Reasoning about agent preferences on a set of alternatives, and the aggregation of such preferences into some social ranking is a fundamental issue in reasoning about multi-agent systems. When the set of agents and the set of alternatives coincide, we get the ranking systems setting. A famous type of ranking systems are page ranking systems in the context of search engines. In this paper we present an extensive axiomatic study of ranking systems. In particular, we consider two fundamental axioms: Transitivity, and Ranked Independence of Irrelevant Alternatives. Surprisingly, we find that there is no general social ranking rule that satisfies both requirements. Furthermore, we show that our impossibility result holds under various restrictions on the class of ranking problems considered. However, when transitivity is weakened, an interesting possibility result is obtained. In addition, we show a complete axiomatization of approval voting using ranked IIA.

Personalized ranking systems and trust systems are an essential tool for collaboration in a multi-agent environment. In these systems, trust relations between many agents are aggregated to produce a personalized trust rating of the agents. In this article, we introduce the first extensive axiomatic study of this setting, and explore a wide array of well-known and new personalized ranking systems. We adapt several axioms (basic criteria) from the literature on global ranking systems to the context of personalized ranking systems, and fully classify the set of systems that satisfy all of these axioms. We further show that all these axioms are necessary for this result. ACM Reference Format:Altman, A., and Tennenholtz, M. 2010. An axiomatic approach to personalized ranking systems.

Ranking systems are a fundamental ingredient of multi-agent environments and Internet Technologies. These settings can be viewed as social choice settings with two distinguished properties: the set of agents and the set of alternatives coincide, and the agents' preferences are dichotomous, and therefore classical impossibility results do not apply. In this paper we initiate the study of incentives in ranking systems, where agents act in order to maximize their position in the ranking, rather than to obtain a correct outcome. We consider several basic properties of ranking systems, and fully characterize the conditions under which incentive compatible ranking systems exist, demonstrating that in general no such system satisfying all the properties exists.

This paper initiates research on the foundations of ranking systems, a fundamental ingredient of basic e-commerce and Internet Technologies. In order to understand the essence and the exact rationale of page ranking algorithms we suggest the axiomatic approach taken in the formal theory of social choice. In this paper we deal with PageRank, the most famous page ranking algorithm. We present a set of simple (graph-theoretic, ordinal) axioms that are satisfied by PageRank, and moreover any page ranking algorithm that does satisfy them must coincide with PageRank. This is the first representation theorem of that kind, bridging the gap between page ranking algorithms and the mathematical theory of social choice.

We propose a machine learning approach to action prediction in oneshot games. In contrast to the huge literature on learning in games where an agent's model is deduced from its previous actions in a multi-stage game, we propose the idea of inferring correlations between agents' actions in different one-shot games in order to predict an agent's action in a game which she did not play yet. We define the approach and show, using real data obtained in experiments with human subjects, the feasibility of this approach. Furthermore, we demonstrate that this method can be used to increase payoffs of an adequately informed agent. This is, to the best of our knowledge, the first proposed and tested approach for learning in one-shot games, which is the most basic form of multiagent interaction.