The retrieval decision problem is considered from the viewpoint of a decision theory approach. A threshold rule based on earlier rules for indexing decisions is considered and analyzed for retrieval decisions as a measure of retrieval performance. The threshold rule is seen as a good descriptive design measure of what a reasonable retrieval system should be able to do. A retrieval mechanism of randomly drawing documents is analyzed to determine the relative strength of the threshold rule. The Neyman-Pearson rule is shown to be a better a priori decision rule for retrieval as it attempts to maximize precision subject to a fixed level of recall, instead of setting a lower limit upon precision, as does the threshold rule. The threshold rule is seen as a necessary, but sufficient, condition for effective retrieval. Finally, a sufficient condition for the threshold rule illustrates the relationship between it and the Neyman-Pearson rule. (Author)