The object of this note is to generalize a result of Dummet and Farquharson [3] on the existence of a choice set, i.e., the existence of an alternative socially considered to be "best" under a system of majority voting. In the first section the motivation of the exercise is explained and the relevance of the problem is discussed. In the second, the generalization is stated in the shape of a theorem and is proved. In the third, some observations are made on the nature of the theorem and its relation to conditions of transitivity of majority decision.