Group Recommendations: Axioms, Impossibilities, and Random Walks

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.Comment: In Proceedings TARK 2017, arXiv:1707.0825

Consistent Continuous Trust-Based Recommendation Systems

Abstract. The goal of a trust-based recommendation system is to generate personalized recommendations from known opinions and trust relationships. Prior work introduced the axiomatic approach to trust-based recommendation systems, but has been extremely limited by considering binary systems, while allowing these systems to be inconsistent. In this work we introduce an axiomatic approach to deal with consistent continuous trust-based recommendation systems. We introduce the model, discuss some basic axioms, and provide a characterization of a class of systems satisfying a set of basic axioms. In addition, as it turns out, relaxing some of the axioms leads to additional interesting systems, which we examine.