Final answer:
The statement is true; majority rule can result in an undecided outcome when there are multiple choices due to the Condorcet paradox, which indicates the cyclic nature of group preferences leading to no clear majority for any option.
Step-by-step explanation:
The statement is true: majority rule can fail to produce a single preferred outcome when there are more than two choices. This is known as the Condorcet paradox in social choice theory, which demonstrates that majority preferences can become cyclic and thus not transitive, leading to no clear winner in a vote when there are three or more options. The paradox arises because individual preferences between options are not necessarily rational when combined collectively; thus, collective preference can cycle with no option being the overall winner.
For instance, in a scenario with three choices (A, B, and C), a majority might prefer A over B, B over C, and yet C over A, creating a cycle without a clear majority for any single option. This demonstrates the complexity that more choices can introduce, making decisions more difficult. This principle is often highlighted in real-world situations such as elections, group decision-making, and even consumer choice where the presence of numerous alternatives could mislead consumers or leave them uncertain about having selected the best available option.