Before revision:  We establish several general results and techniques for proving upper and lower bounds on elicitation complexity. These results provide tight bounds for eliciting the Bayes risk of any loss, a large class of propertieswhich includes spectral risk measuresand several new properties of interest.
After revision:  We establish several general results and techniques for proving upper and lower bounds for the broad class of Bayes risks. We apply these results by proving tight complexity bounds, with respect to identifiable properties, for variance, financial risk measures, entropy, norms, and new properties of interest.