Group Recommendations: Axioms, Impossibilities, and Random Walks

TL;DR

This paper develops an axiomatic framework for group recommendation systems, revealing fundamental impossibilities and proposing a random-walk based solution that extends previous individual recommendation models.

Contribution

It introduces an axiomatic approach to group recommendations, identifies key impossibility results, and proposes a novel random-walk based recommendation method for groups.

Findings

Certain natural axioms are mutually incompatible in group recommendation settings.

A modified set of axioms fully characterizes a group recommendation system based on random walks.

The proposed model extends previous individual recommendation frameworks to groups.

Abstract

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.