It is hard to say. With anonymous reviewing, reviewers are not held responsible except by the editor. If their reviews are public and in their name, this may cause them to write better reviews. Or maybe not according to
this study.
There is some data that indicate that lack of anonymization of authors leads to biased reviewing, in that reviewers favor papers sent in from top US universities. I can't find the study right now, but it was from a natural experiment with a medical journal that changed practice at some point and they compare data before and after. Edit:
Study here.
There is a review of research into reviewing bias
here, generally critical of the evidence offered so far.
In practice, until we get some better software for handling the reviewing process, reviewing will probably have to continue like it does now. This software will have to be written by me or Bo, so it can take a while to get done. We do not get paid for working on this project.
There is no special role for the editor of
OpenPsych journals. Reviewers for each journal form a democratic body. They can choose to elect a new reviewer, or fire a current one. I do not want to police reviewers.
Initially, I (and Piffer) had to select some persons to invite to become a reviewer, but this isn't supposed to be how it is going to be in the future.