Final answer:
True, majority rule can fail to produce a single preferred outcome when there are more than two choices due to vote splitting, which can result in a Condorcet paradox.
Step-by-step explanation:
True: Majority rule can indeed fail to produce a single preferred outcome when there are more than two choices. This situation is often referred to as a Condorcet paradox or vote splitting, where individual preferences may be cyclical and do not yield a clear majority because votes are distributed among three or more options in such a way that no single option obtains the most votes. For example, in a three-candidate race where preferences are divided, no one candidate may receive more than 50% of the vote, leading to a lack of a clear winner when the majority rule is strictly applied.