Final answer:
The statement is true as majority rule can fail to produce a single preferred outcome in cases where there are more than two options, leading to non-transitive collective preferences despite clear individual preferences.
Step-by-step explanation:
The statement is true: Majority rule can indeed fail to produce a single preferred outcome when there are more than two choices.
This phenomenon occurs due to a situation known as Condorcet's Paradox, where collective preferences can become cyclical and non-transitive despite the individual preferences being clear and transitive. For instance, in an election with three candidates A, B, and C, it's possible for a majority to prefer A over B, B over C, and yet C over A, leading to an inconsistency in determining a clear winner through majority preferences alone.