A Multiplicative Model of the Utility of Survival Duration and Health Quality

Survival duration and health quality are fundamentally important aspects of health. A utility model for survival duration and health quality is a model of the subjective value of these attributes. We investigate the hypothesis that the utility (subjective value) of survival duration and health quality is determined by a multiplicative model. According to this model, there are separate subjective scales for the utility of survival duration and health quality. If F ( Y ) equals the utility of surviving Y years, and G ( Q ) equals the utility of living in health state Q , then the multiplicative model proposes that F ( Y ) G ( Q ) equals the utility of surviving Y years in health state Q . This model provides a simple explanation for several intuitively compelling relationships. First, the distinction between better-than-death and worse-than-death health states corresponds to the assignment of positive or negative utilities to different health states. Second, a zero duration of survival removes any reason to prefer one health state over any other, just as multiplying the utility of health quality by zero eliminates differences between the utilities of different health states. Third, the subjective difference between Y years in pain and Y years free from pain increases as Y increases as if the difference in utility between pain and no pain were being multiplied by the utility of surviving Y years. A critical prediction of the multiplicative model is the hypothesis that preferences between gambles for health outcomes satisfy a property called utility independence. After defining this property and explaining how it can be tested in behavioral data, we report an experimental test of whether the health preferences of medical patients satisfy utility independence. Individual analyses revealed that most subjects satisfy utility independence, thereby supporting the multiplicative utility model. Some subjects appear to violate a fundamental assumption of utility theory: They appear to violate the assumption that a single utility scale represents both the ordinal preference relations between certain outcomes and the subjective averaging that underlies the utility of gambles. The violation is inferred from an inconsistency between preferences for multiattribute outcomes when they are viewed as certain outcomes and when they are viewed as the outcomes of gambles.