It is important for the network that it is possible to have pseudonymous accounts without any connection to real data. This possibility makes it possible for the network to survive in a situation where the networks becomes illegal.
On the other hand, pseudonymous accounts are clearly less reliable than accounts where in case of a violation of the contract real personal data of the violator appear on the global black list.
There is also another point where personal data allow to improve reliability. If one considers some person as reliable, one can tell others about this in a simple way: One offers some amount of money to a potential victim if he violates it's promises. Why would one make such promises - which is clearly risky? Very simple - in exchange of a similar promise in the other direction, which increases the own reliability. But this technique has its limitations: If one would like to evaluate the reliability of such promises to pay compensation, one would like to know that the two persons which exchange such support are not simply two pseudonyms of the same person. One solution of this problem would be that above persons have personal data stored in the net and allow a third, reliable person to access and compare these data as being different.
None of this is required: It is the free decision of every person in the net if (and which) personal data will be stored, and who has access to these data for which purposes. The typical application will be that the arbiter has access for the purpose of publishing them in the black list if necessary, and some other person we call notary for verifying various properties of these data (are they really personal data of the person behind the given pseudonym? Are the personal data of different pseudonyms different?).
The personal data will not be accessible to everybody (except one decides to make them so). They will be stored in an encrypted way. They have to be accessible only to those persons which need this access: the arbiter who has the right to decide about publication in this black list, the notary who has to verify the correctness of the data.
The person who checks and verifies personal data is named in our proposal "notary". Similar to other special functions in the network, everybody is allowed to work as a notary. As a consequence, it is our free (and risky) decision if we believe a given notary or not.
After the verification of some part of the personal record, say, the address, the personal record will be stored in a different way: It is no longer possible to change this record, except with a new verification by the notary. But it is also visible to everybody that the given notary has verified the address (or whatever else) of the person.
To check that the notary is reliable is something we do not want to do ourself. We will leave this job to some robot. As in general, there may be different implementations of such robots, based on different algorithms, different levels of reliability and so on. The simplest algorithm (one which is certainly realizable and sufficiently fast) is an explicit list of reliable persons. This would be a simple starting point, sufficient for a small network. For a larger network, more sophisticated algorithms may be used. But there is no necessity: Everybody is free to restrict himself to a subnetwork which is small enough for the simple algorithm: This subnetwork will be nonetheless much larger than and safer than the local informal networks people use today.
It seems also worth to note that an oligarchy (a few number of notarial firms) is not very dangerous. Every user may use all or some of them. There is not much gain such a firm can gain from manipulation, except some bribes of some criminals. But it is quite easy to check, using simple testing, if such a firm takes bribes from unknown persons. Therefore taking bribes will be restricted to a small number of persons personally known to the notary. This makes it a hard job to give bribes to several of such firms.
There are many different types of personal data:
The last two methods usually require some personal contact: the person who wants his data to be verified has to visit the office of the notary. This may become problematic if the network is illegal, but these problems are not unsolvable.