Determining one-dimensional utility functions for each objective in multiattribute utility theory (MAUT) requires substantial time and cognitive effort from decision makers. They must account for decreasing or increasing marginal utility as well as their individual risk attitudes, often resulting in nonlinear utility functions. This assessment process is prone to errors and distortions.
In this study, we analyze the extent to which a linear transformation of one-dimensional utility functions compromises decision quality. Specifically, we examine three aspects: the use of (non)linear utility functions, their impact on the ranking of alternatives, and the stability of the best alternatives depending on utility differences under the assumption of linearity.
Our analysis is based on 2,536 carefully modeled personal decisions conducted by students using the decision support tool Entscheidungsnavi. The results show that 95.9% of participants used at least one nonlinear utility function, and 76.4% of all objectives were evaluated nonlinearly. Simplifying preference-accurate utility functions through linearization led to a rank reversal of the best alternative in 15.5% of the decisions. The set of the top three alternatives changed in 14% of the cases. However, in 98.8% of the decisions, the best alternative remained within the top three under the assumption of linear utility functions.
Based on these findings, we recommend determining utility functions as preference-accurately as possible, including nonlinearities, especially for important decisions. However, no rank reversal of the best alternative was observed when the absolute utility difference between the best and second-best alternative exceeded 0.27 under linearity. In such cases, assuming linear utility functions can be a useful simplification to save time and effort.
Tönsfeuerborn, Mendy; von Nitzsch, Rüdiger; Siebert, Johannes U. “Do Non-Linear Utility Functions Matter? Analyzing the Impact of Non-Linear Utility Functions on the Final Ranking with the Entscheidungsnavi”, Decision Analysis, 23(1), 46–64. https://doi.org/10.1287/deca.2024.0317