Values play a critical part in decision making at both the individual and policy levels. Numerous methodologies for determining the preferences of individuals and groups have been proposed, but agreement has not been reached regarding their scientific adequacy and feasibility. This is the first of a four-part series of papers that analyzes and critiques the state-of-the-art in measuring preferences, particularly the measurement of health-state preferences. In this first paper we discuss the selection of relevant attributes to comprise the health-state descriptions, and the relative merits of three measurement strategies: holistic, explicitly decomposed, and statistically inferred decomposed. The functional measurement approach, a statistically inferred decomposed strategy, is recommended because it simultaneously validates the process by which judges combine attributes, the scale values they assign to health states, and the interval property of the scale.