this system would work well enough in a small local community with little migration. but in a global society of cities of millions of people, there are no wise old men to gather all the folk around the fire and discuss crime. Thats why anarcho-communist ideas also only work in small communities: anonymity removes the peer pressure of contributing to the system if there is no monetary benefit involved.
So probably PDA-s are required, as practice also shows in the case of Somalia.