I'm not sure if this kind of rational/utilitarian approach to thinking about policing is useful, because soon you'll end up with a perfect surveillance state and robo executioners for "the greater good". Maybe throw some precrime work in there as well, because statisticians for example have found correlations between certain looks of people and likelihood to commit crime. What if statistically the benefit outweighs the harm, i.e. more harm is prevented than suffering of innocent people being wrongly accused? Should we then lock up people to prevent crimes they haven't even committed yet?