Premise: A world into the future where technology has advanced to great lengths is dominated by the Sibyl System which is able to quantify if someone has or will commit a crime by measuring their crime coefficient. The Ministry of Welfare Public Safety Bureau or MWPSB is the group that carries out the will of Sibyl, and makes up our story's protagonists.
Story(10/10): Gen Urobuchi has his hand in this. As I would expect nothing less of the one who did Mahou Shoujo Madoka Magica and Saya No Uta, the story is a masterpiece. The MWPSB is made up of a group of people classified as Inspectors or Enforcers, Inspectors act as detectives and keep a leash on Enforcers who are latent criminals judged by Sibyl to be unable to return to a normal life. In fighting fire with fire however, it allows them to track down other criminals more easily. Akane Tsunemori is a new Inspector who lacks experience on the field in law enforcement and she and the rest of the MWPSB gets dragged into a series of cases that all come back to one person who has affected the lives of many members of the MWPSB and is the most dangerous criminal they have to deal with.
Animation(10/10): The animation is excellent. From how the dominators analyze criminals or machines, to how they transform to take the appropiate action to blast a hole in criminals that makes them explode, and to the hand to hand fights. There aren't many hand to hand fights in this anime, but when they happen, adrenline rushes will hit as the fights are strategic and the moves displayed in an exotic way.
Sound(9/10): The soundtrack fits well with many given situations, the main theme when criminals are getting cornered will make it feel like justice is being delivered. And the theme of the main antagonist signifys the threat he represents yet also how charismatic he is. The openings are okay as the lyrics fit the theme of the show, and the second ending in particular is a soothing end to each episode that allows one to clearly take in the crazy events of the episode.
Characters(10/10): The characters are excellent and help to complete the story being told. The unique thing about Psycho-Pass is that all of the main characters are adults. It is unfortunately rare to not see a high school protagonist in most anime. Not that its a bad thing, though having variety is better. The only other few times I can think off the top of my head where it happens is Fate/Zero (also done by Gen Urobuchi) and Hellsing.
For the characters themselves we have Akane mentioned earlier, despite her inexperience her Psycho-Pass does not cloud easily as she always carries out her belief in justice regardless of what anyone or Sibyl thinks. And this belief molds into something spectacular as the show goes on and she gets experience. Then there is Shinya Kogami who had his life affected by the main antagonist and is focused on delivering his version of justice upon him. Ginoza is the other main character who is an inspector as well and is a sort of mentor to Akane. He holds great faith in the Sibyl System and wants Akane to become a great inspector while not allowing her crime coefficient to increase.
Overall(10/10): Psycho-Pass is a must watch, whether you enjoy sci-fi, crime cases, or want a great story told. It has utopian themes and makes refrences to many famous philosophers and writers. Even though Sibyl is not a perfect system it is interesting to watch how an apparant super computer can judge humanity and make it easier to prevent crime.