Question

A stockholder named Sue must cast a vote for chair of the board. Sue prefers Mr. Lee to Ms. Doe, Ms. Doe to Mr. James, and Mr. James to Mr. Lee.

(a) Are Sue's preferences consistent with the transitive property? Please explain.
(b) If all three candidates, Mr. Lee, Ms. Doe, and Mr. James are on the ballot at the same time,

            who would Sue vote for? Please explain.

Answer 1

a). Sue's preferences are not consistent with the transitive property.

Because Sue prefers Mr. Lee to Ms. Doe, Ms. Doe to Mr. James and he should have prefered Mr. Lee to Mr. James but he has prefered Mr. James to Mr. Lee. So here transitive property is not satisfied.

b)  If he is voted on in pairs on the ballot , it would depend on which pair was voted on first. For example, if Lee and Doe were paired first, Lee would win the first vote, and James the second.