Group Recommendations: Axioms, Impossibilities, and Random Walks
This addresses the challenge of recommending joint choices for groups with both opinionated and undecided members, such as for movies or games, but is incremental as it expands on previous individual recommendation work.
The paper tackles the problem of making group recommendations by introducing an axiomatic approach and shows that a natural set of requirements leads to an impossibility, but a modified set fully axiomatizes a group variant of the random-walk recommendation system.
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.