On the satisfaction function of random utility models: A theoretical review with new developments in weibit-based choice models

This study presents a theoretical review of the satisfaction function, the expected maximum utility or minimum disutility of travel choices, which plays an important role in the random utility theory and has wide applications in transportation system analyses. New developments in the satisfaction function of the recently developed weibit-based multiplicative random utility models are discussed and compared with the extensively studied logsum-type satisfaction function derived from logit-based models. A characterization of weibit-based choice probabilities is established based on the weibit-based satisfaction function, which is shown to be a multiplicative analogue of the well-known relationship between logit-based choice probabilities and logsum-type satisfaction functions. A comparison with the conventional logit-based satisfaction function is made, from which we show that the weibit-based satisfaction function is inherently more appropriate for reflecting the percentage variation in disutility. Furthermore, potential applications of the weibit-based satisfaction function are illustrated, including weibit-based choice probability generation, utility-based accessibility measurement, and accessibility-based vulnerability analysis.