Stochastic dominance is often used to study preference between different distributions of outcomes. In the stochastic dominance literature, distributions of outcomes are often assumed to be known. However, complete distribution information is rarely available in practice. In this paper, we study weighted almost first-degree stochastic dominance (WAFSD) under limited distribution information. In particular, we show that it is possible to determine WAFSD with linear canonical utility based on expected rewards when outcomes are bounded from below. Furthermore, we illustrate how WAFSD based on more general forms of canonical utility functions can be ensured when additional moment information is available. The key insight is that finite distribution moments can be sufficient for revealing clear preferences in practice, despite the fact that finite distribution moments are generally insufficient for ensuring preferences across all utility functions.
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