assessing stochastic dominance?

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According to wikipedia and other scattered software documentation Kruskal Wallis tests assess "stochastic dominance". But which type of stochastic dominance from those discussed here? The original paper cited in that article doesn't even mention "dominance". Nor does Dunn's much-cited 1964 paper. A stata function documentations mention that it tests dominance "that is, the probability that a randomly drawn observation from one group will be greater than a randomly drawn observation from another." https://journals.sagepub.com/doi/pdf/10.1177/1536867X1501500117 . How does that relate to formal stochastic dominance, e.g. from decision theory here. Can someone help clarifying what approaches there are to assess stochastic dominance (properly-defined) and particulary how and why are they related to Kruskal Wallis type approaches. Or even just a reference which is clear. Many thanks for the pointers!

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