A mathematical model of collaborative reputation systems

This paper provides a mathematical framework for modelling collaborative reputation systems (CRSs), which are useful in many fields of electronic commerce. A CRS is an algorithm that, at discrete points in time, receives in input from a set of users some ratings of a set of objects and generates a reputation for both the raters and the evaluated objects. Sufficient conditions for the convergence of a CRS are given, using basic results of the fixed point theory, and in particular for a broad class of iterative filtering methods and their related CRSs, generalizing some previous results. Finally, we analyse a simple kind of CRS which allows to use a priori information on the reliability of a subset of raters. Experimental results provide evidence that such CRSs exhibit high level of robustness against unfair raters.