If you liked
Psycho-Pass
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...then you might like
Chikyuugai Shounen Shoujo
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Very similar in the series are the philosophical topics of Artificial Intelligence and free will. In both series super human intelligence plays a major role. They cover the topics of: -AI alignment issues -Problems/Dangers of AIs in general -How much humans should follow the AIs lead versus following their own intuition
If you liked
Juuni Taisen
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...then you might like
Darwin's Game
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Both anime feature a battle royal game, with characters having special abilities. Also both focus much on internal monologue for fleshing out the characters motivations and strategies. In contrast to Darwins Game, Juuni Taisen shows varying characters per episode, while Darwin stays at the main character.
If you liked
Kami nomi zo Shiru Sekai
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...then you might like
Aishen Qiaokeli-ing...
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Somewhat smart mc who has to deal with the problems of the many harem girls. Both also have a supernatural element
If you liked
Kurogane Communication
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...then you might like
Planetarian: Chiisana Hoshi no Yume
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Both shows are about the interaction of human and robot in a post apocalyptic world. Kurogane is more lighthearted with comedy elements while planetarian is more serious.
If you liked
Shinpi no Sekai El-Hazard
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...then you might like
Isekai no Seikishi Monogatari
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Pretty similar in how the world feels like and the character constellation. Strange new world with harem/romance undertones
If you liked
Zegapain
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...then you might like
Glass no Hana to Kowasu Sekai
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without being able to spoil it: the world is similar in some way the rest on the other hand is pretty different: ranging from characters, to story to structure.
If you liked
DearS
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...then you might like
Mahoromatic: Automatic Maiden
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The perverted, intrusive female teacher , the maid/servant and overall mood is very similar. One has a aliens, the other has a robot, but both are unfamiliar with normal humans and idealize their master. The two shows belong to the sudden girlfriend genre, only with slight differences.
If you liked
Macross
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...then you might like
Outbreak Company
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In both cases culture (otaku culture and protoculture) is used as military means in a comedic fashion. Besides that major point, both anime are pretty different.
If you liked
The Third: Aoi Hitomi no Shoujo
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...then you might like
Kaze no Na wa Amnesia
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Both are post apocalyptic road movies/series and have a melancholic, philosophical feeling to it. While the third, the civilization had already more recovered in Amnesia, the collapse is still more recent.
If you liked
Project A-Ko
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...then you might like
Kill la Kill
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both Anime are extremely similar (both have): -super over the top action with school setting -lots of fanservice (even with super skimpy costumes, which give you super powers) -very humorous/light hearted -similar characters with two girls as rivals and one comic relief side-character
If you liked
Macross Plus
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...then you might like
Key the Metal Idol
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Both are about artificial idols controlled by humans. They portray Idols in a negative, critic way. Both anime (in particular key the metal idol)have psychological aspects and a cyberpunkish, sad and dark atmosphere.
If you liked
Appleseed
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...then you might like
Psycho-Pass
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Both are set in a utopian, perfect, utilitarian society controlled by a supercomputer. The viewer and characters question the usefulness of the system and society as a whole.
If you liked
Serial Experiments Lain
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...then you might like
Key the Metal Idol
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Both are slow paced series share very similar themes and concepts. Mystery, psychology, religion and humanity in a futuristic environment.