So why is the goal of utilitarianism to maximize the sum of utilities?
There are different kinds of utilitarianism. What they have in common is that they recommend maximising some measure of utility. Where they differ is in how that utility is measured, and how different people’s utilities are combined. Summing is one way; averaging is another; maximining yet another.
Mathematical arguments can tell you that if a person’s preferences have certain properties, a utility measure can be constructed for them (e.g. the VNM theorem). Mathematics can draw out non-obvious properties of proposed measures of utility. But no mathematical argument will tell you the right way to measure and combine utilities, any more than it will tell you that you should be a utilitarian in the first place.
But no mathematical argument will tell you the right way to measure and combine utilities . . .
Much the same could be said about potential probability functions.
I think what I’m looking for is some equivalent to Jaynes’s “Desiderata” for probability, but in the realm of either basic utility functions or how to combine them.
. . . any more than it will tell you that you should be a utilitarian in the first place.
Being new to this, I’m also interested in a pointer to some kind of standard argument for (any kind of) utilitarianism.
I mean something more than Yvain’s wonderful little Consequentialism FAQ.
I think what I’m looking for is some equivalent to Jaynes’s “Desiderata” for probability, but in the realm of either basic utility functions or how to combine them.
The VNM theorem goes from certain hypotheses about your preferences to the existence of a utility function describing them. However, the utility function is defined only up to an affine transformation. This implies that given only that, there is no way to add up utilities, even the utilities of a single person. (You can, however , take weighted averages of them.) It also deals only with a single person, or rather, a single preference relation. It is silent on the subject of how to combine different people’s preference relations or utility functions. There is no standard answer to the question of how to do this.
Being new to this, I’m also interested in a pointer to some kind of standard argument for (any kind of) utilitarianism.
Use non-standard (AKA infinitesimal) numbers: a dust speck is an infinitesimal; there is a clear (and linear) disutility in increasing number of people with specks in their eyes, but no matter how many of them you sum up, you never achieve a disutility of a single person experiencing torture. Add second order if you want to have it more finely grained.
(Of course, this breaks down if you have an infinite number of people with dust specks. But our intuition breaks down anyway when faced with the infinite).
So why is the goal of utilitarianism to maximize the sum of utilities?
Rather than, say, to maximize the minimal utility being considered?
I ask because the torture/dust specks question seems to be down to whether you think the way to combine multiple people’s utility functions is by
a) Summing them (ie: “shut up and multiply”), or
b) Only looking at the worst-off individual (ie: “raise the floor”)
And I can’t find actual mathematical arguments about this.
(I know I’m years late, so if this is well settled, a quick pointer to that settlement would be much appreciated!)
There are different kinds of utilitarianism. What they have in common is that they recommend maximising some measure of utility. Where they differ is in how that utility is measured, and how different people’s utilities are combined. Summing is one way; averaging is another; maximining yet another.
Mathematical arguments can tell you that if a person’s preferences have certain properties, a utility measure can be constructed for them (e.g. the VNM theorem). Mathematics can draw out non-obvious properties of proposed measures of utility. But no mathematical argument will tell you the right way to measure and combine utilities, any more than it will tell you that you should be a utilitarian in the first place.
Much the same could be said about potential probability functions.
I think what I’m looking for is some equivalent to Jaynes’s “Desiderata” for probability, but in the realm of either basic utility functions or how to combine them.
Being new to this, I’m also interested in a pointer to some kind of standard argument for (any kind of) utilitarianism. I mean something more than Yvain’s wonderful little Consequentialism FAQ.
The VNM theorem goes from certain hypotheses about your preferences to the existence of a utility function describing them. However, the utility function is defined only up to an affine transformation. This implies that given only that, there is no way to add up utilities, even the utilities of a single person. (You can, however , take weighted averages of them.) It also deals only with a single person, or rather, a single preference relation. It is silent on the subject of how to combine different people’s preference relations or utility functions. There is no standard answer to the question of how to do this.
You could try Peter Singer and the people who take that argument seriously.
Use non-standard (AKA infinitesimal) numbers: a dust speck is an infinitesimal; there is a clear (and linear) disutility in increasing number of people with specks in their eyes, but no matter how many of them you sum up, you never achieve a disutility of a single person experiencing torture. Add second order if you want to have it more finely grained.
(Of course, this breaks down if you have an infinite number of people with dust specks. But our intuition breaks down anyway when faced with the infinite).
But even with that scheme, it seems that you could just as easily want to maximize the minimal utility as maximize the sum.