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The PRP with retrieval costs

Suppose, instead, that we assume a model of retrieval costs. Let $C_1$ be the cost of not retrieving a relevant document and $C_0$ the cost of retrieval of a nonrelevant document. Then the Probability Ranking Principle says that if for a specific document $d$ and for all documents $d'$ not yet retrieved

C_0\cdot P(R=0\vert d) - C_1\cdot P(R=1\vert d) \le C_0\cdot P(R=0\vert d') - C_1\cdot P(R=1\vert d')
\end{displaymath} (62)

then $d$ is the next document to be retrieved. Such a model gives a formal framework where we can model differential costs of false positives and false negatives and even system performance issues at the modeling stage, rather than simply at the evaluation stage, as we did in Section 8.6 (page [*]). However, we will not further consider loss/utility models in this chapter.

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