The responsibility gap is a set of outcomes of a collective decision-making mechanism in which no single agent is individually responsible. In general, when designing a decision-making process, it is desirable to minimise the gap. The paper studies the class of mechanisms for which the gap is empty and proposes a concept of an elected dictatorship. It shows that, in a perfect information setting, the gap is empty if and only if the mechanism is an elected dictatorship. It also proves that in an imperfect information setting, the class of gap-free mechanisms is positioned strictly between two variations of the class of elected dictatorships.