Final answer:
The statement is true. Majority rule can indeed fail to produce a single preferred outcome when there are more than two choices.
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. More specifically, this is known as the 'Condorcet paradox' or 'Condorcet's voting paradox', named after the French mathematician and philosopher Marquis de Condorcet.
This paradox arises from the fact that when there are multiple options, it is possible for no single option to consistently secure a majority of votes when compared pairwise to the other choices. In such cases, the preference of the majority can be inconsistent and lead to different outcomes depending on the specific pairing of choices being considered.
For example, consider a scenario where three options A, B, and C are being voted on. In one pairwise comparison, A might be preferred over B, and in another comparison, B might be preferred over C, and yet in another comparison, C might be preferred over A. This inconsistency can make it impossible to determine a single preferred outcome based on majority rule alone.