An axiomatic approach to personalized ranking systems

Abstract

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.

Computational challenges in e-commerce

“…Player j cannot reduce the i-j path length and improve the i-j trust by adding fake nodes and (directed) edges, as these nodes and edges can only affect shortest paths that flow through j and thus must leave the i-j path unaffected. 4 A similar argument establishes that node j cannot reduce the i-k trust for any node k that i trusts more than j. The only paths affected would be those that go through j and therefore ultimately reach nodes less trusted by i than j.…”

Multi-Armed Bandit Policies for Reputation Systems

“…Then, the reputation of an agent is an agregation of all the trust values about this agent. Many reputation systems have been proprosed [4][5][6][7][8][9][10][11]. They can be classified in three families: symmetric (e.g.…”

“…Let us notice that EigenTrust is known to be manipulable by a simple coalition of agents [12]. The problem of the robustness of reputation systems has been strongly studied [10,11,13]. Cheng and Friedman [13] proved that no symmetric reputation system can be robust to false-identity collusions and only assymetric reputation systems can be robust if they satisfy some strong conditions.…”

“…Cheng and Friedman [13] proved that no symmetric reputation system can be robust to false-identity collusions and only assymetric reputation systems can be robust if they satisfy some strong conditions. Altman et al [11] defined, among other axioms for reputation and ranking systems, the incentive compatibility which corresponds to a robustness against manipulation, and they proved that most of the ranking systems do not satisfy it. However, both Cheng and Friedman, and Altman et al considered manipulations at a given instant: a system is robust if the manipulation does not change the reputation value (or rank) at the time the manipulation is perfomed.…”

Multiagent systems: algorithmic, game-theoretic, and logical foundations

“…Our section on ranking systems follows Altman and Tennenholtz [2008]. Other interesting directions in ranking systems include developing practical ranking rules and/or axiomatizing such rules (e.g., Page et al [1998], Kleinberg [1999], Borodin et al [2005], and Altman and Tennenholtz [2005]), and exploring personalized rankings, in which the ranking function gives a potentially different answer to each agent (e.g., Altman and Tennenholtz [2007]). …”