Alice is a once-in-multiple-lifetimes genius at something. What it is doesn't matter - a brilliant general, a mathematician, a painter. Bob has a very good reason to want to kill her and is in a position where he can easily do so. He decides against it despite the fact that he could safely get away with it.
Why? Because the life of someone so brilliant has intrinsic value, and he doesn't want to deprive the world of it. Some overlap with Kill Me Now or Forever Stay Your Hand, and a sister trope to Uniqueness Value. While that trope demands uniqueness, this one required exceptional genius at something in particular—if there happened to be five brilliant physicists, the character acting out this trope would still have as much trouble killing them as if there were only one at that level.
Frequently, the "genius" in question becomes a Morality Pet. A subtrope of You Will Be Spared.
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Anime and Manga
Played with in the 'ant' arc of Hunter × Hunter. First, all the humans in the country the King has taken over are to be tested to destruction in such a way that the most potentially powerful can be converted into the superpowered mindslave footsoldiers of his world conquest. Then to keep him busy for a few months while they get this plan into operation, his bodyguards start bringing the most accomplished strategy gamers they can find; once he beats the national chess champion, the man is killed and eaten, et cetera. Then he can't best this blind girl with a runny nose, Komugi, and starts to get obsessed with doing so. That's all stage one.
Stage two, she starts visibly improving in response to his challenge, and he comes to the thoughtful realization that human beings have an endless and mysterious potential to improve, and that child that he ate on the way to the palace might have had the potential to exceed him, the King, in some particular way. His bodyguards are at this point in the speech freaking out at what looks like an impending Heel-Face Turn... and then we get a giant Slasher Smile and the declaration that if they are all that, and he can kill any of them, that makes him even more supremely awesome than he'd realized.
Stage three, he develops even more respect for Komugi and some form of emotional maturity (the guy is three months old), which combined with his appreciation for the skill and determination of the Hunter strike force, or at least Netero, prompts him to offer very reasonable terms, which are not accepted. He eventually dies of radiation poisoning inflicted by Netero's dying act, while playing against Komugi. He never did beat her.
The King's arrival at any kind of civilized interaction with humans was thus built on a foundation of this trope, via Komugi and Netero.
Ultimately subverted when Ren admires Baam's incredible talent and would love to recruit him into the Royal Enforcement Division, but decides to still kill him.
Ren: It's really a shame...but I can't let an Irregular live.
Played straight when Love, despite his desire to enact his revenge on the organization Viole belongs to, decides to spare him out of curiosity where his immense talent will take him, under the condition that Viole renounces his affiliations with FUG.
Joseph: I was just thinking about how you're going to have to live the rest of long life always thinking about that how you were injured by a human. The only way to get over that... well, would be to fight a properly trained me, is what I was thinking.
Happens in Dragon Ball at the climax of the Saiyan Saga: After pushing Goku to use Kaio-ken x3, blasted into the stratosphere by by Kaio-ken x4-charged Kamehameha, having his tail chopped off, hit with the Spirit Bomb, having his back cut and crushed by a Giant Ape Gohan falling on him; Vegeta still had enough strength to crawl back to his space pod. While briefly impressed with his sheer resilience, Krillin decides to kill him with Yajirobe's sword to finally end the Saiyan threat. But Goku calls out to Krillin to ask for Vegeta's life to be spared, since he admired his incredible strength, and thought it'd be a waste to deprive the universe of such a strong warrior, and while not convinced he'd turn like Piccolonote Though he eventually did, he wished to have the opportunity fight him once again, Krillin accepts Goku's request.
In Bleach, it's been revealed that Kenpachi subconsciously does this. He enjoys a good fight so much that he holds the majority of his power back from fear that he will kill anyone talented enough to challenge him.
In Naruto flashbacks, it's shown that before Hanzo became paranoid and power-hungry, he used to spare the lives of enemies strong-willed enough to put up a good fight against him.
The Man In Black: I would sooner destroy a stained glass window as an artist like yourself. However, since I can't have you following me either... (Tap on the Head)
In Hellboy II: The Golden Army, Prince Nuada pulls this gambit to try to turn Hellboy over to his side. It rings just a little bit false, because Nuada himself unleashed the creature in question as a weapon.
Nuada: What are you waiting for? This is what you want, isn't it? Look at it. The last of its kind. Like you and I. If you destroy it, the world will never see its kind again...
Clarice Starling: Where are you, Dr. Lecter? Hannibal Lecter: I've no plans to call on you, Clarice. The world is more interesting with you in it.
Jeane-Claude of the Anita Blake series says he doesn't turn people often because he doesn't like the idea of taking a great artist or mind—and though vampires don't die, he says they get a good dose of Creative Sterility.
The Ace of Labyrinths of Echo series by Max Frei was convinced that the life of people who show a talent for the magic using forces of the Universe — as opposed to forces of the world, which anyone can in a magical enough place — is "almost sacred". Which is why he devised a complicated trap to capture the Big Bad instead of killing him. That's the man who slaughtered so much powerful mages that he became the most feared and hated being for the magical Orders in the middle of a civil war despite pretending he's no one's enemy and kills just for money (they still hired him, of course).
In Memory, Sorrow, and Thorn, this is part of the reason why Prester John spares Camaris. Camaris was widely considered to be the greatest knight who ever lived, with John being the only one who had a chance of holding his own against him in battle.
Live Action Television
Doctor Who: In The Seeds of Death, The Doctor invokes this when captured by Ice Warriors.
Doctor: You can't kill me! Your leader will be very angry if you kill me! I'm a genius!
Played with in "Asylum of the Daleks." The Daleks have an entire planet for Daleks they deem too insane or out-of-control to be of any use. When asked why they don't destroy these mad Daleks, as they tend to do to anything they feel has outlived its usefulness:
Dalek Prime Minister: It is offensive to us to extinguish such divine hatred. (...) Does it surprise you to know the Daleks have a concept of beauty?
Discussed but averted in Mass Effect 1. After Shepard's squad kills a unique, 10,000-year-old creature known as the Thorian, an asari named Shiala briefly expresses some regret that this was necessary, and so does the Council. Why? Because the Thorian was the only one of its kind, and it was such a shame that the universe will never see its kind again.
In Erfworld, it is impossible to intentionally create casters, so they are usually captured rather than croaked when their side is destroyed.
Operation Paperclip was a secret mission by OSS (CIA's predecessor) to extract German rocket scientists and medical doctors after World War II to the US, regardless of their past affiliations with the Nazi party and even war crimes.
The Greek mathematician Archimedes was supposedly killed by a Roman soldier despite orders that he not be harmed.
The Colombian ecovillage of Gaviotas woke up one morning to find that they'd been occupied by the [[Useful Notes/Colombia FARC]]. The heavily armed guerrillas lined all the villagers up and demanded that they declare their allegiance. One of the villagers stepped forward and said that they had no allegiance save peace, and would take no sides in any armed conflict. "What," she asked, "will you do us now?" "Nothing" came the reply. "We have orders to hurt no one here. What you're doing is too important."