  Reasoning about agent preferences on a set of alternatives, and the
aggregation of such preferences into some social ranking is a fundamental issue
in reasoning about uncertainty and multi-agent systems. When the set of agents
and the set of alternatives coincide, we get the so-called reputation systems
setting. Famous types of reputation systems include page ranking in the context
of search engines and traders ranking in the context of e-commerce. In this
paper we present the first axiomatic study of reputation systems. We present
three basic postulates that the desired/aggregated social ranking should
satisfy and prove an impossibility theorem showing that no appropriate social
ranking, satisfying all requirements, exists. Then we show that by relaxing any
of these requirements an appropriate social ranking can be found. We first
study reputation systems with (only) positive feedbacks. This setting refers to
systems where agents' votes are interpreted as indications for the importance
of other agents, as is the case in page ranking. Following this, we discuss the
case of negative feedbacks, a most common situation in e-commerce settings,
where traders may complain about the behavior of others. Finally, we discuss
the case where both positive and negative feedbacks are available.
