ABSTRACT High-quality, personalized recommendations are a key feature in many online systems. Since these systems often have explicit knowledge of social network structures, the recommendations may incorporate this information. This paper focuses on networks which represent trust and recommendations which incorporate trust relationships. The goal of a trust-based recommendation system is to generate personalized recommendations from known opinions and trust relationships. In analogy to prior work on voting and ranking systems, we use the axiomatic approach from the theory of social choice. We develop an natural set of five axioms which we desire any recommendation system exhibit. Then we show that no system can simultaneously satisfy all these axioms. We also exhibit systems which satisfy any four of the five axioms. Next we consider ways of weakening the axioms, which can lead to a unique recommendation system based on random walks. We consider other recommendation systems (personal page rank, majority of majorities, and min cut) and search for alternative axiomatizations which uniquely characterize these systems. Finally, we determine which of these systems are incentive compatible. This is an important property for systems deployed in a monetized environment: groups of agents interested in manipulating recommendations to make others share their opinion have nothing to gain from lying about their votes or their trust links
