Many purported demonstrations of irrational behavior rely on the assumption that participants believe key task parameters that are merely asserted by experimenters. For example, previous researchers have found that participants who first reported confidence in items presented in a yes-no format did not change confidence to the degree prescribed by the normative model when those same items were later presented in a forced-choice format. A crucial assumption, however, was that participants fully believed the assertion that the forced-choice items were mutually exclusive and exhaustive. In this article, the authors derive and test a new normative model in which it is not assumed that participants fully believe the assertion. Two visual identification experiments show that the new normative model provides a compelling account of participants' confidence reports.