Final answer:
The statement that majority rule can fail to produce a preferred outcome when there are multiple choices is true, representing a Condorcet paradox where cyclical majorities prevent a clear collective preference.
Step-by-step explanation:
The statement majority rule can fail to produce a single preferred outcome when there are more than two choices is true. This situation is known as a Condorcet paradox or a voting paradox, where a collective preference does not transpire even if each individual has clear preferences, due to cyclical majorities. As an example, consider a scenario where three friends are choosing an activity for their getaway, and each of them ranks the options differently causing a cycle with no clear winner. This illustrates the difficulty in decision-making in groups where preferences are diverse and a number of choices are present.