In this paper, we study asymptotic expansions for distorted probabilities under ambiguity, revisiting the framework and analysis of Izhakian (2020b). We argue that the first order terms in these expansions need to be corrected and provide alternatives. We also revisit later results in this paper on the separation of ambiguity and ambiguity attitudes. We argue that a crucial lemma is flawed implying that Izhakian’s ambiguity measure is not an equivalent way of representing the preferences it is supposed to represent.

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