Final answer:
Majority rule can fail to produce a single preferred option when there are more than two choices due to the possibility of inconsistent collective preferences and the existence of cyclical majorities, as explained by Condorcet's paradox.
Step-by-step explanation:
Majority rule can indeed fail to produce a single preferred outcome when there are more than two choices. This situation is often related to the voting paradox where the collective preferences of an electorate can become inconsistent when three or more options are available, resulting from cyclical majorities where no option is the most preferred when all pairs are considered. This can be further explained by the concept of Condorcet's paradox, which illustrates how collective preferences can be non-transitive, even if individual preferences within the group are transitive.