All of us are smarter than any of us: more on the robustness of the Consensus hierarchy (Part II) Wai-Kau Lo and Vassos Hadzilacos ABSTRACT A \emph{wait-free hierarchy} classifies shared object types according to their strength in supporting wait-free implementations of other types. Such a hierarchy is \emph{robust} if it is not possible to implement types the hierarchy classifies as strong by using only types that it classifies as weak. The Consensus hierarchy is the most closely studied wait-free hierarchy. In \cite{LH96} we proved that the Consensus hierarchy is not robust if nondeterministic types are allowed. This naturally raises the question whether some other wait-free hierarchy is robust. In this paper we show that, if nondeterministic types areallowed, the only robust wait-free hierarchy is the trivial one, which lumps all types into a single level.