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taw comments on Post Your Utility Function - Less Wrong
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I don't really see why not (at least without further argument).
Relativity and contextuality introduce additional arguments into the utility function, they don't imply that the output can't be scalar. Lots of people include relativity and contextual concerns into scalar utility all the time.
Semi-independent positive and negative axes only prevent you from using scalar utility if you think they're incommensurable. If you can assign weights to the positive and negative axes, then you can aggregate them into a single utility index. (How accurately you can do this is a separate question.)
Of course, if you do think there are fundamentally incommensurable values, then scalar utility runs into trouble.* Amartya Sen and others have done interesting work looking at plural/vector utility and how one might go about using it. (I guess if we're sufficiently bad at aggregating different types of value, such methods might even work better in practice than scalar utility.)
* I'm sceptical; though less sceptical than I used to be. Most claims of incommensurability strike me as stemming from unwillingness to make trade-offs rather than inability to make trade-offs, but maybe there are some things that really are fundamentally incomparable.
I was pretty convinced for commensurability and thought cognitive biases would just introduce noise, but lack of success by me, and apparently by everyone else in this thread, changed my mind quite significantly.
Not knowing how to commensurate things doesn't imply they're incommensurable (though obviously, the fact that people have difficulty with this sort of thing is interesting in its own right).
As a (slight) aside, I'm still unclear about what you think would count as "success" here.
It's not a hard implication, but it's a pretty strong evidence against existence of traditional utility functions.
A success would be a list of events or states of reality and their weights, such that you're pretty convinced that your preferences are reasonably consistent with this list, so that you know how many hours of standing in queues is losing 5kg worth and how much money is having one thousand extra readers of your blog worth.
It doesn't sound like much, but I completely fail as soon as it goes out of very narrow domain, I'm surprised by this failure, and I'm surprised that others fail at this too.
I'm surprised at your surprise. Even granting that humans could possibly be innately reflectively self-consistent, there's a huge curse of dimensionality problem in specifying the damn thing. ETA: The problem with the dimensionality is that interactions between the dimensions abound; ceteris paribus assumptions can't get you very far at all.
I was expecting noise, and maybe a few iterations before reaching satisfying results, but it seems we cannot even get that much, and it surprises me.