Intransitive indifference with direction-dependent sensitivity

Abstract Intransitive indifference is a well-documented phenomenon in which the decision maker is forced to choose between alternatives with a subtle difference. In this paper, we establish a general model that extends the semiorder/interval order approach (e.g., Fishburn in J Math Psychol 7: 144–149, 1970a. https://doi.org/10.1016/0022-2496(70)90062-3 ; Luce in Econometrica 24: 178–191, 1956. https://doi.org/10.2307/1905751 ) by adopting the set of lotteries as the domain of choice and a direction-dependent just-noticeable difference function. The model can distinguish two classes of intransitive indifference, that is, imperfect discrimination , which is relevant to previous studies on intransitive indifference, and uncertainty about tastes , which is relevant to incomplete preferences. The main theorem axiomatizes the essentially unique expected utility with direction-dependent sensitivity representation. The key axioms for this characterization are irresolute independence , wherein mixing alternatives with another alternative may change a strict preference to indifference while preserving indifference, and strict preference convexity , which derives the convexity of strict upper and lower contour sets. We also obtain two special cases of our model—one-directional and categorical sensitivity—which highlight the two classes of intransitive indifference, and discuss a possible change in the domain of choice to a vector space.