Dictatorship in social choice ($f(R)=\mathrm{top}(R_d)$)

A dictatorship always selects the top alternative of one fixed agent $d$. Other agents cannot alter the selection against that agent's preference. This is the social-choice meaning of dictatorship, rather than a political classification.

A dictator is the fixed agent whose top-ranked alternative is always selected by a dictatorship in social choice.