  We introduce an axiomatic approach to group recommendations, in line of
previous work on the axiomatic treatment of trust-based recommendation systems,
ranking systems, and other foundational work on the axiomatic approach to
internet mechanisms in social choice settings. In group recommendations we wish
to recommend to a group of agents, consisting of both opinionated and undecided
members, a joint choice that would be acceptable to them. Such a system has
many applications, such as choosing a movie or a restaurant to go to with a
group of friends, recommending games for online game players, & other communal
activities.
  Our method utilizes a given social graph to extract information on the
undecided, relying on the agents influencing them. We first show that a set of
fairly natural desired requirements (a.k.a axioms) leads to an impossibility,
rendering mutual satisfaction of them unreachable. However, we also show a
modified set of axioms that fully axiomatize a group variant of the random-walk
recommendation system, expanding a previous result from the individual
recommendation case.
