Range-Fixed Trade-Off Method: A Preference Elicitation Approach Considering the Dependence of Probability Weighting on Outcome Range

Among existing preference elicitation methods, the trade-off method offers an advantage over others in mitigating the influence of probability weighting on preferences, as it does not require assuming a specific form for the probability weighting function. However, when accounting for the dependence of probability weighting on the choice-set outcome range (CSOR), the conventional trade-off method may lead to improper elicitation of preferences due to its inability to control the CSOR. In order to concurrently circumvent the impacts of the CSOR and probability weighting on preferences in the elicitation procedure, we introduce the Range-Fixed Trade-off Method (RFTM) and provide its full derivation and concrete implementation steps under the framework of rank-dependent utility theory (RDU). The RFTM not only retains the advantages of the conventional trade-off method but also evades the effects of the CSOR on preferences by fixing the CSOR. The results of empirical investigations into the efficacy of RFTM indicate that, compared to the existing trade-off method, utility functions derived from RFTM exhibit a lower degree of risk aversion. This result is compatible with existing experimental observations and conclusions, thus implying that RFTM can effectively elicit individual preferences, thereby preventing or mitigating the bias in preferences arising from CSOR variations in the conventional trade-off approach. Furthermore, the experimental results demonstrate that the probability weighting function remains nonlinear even within a fixed CSOR. This indicates that, under the premise of preferences depending on the CSOR, non-expected utility theories still hold promising development prospects in the future. In summary, RFTM not only provides a more effective and reliable approach for preference elicitation but also makes it feasible to study the impact of changes in the CSOR on preferences, thereby providing methodological support for the future development of CSOR-dependent non-expected utility theories.