Final answer:
The statement is true, majority rule can fail to produce a single preferred outcome when there are more than two choices, due to the possibility of cyclical preferences as shown in the Condorcet paradox.
Step-by-step explanation:
The statement that majority rule can fail to produce a single preferred outcome when there are more than two choices is true. This situation is known as the Condorcet paradox or voting paradox, where collective preferences can be cyclical even if the individual preferences are not. This can occur in a scenario where three options, A, B, and C, are on offer, and different subsets of the group prefer each option in a pairwise comparison (A > B, B > C, C > A), making it impossible to determine a clear winner through simple majority votes. This leads to the difficulty of reaching a group decision, as preferences can cycle without a conclusive outcome.
For example, concerning the weekend getaway choices for Anastasia, Emma, and Greta, each with their preferred activities, it's possible that mountain biking may be preferred over canoeing, canoeing may be preferred over the beach, and yet the beach might be preferred over mountain biking when these are put to a vote. This clearly demonstrates the lack of a consistent group preference and hence the problem with reaching a decision through majority rule.