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

This note completes the main result of [Zimper A., (2010) Re-examining the law of iterated expectations for Choquet decision makers. Theory and decision, DOI 10.1007/s11238-010-9221-8], 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; (d!)] = E[E[f(!i;j); (Ai;j jAi)]; (Ai)]; is valid only when the act f is comonotonic with its dynamic form, that we name "conditional certainty equivalent act".