Estimation of cardinal utility based on a nonlinear theory

Empirical studies have demonstrated that cardinal utility functions assessed via gamble-based methods are often incoherent because of the probability and certainty effects. These effects are caused by apparent risk attitudes different from those admissible within the linear (expected) utility theory. The incoherences can also be accentuated by the effects of chaining and serial positioning of responses. To filter out these effects and obtain an unbiased measurement of the strength of preference, and a simultaneous measurement of risk attitude, we devised the independent-gamble, nonlinear-inference (IGNI) method: the utility function of outcomes and the risk function of probabilities are estimated jointly from assessed certainty equivalents of independent gambles by using a nonlinear utility theory for inference. The method contrasts with all popular utility assessment techniques in that it estimates a cardinal function in the two-dimensional space of outcomes and probabilities. Hence, it allows us to obtain novel insights into the nature of utility functions and the probability effect. Both are illustrated by empirical results for fifty-four subjects.