Why do people in Shin Sekai Yori die if they kill other humans? Why do people in Shin Sekai Yori die if they kill other humans?

I remember that during the anime they go through some ritual, but why does that ritual work? What is that ritual exactly? Is it something religious or is it just portrayed religiously but has scientific reasons it works? Do they psychologically affect the subconscious of humans? Is it a religious "magic" that does the trick? What gets triggered in the human brain after when people try to kill other humans? By what mechanism do they die?
Why is the ritual needed?

Also, what was the name of this thing? Was it death of shame? Why is that the name?

NOTE: I have watched (not recently) the whole show, so no risk of spoilers. Sorry the story is not very fresh on my mind.
This is all spoilers if you haven't seen the entire show.

The Death Feedback is part genetic and part conditioned. From episode 4, they mention that the human genome was modified and that the Death Feedback works by the subconscious becoming aware of an attempt to harm another human and it uses their power to stop liver functions and parathyroid glands. This is further reinforced by education, conditioning and hypnosis. I think in episode 12 Tomiko speculates that it could be possible to circumvent the Death Feedback if the user was on some kind of stimulants or somehow didn't recognize their targets as human.

(Taken from part of my answer to this question which is also related.