A Functional Model for the Integration of Gains and Losses under Risk: Implications for the Measurement of Subjective Value

In order to be treated quantitatively, subjective gains and losses (utilities/disutilities) must be psychologically measured. If legitimate comparisons are sought between them, measurement must be at least interval level, with a common unit. If comparisons of absolute magnitudes across gains and losses are further sought, as in standard definitions of loss aversion, a common known zero must be added to the common unit requirement. These measurement issues are typically glossed over in complex models of decision under risk. This paper illustrates how Functional Measurement (FM) affords ways of addressing them, given some conditions. It establishes a relative ratio model for the integration of gains and losses in a mixed gamble situation with independent outcome probabilities. It subsequently documents how this model yields functional estimates of gains and losses on a common unit scale with a known zero. The psychological significance of the found integration model is discussed, and some of its implications for measurement further explored across two studies.