A decision maker is characterized by two binary relations. The first reflects decisions that are rational in an “objective” sense: the decision maker can convince others that she is right in making them. The second relation models decisions that are rational in a “subjective” sense: the...

As in Gilboa, Maccheroni, Marinacci, and Schmeidler \cite{GMMS}, we consider a decision maker characterized by two binary relations: $\succsim^{\ast}$ and $\succsim^{{\small \wedge}}$. The first binary relation is a Bewley preference. It\ models the rankings for which the decision maker is sure....