I think you misunderstood my question. I wasn't asking about what would the difference between summing and averaging be, but how to sum utility functions of different people together in the first place.
Oh, I completely misunderstood that.
The right answer is that utilitarians aren't summing utility functions, they're just summing some expression about each person. The term hedonic function is used for these when they just care about pleasure or when they aren't worried about being misinterpreted as just caring about pleasure and the term utility function is used when they don't know what a utility function is or when they are willing to misuse it for convenience.
This is for anyone in the LessWrong community who has made at least some effort to read the sequences and follow along, but is still confused on some point, and is perhaps feeling a bit embarrassed. Here, newbies and not-so-newbies are free to ask very basic but still relevant questions with the understanding that the answers are probably somewhere in the sequences. Similarly, LessWrong tends to presume a rather high threshold for understanding science and technology. Relevant questions in those areas are welcome as well. Anyone who chooses to respond should respectfully guide the questioner to a helpful resource, and questioners should be appropriately grateful. Good faith should be presumed on both sides, unless and until it is shown to be absent. If a questioner is not sure whether a question is relevant, ask it, and also ask if it's relevant.