Reputation Systems: An Axiomatic Approach

TL;DR

This paper provides the first axiomatic analysis of reputation systems, demonstrating the impossibility of satisfying all desirable properties simultaneously and exploring relaxations for systems with positive, negative, or mixed feedbacks.

Contribution

It introduces an axiomatic framework for reputation systems, proves an impossibility theorem, and analyzes how relaxing certain axioms enables feasible social rankings.

Findings

No social ranking satisfies all three axioms simultaneously.

Relaxing any one axiom allows for a compatible social ranking.

Different feedback types (positive, negative, mixed) affect the axiomatic feasibility.

Abstract

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 uncertainty and multi-agent systems. When the set of agents and the set of alternatives coincide, we get the so-called reputation systems setting. Famous types of reputation systems include page ranking in the context of search engines and traders ranking in the context of e-commerce. In this paper we present the first axiomatic study of reputation systems. We present three basic postulates that the desired/aggregated social ranking should satisfy and prove an impossibility theorem showing that no appropriate social ranking, satisfying all requirements, exists. Then we show that by relaxing any of these requirements an appropriate social ranking can be found. We first study reputation systems with (only) positive feedbacks. This setting refers to systems where agents' votes are interpreted as indications for the importance of other agents, as is the case in page ranking. Following this, we discuss the case of negative feedbacks, a most common situation in e-commerce settings, where traders may complain about the behavior of others. Finally, we discuss the case where both positive and negative feedbacks are available.