I'm an outsider to the philosophy community (I'm a mathematics PhD student), and I'm curious of whether the following critique has been addressed. During some superficial discussions I had on utilitarianism, I frequently encountered the assumption that the total utility of an (intelligent) agent is 1. additive and 2. one-dimensional. To be precise, if an agent undergoes experiences E1, ... En, then each unit of experience has the associated utilities u1, ... un, which are real numbers, and the agent's total utility is u1 + ... + un (to account for infinitely many experiences, use an integral instead). At the very least, this was what I understood to be assumed in the original proposal of utilitarianism and its elementary criticisms.
I have two objections regarding this model of utilitarianism. I think that the assumption of regarding u1, ... un as real numbers is too restrictive, and I also think that using the total sum u1 + ... + un as the total utility is too restrictive.
A simple proposal is to model u1, ... un as vectors in higher dimensional spaces, possibly infinite. This will allow capturing various aspects of experiences in many coordinates of each experience. For example, one can think of each coordinate as "joy", "sadness", "familial bond", and so on. Note that even sadness is seen as good in the right context, for example in viewing a masterfully created film of high emotional value.
Instead of directly taking u1 + ... + un, the framework of utilitarianism should allow history-dependence, such as diminishing return. We are well aware that repeating the same type of experience repeatedly makes the experience have less value on us.
Utility should also allow perspective-dependence, which can change wildly through our lives. Depending on our value system, pain and suffering can have great utility, which can encapsulate anything from sensual pleasure to martyrdom. This value system can very well change through our lives, and thus I think that an agent's aggregate experience should be able to be filtered through a 'perspective function', to yield lower-dimensional (possibly 1-dimensional) utility.
Thus a simple extended model of utility I propose would be equipped with the following:
- A real vector space H, whose elements represent events in an agent's life.
- A sequence An = (E1, E2, ..., En) of elements of H, representing an agent's life.
- A set P of perspective functions H^k -> R, ranging over all natural numbers k
- A model of utility f(An) that depends on the timestep n and the perspective function f.
It seems likely that these concerns have been addressed in the philosophy community one way or another. Some simple Google searches at least reveal some papers in economics that deal with higher dimensional models of utility. Are there existing references to my concerns? Thank you in advance.