Which dictatorial domains are superdictatorial? A complete characterization for the Gibbard-Satterthwaite impossibility

A γ-dictatorial domain is one over which the Gibbard-Satterthwaite impossibility can be proven. A γ-dictatorial domain whose superdomains are all γ-dictatorial is qualified to be γ-superdictatorial. We provide a complete characterization of γ-superdictatorial product domains.