Some authors have repeatedly pointed out that the use of the accuracy, in particular for comparing classifiers, is not adequate. The main argument discusses the validity of some assumptions underlying the use of this criterion. In this paper, we study the hardness of the accuracy's replacement in various ways, using a framework very sensitive to these assumptions: Inductive Logic Programming. Replacement is investigated in three ways: completion of the accuracy with an additional requirement, replacement of the accuracy by the ROC analysis, recently introduced from signal detection theory, and replacement of the accuracy by a single criterion. We prove strong hardness results for most of hte possible replacements. The major point is that allowing arbitrary multiplication of clauses appears to be totally useless. Another point is the equivalence in difficulty of various criteria. In contrast, the accuracy criterion appears to be tractable in this framework.
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