In fact there is more to the non-dictatorship condition than meets the eye. An Arrovian dictator is just someone whose strict preferences invariably are a subset of the society’s strict preferences, and that by itself doesn’t mean that his preferences form a basis for social preferences, or that the dictator has any power or control over these. Aanund Hylland once made a related point while objecting to the unreflective imposition of D in single profile analyses of social choice: