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A decision maker (DM) observes a noisy signal of the quality of a project before deciding to accept or reject the project. We show (i) as the amount of noise increases, the minimum signal required for acceptance may either increase or decrease, and may be nonmonotonic. (ii) Consequently, the average quality of accepted projects may either increase or decrease in the amount of noise. (iii) The effect of increased noise on decisions depends in a straightforward way on which kind of mistake leaves the DM worse off, a rejection of a good project or an acceptance of a bad project.
