Erratum: Corrigendum to “The impossibility of extending random dictatorship to weak preferences” (Economics Letters (2016) 141 (44–47))

The present note corrects an error in the proof of Theorem 1 of Brandl et al. (2016). The proof for the case of [display formula] and [display formula] and the reduction of the case [display formula] to the case [display formula] are correct. However, the reduction of the case [display formula] to the case [display formula] is incorrect, since [display formula] as constructed in this step is not necessarily an extension of [display formula]. To fix this, let [display formula] be defined whenever for each agent, the set of his most-preferred alternatives either is a singleton or contains all alternatives that are uniquely most-preferred by some other agent. Additionally we require that at least one agent has a unique most-preferred alternative. The lottery returned by [display formula] is obtained by choosing an agent with a unique most-preferred alternative uniformly at random and returning that agent's most-preferred alternative. With this definition of [display formula] the proof of Theorem 1 is correct. All other statements are unaffected. The authors thank Manuel Eberl for bringing this mistake to their attention.