Reid Andersen from Microsoft Research is talking about trust-based recommendation systems (PDF). To build a personalized recommendation, you need a trust graph among users. What system should you use to determine the recommendation? The researchers use an axiomatic approach.

The context of their axiomatic system is social choice theory (see Arrow's impossibility theorem for voting systems from 1951). More recent treatments are Webpage ranking systems (Altman, Teeneholtz, '05).

The details are fairly complex, but the basic idea is that by proposing axioms until you get an inconsistency in the axiom set and then backing off and exploring other axioms to add to the set, you can generate unique recommendation systems that have a provable set of properties.

The overall model is simple, but there are several nice result including being able to show incentive compatibility which avoids self-interested bias in the recommendations. For details, see the paper (PDF).

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