I don't think either this, or anything else in this subthread, captures it. Let me have a go.

People like some things and not others. For each person, we can give a number to each thing that says how much they like it or don't. Suppose you must do one of two things. For each, look at how the world will be if you do it -- every thing in the world -- and all the people in the world, and add up all those numbers saying whether they like the things or not. Then do the thing that gives the biggest total.

Those numbers should be such that if one of two things will happen, each as often as the other, the number for this is half way between the numbers for those two things. And they should be such that each person will always do what makes their numbers biggest. And if two people care the same about a thing, they should give it the same number. We can't really make all those things true, but we do the best we can.

(What if you must do one of two things, and one makes there be more people, or fewer people, or other people? That is hard and I will not try to say what to do then.)

It's not perfect but I think it captures the key points: equal weights for all, consider all people, add up utilities, utilities should correspond to people's preferences. And it owns up to some of the difficulties that I can't solve in upgoer5 language because I can't solve them at all.

Hmm. That's part of it, but it doesn't seem to capture the full scope of the philosophy; you seem to be emphasizing its egalitarian aspects more than the aggregation algorithm, and I think the latter's really the core of it. Here's my stab at preference utilitarianism:

An act is good if it helps people do what they want and get what they need. It's bad if it makes people do things they don't want, or if it keeps them from getting what they need. If it gives them something they want but also makes them do something they don't want just as much, it isn't good or bad.

There are no right or wrong things to want, just right or wrong things to do. Also, it doesn't matter who the people are, or even if you know about them. What matters is what happens, not what you wanted to happen.

That is not what utilitarianism means. It means doing something is good if what happens is good, and doing something is bad if what happens is bad. It doesn't say which things are good and bad.