Abstract Sequential voting rules and correspondences provide a way for agents to make group decisions when the set of available options has a multi-issue structure. One important question about sequential voting rules (correspondences) is whether they satisfy two crucial criteria, namely neutrality and ef- fificiency. Recently, Benoit and Kornhauser established an important result about seat-by-seat voting rules (which are a special case of sequential voting rules): they proved that if the multi-issue domain satisfifies some properties, then the only seat-by-seat rules being either effificient or neutral are dictatorships. However, there are still some cases not covered by their results, including a very important and interesting case—voting correspondences. In this paper, we extend the impossibility theorems by Benoit and Kornhauser to voting correspondences, and obtain a dichotomy theorem on the existence of effificient or neutral sequential (seat-by-seat) voting rules and correspondences. Therefore, the question of whether sequential (seat-by-seat) voting rules (correspondences) can be effificient or neutral is now completely answered