The Probability Ranking Principle is Not Optimal in Adversarial Retrieval Settings

The probability ranking principle (PRP) - ranking documents in response to a query by their relevance probabilities - is the theoretical foundation of most ad hoc document retrieval methods. A key observation that motivates our work is that the PRP does not account for potential post-ranking effects, specifically, changes to documents that result from a given ranking. Yet, in adversarial retrieval settings such as the Web, authors may consistently try to promote their documents in rankings by changing them. We prove that, indeed, the PRP can be sub-optimal in adversarial retrieval settings. We do so by presenting a novel game theoretic analysis of the adversarial setting. The analysis is performed for different types of documents (single topic and multi topic) and is based on different assumptions about the writing qualities of documents' authors. We show that in some cases, introducing randomization into the document ranking function yields overall user utility that transcends that of applying the PRP.