JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. International Statistical Institute (ISI) is collaborating with JSTOR to digitize, preserve and extend access to International Statistical Review / Revue Internationale de Statistique. 2University of Plymouth, UK Summary Folklore has it that a very simple supervised classification rule, based on the typically false assumption that the predictor variables are independent, can be highly effective, and often more effective than sophisticated rules. We examine the evidence for this, both empirical, as observed in real data applications, and theoretical, summarising explanations for why this simple rule might be effective.