A distribution of voters is symmetric and unimodal, and the first two candidates have chosen different positions, A and B, that are equidistant from the median. A is below the median and B is above the median, and two thirds of the voters lie between A and B. To win the election, a third candidate should take a position C that lies:

Question

Quizplus · Accepted Answer

A third candidate would want to take a position that captures the remaining one third of the voters. Since we know that two thirds of the voters lie between A and B, it would make sense for the third candidate to position themselves in that range as well. Choosing a position below A or above B would likely lead to less support and make it harder to win the election. Therefore, the best choice for the third candidate is to take a position between A and B.

A Distribution of Voters Is Symmetric and Unimodal, and the First