The present article provides a brief historical background on the development of utility measurement and cost-utility analysis in healthcare. It then outlines a number of research ideas in this field that the author never got to. The first idea is extremely fundamental. Why is health economics the only application of economics that does not use the discipline of economics? And, more importantly, what discipline should it use? Research ideas are discussed to investigate precisely the underlying theory and axiom systems of both Paretian welfare economics and the decision-theoretical utility approach. Can the two approaches be integrated or modified in some appropriate way so that they better reflect the needs of the health field? The investigation is described both for the individual and societal levels. Constructing a 'Robinson Crusoe' society of only a few individuals with different health needs, preferences and willingness to pay is suggested as a method for gaining insight into the problem. The second idea concerns the interval property of utilities and, therefore, QALYs. It specifically concerns the important requirement that changes of equal magnitude anywhere on the utility scale, or alternatively on the QALY scale, should be equally desirable. Unfortunately, one of the original restrictions on utility theory states that such comparisons are not permitted by the theory. It is shown, in an important new finding, that while this restriction applies in a world of certainty, it does not in a world of uncertainty, such as healthcare. Further research is suggested to investigate this property under both certainty and uncertainty. Other research ideas that are described include: the development of a precise axiomatic basis for the time trade-off method; the investigation of chaining as a method of preference measurement with the standard gamble or time trade-off; the development and training of a representative panel of the general public to improve the completeness, coherence and consistency of measured preferences; and the investigation, using a model of a very small society, of the conflict between the patient perspective and the societal perspective regarding preferences. Finally, it is suggested that an important area of research, which the author never got to, would be to work closely with specific decision makers on specific decision problems, to help them formulate the problem, provide useful analyses, and to publish these as case studies to give the field a better understanding of the problems and the needs of decision makers.