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.
xkcd's Up-Goer Five comic gave technical specifications for the Saturn V rocket using only the 1,000 most common words in the English language.
This seemed to me and Briénne to be a really fun exercise, both for tabooing one's words and for communicating difficult concepts to laypeople. So why not make a game out of it? Pick any tough, important, or interesting argument or idea, and use this text editor to try to describe what you have in mind with extremely common words only.
This is challenging, so if you almost succeed and want to share your results, you can mark words where you had to cheat in *italics*. Bonus points if your explanation is actually useful for gaining a deeper understanding of the idea, or for teaching it, in the spirit of Gödel's Second Incompleteness Theorem Explained in Words of One Syllable.
As an example, here's my attempt to capture the five theses using only top-thousand words:
If you make a really strong computer and it is not very nice, you will not go to space today.
Other ideas to start with: agent, akrasia, Bayes' theorem, Bayesianism, CFAR, cognitive bias, consequentialism, deontology, effective altruism, Everett-style ('Many Worlds') interpretations of quantum mechanics, entropy, evolution, the Great Reductionist Thesis, halting problem, humanism, law of nature, LessWrong, logic, mathematics, the measurement problem, MIRI, Newcomb's problem, Newton's laws of motion, optimization, Pascal's wager, philosophy, preference, proof, rationality, religion, science, Shannon information, signaling, the simulation argument, singularity, sociopathy, the supernatural, superposition, time, timeless decision theory, transfinite numbers, Turing machine, utilitarianism, validity and soundness, virtue ethics, VNM-utility