else would seem weirdly arbitrary. :)
Less so! The “total” still indicates the same conclusion I thought would be jumping the gun a bit, but if that’s your takeaway it’s certainly fine to leave it. Personally I would just write “utilitarianism” instead of “total utilitarianism.”
In this case, I think it’s harder to argue that we should care about ex ante expected individual hedonistic utility and for the 1st and 3rd axioms, because we had rationality based on preferences and something like Pareto to support these axioms before, but we could now just be concerned with the distribution of hedonistic utility in the universe, which leaves room for prioritarianism and egalitarianism. I think the only “non-paternalistic” and possibly objective way to aggregate hedonistic utility within an individual (over their life and/or over uncertainty) would be to start from individual preferences/attitudes/desires but just ignore concerns not about hedonism and non-hedonistic preferences, i.e. an externalist account of hedonism. Roger Crisp defends internalism in “Hedonism Reconsidered”, and defines the two terms this way:
Otherwise, I don’t think there’s any reason to believe there’s an objective common cardinal scale for suffering and pleasure, even if there were a scale for suffering and a separate scale for pleasure. Suffering and pleasure don’t use exactly the same parts of the brain, and suffering isn’t just an “opposite” pattern to pleasure. Relying on mixed states, observing judgements when both suffering and pleasure are happening at the same time might seem promising, but these judgements happen at a higher level and probably wouldn’t be consistent between people, e.g. you could have two people with exactly the same suffering and pleasure subsystems, but with different aggregating systems.
I’m personally more sympathetic to externalism. With antifrustrationism (there are actually arguments for antifrustrationism; see also my comment here), externalism leads to a negative hedonistic view (which I discuss further here).
It doesn’t have to be the group, it can be an impartial observer with their own social welfare function, as long as it is increasing with individual expected utility, i.e. satisfies ex ante Pareto. Actually, that’s how it was originally stated.
EDIT: woops, condition 2 is weaker than ex ante Pareto; it’s just vNM rationality with respect to outcomes for social/ethical preferences/views. It’s condition 3 that connects individual vNM utility and social/ethical vNM utility.
I’ve retracted my previous reply. The original 2nd condition is different from ex ante Pareto; it’s just vNM rationality with respect to outcomes for social/ethical preferences/views and it says nothing about the relationship between individual preferences and social/ethical ones. It’s condition 3 that connects individual vNM utility and social/ethical vNM utility.