An Enhanced Approach to the Random Utility Maximization Model: Incorporating Relative Utility Differences Among Alternatives

This study proposes the Random Combined Utility Maximization (RCM) model, a novel utility framework for transportation choice that integrates independent utility with relative utility comparisons on a consistent scale. The RCM model retains the behavioral foundation of random utility maximization while explicitly representing comparison-based decision making across alternatives. The relative utility incorporates the Irrelevance of Statewise Dominated Alternatives (ISDA), implying that comparisons become behaviorally negligible when utility differences are extreme. To operationalize ISDA in a smooth and estimable form, we apply a hyperbolic secant transformation, such that relative utility is primarily generated among alternatives with similar utility levels. This formulation provides a structural refinement that addresses limitations of existing utility specifications without introducing additional explanatory variables. Using multiple transportation choice datasets and a common specification based on time and cost, we benchmark the RCM model against widely used alternatives, including Random Utility Maximization, Random Regret Minimization, and Relative Advantage Maximization. Across all datasets considered, the RCM model delivers the best overall performance in terms of model fit and predictive accuracy. Although the magnitude of improvement varies across datasets, the consistent gains across evaluation criteria indicate that the RCM model captures observed choice behavior more reliably than conventional utility formulations.