__Abstract.__

We study elicitation of latent prior beliefs when the agent can acquire information via a costly attention strategy. We introduce a mechanism that simultaneously makes it strictly dominant to (a) not acquire any information, and (b) report truthfully. We call such a mechanism a *robust scoring rule*. Robust scoring rules are crucial for lab experiments, e.g., they are notably needed for testing Bayesian rationality. We prove that a robust scoring rule exists under mild axioms. These axioms are shown to characterize the class of posterior-separable cost functions. Our existence proof is constructive, thus identifying an entire class of robust scoring rules for each posterior-separable cost function. For the most common special case (viz., with entropic attention costs), we characterize the class of robust quadratic scoring rules by means of a simple inequality. Finally, we discuss potential experimental designs for testing Bayesian rationality.