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Building a framework for the probability ranking principle by a family of expected weighted rank

A new principles framework is presented for retrieval evaluation of ranked outputs. It applies decision theory to model relevance decision preferences and shows that the Probability Ranking Principle (PRP) specifies optimal ranking. It has two new components, namely a probabilistic evaluation model and a general measure of retrieval effectiveness. Its probabilities may be interpreted as subjective or objective ones. Its performance measure is the expected weighted rank which is the weighted average rank of a retrieval list. Starting from this measure, the expected forward rank and some existing retrieval effectiveness measures (e.g., top n precision and discounted cumulative gain) are instantiated using suitable weighting schemes after making certain assumptions. The significance of these instantiations is that the ranking prescribed by PRP is shown to be optimal simultaneously for all these existing performance measures. In addition, the optimal expected weighted rank may be used to normalize the expected weighted rank of retrieval systems for (summary) performance comparison (across different topics) between systems. The framework also extends PRP and our evaluation model to handle graded relevance, thereby generalizing the discussed, existing measures (e.g., top n precision) and probabilistic retrieval models for graded relevance.