Intransitive indifference with direction-dependent sensitivity

Abstract

Much of the literature has argued that intransitive indifference is more likely to occur when alternatives have conflicting criteria than when one alternative dominates the other. To study such a phenomenon, we first axiomatize the essentially unique expected utility with direction-dependent sensitivity (EUDS) representation on the set of lotteries which extend the classic models of imperfect discrimination (e.g., Fishburn, 1970a; Luce, 1956) to enable a direction-dependent just-noticeable difference function. The key axioms in this characterization are irresolute independence, wherein mixing alternatives with another may (or may not) alter a strict preference for indifference while preserving indifference, and strict preference convexity, which obtains the convexity of strict upper and lower contour sets. Thereafter, we indicate that intransitive indifference in EUDS can be divided into that caused by imperfect discrimination (Fishburn, 1970a; Luce, 1956) and that caused by uncertainty about tastes (Dubra et al., 2004) by considering the transitive core (Nishimura, 2018) of EUDS. We also obtain two special cases of our model, i.e., one-directional and categorical sensitivity.