Summary: In Arrovian social choice theory assuming the independence of irrelevant alternatives, Y. Murakami [Logic and social choice. New York, NY: Dover Publications (1968)] proved two theorems about complete and transitive collective choice rules satisfying strict non-imposition (citizens’ sovereignty), one being a dichotomy theorem about Paretian or anti-Paretian rules and the other a dictator-or-inverse-dictator impossibility theorem without the Pareto principle. It has been claimed in the later literature that a theorem of M. Malawski and L. Zhou [Soc. Choice Welfare 11, No. 2, 103–107 (1994; Zbl 0803.90007)] is a generalization of Murakami’s dichotomy theorem and that R. Wilson’s impossibility theorem [“Social choice theory without the Pareto principle”, J. Econ. Theory 5, No. 3, 478–486 (1972; doi:10.1016/0022-0531(72)90051-8)] is stronger than Murakami’s impossibility theorem, both by virtue of replacing Murakami’s assumption of strict non-imposition with the assumptions of non-imposition and non-nullness. In this note, we first point out that these claims are incorrect: non-imposition and non-nullness are together equivalent to strict non-imposition for all transitive collective choice rules. We then generalize Murakami’s dichotomy and impossibility theorems to the setting of incomplete social preference. We prove that if one drops completeness from Murakami’s assumptions, his remaining assumptions imply (i) that a collective choice rule is either Paretian, anti-Paretian, or dis-Paretian (unanimous individual preference implies noncomparability) and (ii) that adding proposed constraints on noncomparability, such as the regularity axiom of K. Eliaz and E. A. Ok [Games Econ. Behav. 56, No. 1, 61–86 (2006; Zbl 1151.91409)], restores Murakami’s dictator-or-inverse-dictator result.