Question

True or false: Majority rule can fail to produce a single preferred outcome when there are more than two choices.

Short answer

True. Majority rule can fail to produce a single preferred outcome when there are more than two choices, as no single choice may have a majority of votes. Runoff elections can sometimes provide a solution, but the initial majority rule process can still fail to achieve a clear outcome.

Step-by-step solution

Understand Majority Rule

Majority rule is a decision-making process in which the option with more than half of the total votes becomes the preferred outcome. It is often used in democratic systems, as it is simple to understand and implement.

Consider the Scenario with More Than Two Choices

When there are more than two choices, it is possible that no single choice will receive more than half of the total votes. In this case, the majority rule may either fail to produce a single preferred outcome or require additional steps to resolve the decision.

Analyze an Example of Majority Rule Failure

Let's analyze a simple example with three choices (A, B, and C) and five voters. Each voter must choose only one option, and the votes are as follows: 1. A: 2 votes 2. B: 2 votes 3. C: 1 vote In this example, no single choice has a majority (more than half) of the votes. Thus, the majority rule fails to produce a single preferred outcome.

Consider the Role of Runoff Elections

In some cases, the problem of not having a single outcome with a majority vote can be resolved through the use of a runoff election. For example, the two choices with the most votes (A and B in our example) can enter a second round of voting. Voters would then choose between only A and B, which may result in one of the options receiving a majority vote.

Conclusion

The statement "Majority rule can fail to produce a single preferred outcome when there are more than two choices" is true. Majority rule is not always effective in determining a single preferred outcome in situations where there are more than two choices, as no single choice may have a majority of votes. While runoff elections can sometimes provide a solution, the initial majority rule process still can fail to achieve a clear outcome.