The construction of mapping models is an increasingly popular mechanism for obtaining health state utility data to inform economic evaluations in health care. There is great variation in the sophistication of the methods utilized but to date very little discussion of the appropriate theoretical framework to guide the design and evaluation of these models. In this paper, we argue that recognizing mapping models as a form of indirect health state valuation allows the use of the framework described by Dolan for the measurement of social preferences over health. Using this framework, we identify substantial concerns with the method for valuing health states that is implicit in indirect utility models (IUMs), the conflation of two sets of respondents' values in such models, and the lack of a structured and statistically reasonable approach to choosing which states to value and how many observations per state to require in the estimation dataset. We also identify additional statistical challenges associated with clustering and censoring in the datasets for IUMs, additional to those attributable to the descriptive systems, and a potentially significant problem with the systematic understatement of uncertainty in predictions from IUMs. Whilst recognizing that IUMs appear to meet the needs of reimbursement organizations that use quality-adjusted life years in their appraisal processes, we argue that current proposed quality standards are inadequate and that IUMs are neither robust nor appropriate mechanisms for estimating utilities for use in cost-effectiveness analyses.