A note on “Re-examining the law of iterated expectations for Choquet decision makers”

This note completes the main result of Zimper (Theory and decision, doi:<ExternalRef> <RefSource>10.1007/s11238-010-9221-8</RefSource> <RefTarget Address="10.1007/s11238-010-9221-8" TargetType="DOI"/> </ExternalRef>, <CitationRef CitationID="CR7">2010</CitationRef>), by showing that additional conditions are needed in order the law of iterated expectations to hold true for Choquet decision makers. Due to the comonotonic additivity of Choquet expectations, the equation E[f, ν(dω)]=E[E[f(ω <Subscript> i, j </Subscript>), ν(A <Subscript> i, j </Subscript>|A <Subscript> i </Subscript>)], ν(A <Subscript> i </Subscript>)], is valid only when the act f is comonotonic with its dynamic form, that we name “conditional certainty equivalent act”. Copyright Springer Science+Business Media New York 2013