I don't see why Precrime isn't efficient.
The concept of precrime isn't to decide a person's future for them and then imprison them for it. Precrime does not effect how a person will react to something, it only shows how they will react in the future of their own free will (if you were to video tape a baseball game and watch the tape later, you would already know how the players would react to different events in the game, but you would not personally be involved in those decisions).

In the case of Anderton, he knew the future that he would create, therefore he could make a consious decision to not accept that future (though, ironically, he ends up accepting it anyway). However, according to the Precogs, Anderton would only commit the murder after seeing the "majority report". I think that the system would be more efficient if the precrime system operated with telling the criminals what they were going to do in order to allow them the conscious choice of avoiding it, then, the precogs' reports would be examined to see what the outcome would be after telling the criminal, and if they were still going to commit the murder then he could be arrested.

Overall i thought it was an interesting story, it was slightly confusing at parts and too wordy, but it had a better plot than the movie, which i don't remember even explaining what the minority report was, maybe i was too young to remember.