Final answer:
It is not always unethical to remain silent with a relevant idea in a group discussion, as ethics depend on the context. True, majority rule can indeed fail to produce a preferred outcome with more than two choices, a situation known as the Condorcet Paradox.
Step-by-step explanation:
The statement, "Is it unethical to remain silent in a group discussion when you have a relevant idea that has not been mentioned?" can be approached from various ethical frameworks, and under some circumstances may be considered true. However, it's not an absolute ethical mandate to always voice every relevant idea in every context. The ethics of such a situation can depend on factors such as the dynamics of the group, the nature of the discussion, personal roles within the group, and the potential impact of the idea.
In response to the second statement, "true or false: Majority rule can fail to produce a single preferred outcome when there are more than two choices," the answer is true. This phenomenon is known as the Condorcet Paradox, where a collective preference does not always emerge through majority rule when three or more options are available. It illustrates situations in which the aggregation of individual preferences into a collective decision can lead to cycles and inconsistencies, ultimately not resulting in a clear majority winner.