Alon Altman

Ranking systems: the PageRank axioms

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.

Axiomatic foundations for ranking systems

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. Each of these axioms can be individually satisfied. Moreover, we show a complete axiomatization of approval voting using one of these axioms.

An axiomatic approach to personalized ranking systems

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.

Computational Pool: A New Challenge for Game Theory Pragmatics

Computational pool is a relatively recent entrant into the group of games played by computer agents. It features a unique combination of properties that distinguish it from oth- ers such games, including continuous action and state spaces, uncertainty in execution, a unique turn-taking structure, and of course an adversarial nature. This article discusses some of the work done to date, focusing on the software side of the pool-playing problem. We discuss in some depth CueCard, the program that won the 2008 computational pool tournament. Research questions and ideas spawned by work on this problem are also discussed. We close by announcing the 2011 computational pool tournament, which will take place in conjunction with the Twenty-Fifth AAAI Conference.

Scope Dominance with Upward Monotone Quantifiers

We give a complete characterization of the class of upward monotone generalized quantifiers Q1 and Q2 over countable domains that satisfy the scheme Q1xQ2y φ → Q2yQ1x φ. This generalizes the characterization of such quantifiers over finite domains, according to which the scheme holds iff Q1 is ∃ or Q2 is ∀ (excluding trivial cases). Our result shows that in infinite domains, there are more general types of quantifiers that support these entailments.

A Distributed Agent for Computational Pool

Games with continuous state and action spaces present unique challenges from an artificial intelligence (AI) viewpoint. Billiards, or pool, is one such domain that has been the focus of several research efforts aimed at designing AI agents to play successfully. Due to the continuous nature of the actions, it is natural to believe that the more time an agent has to investigate actions, the better it will perform. This paper gives a thorough description of a successful agent with a novel distributed architecture, designed for being able to grant further time for shot simulation and analysis through the utilization of many CPUs. A brief analysis of the distributed component of the agent is presented, as well as how much the extra time thus obtained contributed to its success, especially when compared to its other novel components. The described agent, CueCard, won the Computer Olympiad computational pool tournament held in 2008.