Final answer:
The statement is true: majority rule can fail to produce a single preferred outcome when there are three or more choices, a situation described by the Condorcet Paradox, where no clear winner emerges due to cyclic preferences.
Step-by-step explanation:
True: Majority rule can indeed fail to produce a single preferred outcome when there are more than two choices. This phenomenon is known as the Condorcet Paradox, which occurs in voting systems when collective preferences can be cyclic (non-transitive), even if the individual preferences within the group are transitive.
In a scenario with three or more options, it's possible that no single option will receive a majority of the votes, leading to an outcome where there is no clear winner based on majority preference. Voters may prefer option A over option B, option B over option C, and yet option C over option A, creating a cycle with no clear majority winner.