Utilitarianism?

I have very little background in philosophy (though I did once take a course on “moral reasoning” titled The Public and the Private in Politics, Morality, and Law), but I’ve been wondering a bit recently about utilitarianism and I thought this would be a good place to put some of those thoughts down.

As far as I know, the basic tenet of utilitarianism is that the right way to measure global well-being is to compute the well-beings of individuals and add them up.  This sounds obvious, but actually it’s not universally accepted: lots of people believe in things like family honor, or nationalism, or heresy, or etc., and so think that it makes sense to ask whether (e.g.) an event is “good for the Jews” rather than asking if its net aggregate effect on all individuals is positive.  However, I am basically willing to submit that I subscribe to this utilitarian tenet, with the following reservations:

  1. I don’t know how to compute the well-being of individuals.
  2. I don’t know what “add them up” means.

The first problem is what we might call a practical impediment, but it’s not really a theoretical objection: it seems possible to imagine that there is something called “individual well-being” that is well-defined, even if it’s not clear how to measure it, and we can probably even find broad agreement on the sorts of characteristics it must satisfy (though of course it seems like quite a lot of philosophy consists of people arguing about exactly this sort of question and not converging on agreement).  So let’s set problem 1 aside and talk about problem 2.

Probably the statement of problem 2 sounds like a joke; at least, the economist’s view is that well-being can be measured, the units are dollars, and the way to combine them is addition.  (The last sentence seems to me uncharitable, but I’m not sure if it’s uncharitable to the view described or to economists.)  But actually this is a common sort of problem in the real world: some things add when you combine them (the number of apples in two piles of apples taken together is the sum of the numbers of apples in each pile) but other things don’t (the aggregate temperature of two piles of apples taken together is not the sum of the temperatures of each pile).  It’s not clear what the units of well-being are, and so it’s not clear that necessarily the sensible thing to do is just add them.  (It’s not even clear to me whether well-being takes negative as well as positive values.)

Probably a reasonable utilitarian tenet is that the global well-being function should be symmetric in the inputs, i.e., one person’s well-being shouldn’t matter more than another’s.  I also feel that the function has some sort of concavity, i.e., that moving two people closer together in well-being while preserving the sum of the well-beings doesn’t decrease total well-being.  (I would like to claim that the previous sentence is as benign and self-evident as the one that precedes it, but I fear that instead it just helps provides evidence of where I lie on the political spectrum.)  Also obviously the number of people in the world is constantly changing, so probably there should be some normalization to avoid silly dead-ends related to the question of whether having two identical copies of everyone would be twice as good.  But aside from these three basic principles, I don’t feel like I can say a lot about this function.

So, what I’m left with are a few questions: have actual philosophers wandered down this path before?  If so, what have they found?  In particular, suppose you take as axioms the three principles in the preceding paragraph; how much does this constrain a good (i.e., well-being-maximizing) public policy?

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