Assessment is a growing sub-field in education studies. There are many references. The main categories of assessment in the field of education is formative/summative rather than self/peer.
A useful reference for me is:
Carless, D. (2011). From testing to productive student learning : implementing formative assessment in confucian-heritage settings. New York: Routledge.
In my opinion, the theoretical foundation for differentiation of self/peer assessment would be:
1. Glorification of scientific 'objectivity' and dismissal of any 'subjectivity' in the past
2. The rise of 'subjective' observation's validity, at least in social sciences (which is not science 'per se' for hard-scientists). In this account, all observations have 'no escape' from subjectivity.
3. Hence, self-assessment has its own (to some extent) value. Still, people tend to trust more 'peer' assessment; for them, 'peers' as a collective whole is more 'objective' (than, for example, my own self/selfish/vain/biased etc assessment..as though peers themselves are never biased!).
4. So, we are back in the point 1 and restart the argument
The foundation of self assessment is inherent in eduction: eventually we want a learner to do without help, to be autonomous in a certain area. To have learned something consciously (i.e. not by covert indoctrination or sheer habit) is equal to having mastered and understood the required criteria. Learners needs self evaluation to be able to decide when they are ready.
The foundation for peer assessment is inherent in learning to co-operate: a group needs mutual feed back to optimize working together. Peer assessment is a means for learning how to address feed back in a friendly and effective way.
You will find all answers in my project, together with Ian Kennedy, on Peer Assessment Scoring Systems (PASS). Quite recently we wrote two papers and presented them at two conferences (UK, D). But the most interesting details you will find in more than 100 technical updates to this project, many with easy-to-follow diagrams.
I worked out a comprehensive taxonomy of different scoring models, both additive and multiplicative, well-defined and working. Caution: this is an ongoing highly active project, so you won't yet find the latest developments!
Of course, you need a tool to support your peer assessment project, but usually (for in-class applications) Excel will do.
Contact me if you need urgent advice, otherwise look for the many contributions I already made here on ResearchGate.