Characterizing Fractional-Degree Stochastic Dominance by Invariance Laws

Classic notions of stochastic dominance have integer degrees. Recent studies have imposed distinct preference conditions for refinement, resulting in a range of fractional-degree stochastic dominance rules. However, preference conditions are generally not mutually exclusive, making it challenging to establish a strict criterion for rule selection. To address this, we establish fractional-degree stochastic dominance rules based exclusively on invariance laws under a general condition that is applicable to all intermediate utility sets. This approach enables practitioners to rely solely on the mutual compatibility and exclusivity of invariance properties to compare and select the appropriate rules. We illustrate the usefulness of our approach through an application to the problem of mutual fund selection. Funding: T. Mao is supported by the National Natural Science Foundation of China [Grants 12371476 and 71921001]. R. Wang is supported by the Natural Sciences and Engineering Research Council of Canada [Grants CRC-2022-00141 and RGPIN-2024-03728]. L. Zhao is supported by the National Natural Science Foundation of China [Grants 72125003 and 72131003].