Several norms for how people should assess a question's usefulness have been proposed, notably Bayesian diagnosticity, information gain (mutual information), Kullback-Liebler distance, probability gain (error minimization), and impact (absolute change). Several probabilistic models of previous experiments on categorization, covariation assessment, medical diagnosis, and the selection task are shown to not discriminate among these norms as descriptive models of human intuitions and behavior. Computational optimization found situations in which information gain, probability gain, and impact strongly contradict Bayesian diagnosticity. In these situations, diagnosticity's claims are normatively inferior. Results of a new experiment strongly contradict the predictions of Bayesian diagnosticity. Normative theoretical concerns also argue against use of diagnosticity. It is concluded that Bayesian diagnosticity is normatively flawed and empirically unjustified.