Suppose a store is robbed, and there’s a video.
The police identity some suspects - the guy who just got out of jail for robbing the same store, and another person the store owner had a dispute with. Neither of them look like the robber in the video. Then the police take a still from the video and knock on some doors around the block. Somebody recognizes the person in the video, and the police investigate that person. This scenario seems pretty fair to me.
Now suppose the police run it through the facial recognition system. It identifies one person as a 99% match, and the police go investigate this person. This scenario does not seem so fair to me.
Here’s how I see the math:
P(A) = P(robber has a doppelgänger living on the same block) = .01
P(B) = P(robber had a doppelgänger somewhere in the database) = .9
P(X) = P(police screw up investigation, and will convict the suspect whether or not they are guilty) = .2
P(AX) = .002
P(BX) = .18
The exact numbers are made up, but as long as P(A) << P(B), you can see you this tech will result in a huge increase in false convictions. Even if P(X) is low, the number of false convictions increases by P(B)/P(A).