This paper axiomatizes models of second-order ambiguous beliefs in the original domain of preferences of Anscombe and Aumann (Ann Math Stat 34:199–205, <CitationRef CitationID="CR2">1963</CitationRef>) by weakening the first-stage independence postulate. The models we propose include the second-order subjective expected utility (SOSEU)...</citationref>

<Para ID="Par1">Recently, there has been some interest on models of incomplete preferences under uncertainty that allow for incompleteness due the multiplicity of tastes and beliefs. In particular, Galaabaatar and Karni (Econometrica 81(1):255–284, <CitationRef CitationID="CR6">2013</CitationRef>) work with a strict partial order and present...</citationref></para>

We develop the ordinal theory of (semi)continuous multi-utility representation for incomplete preference relations. We investigate the cases in which the representing sets of utility functions are either arbitrary or finite, and those cases in which the maps contained in these sets are required...