Three-Way Election and Amy's Proposed Runoff

Amy, Bob, and Kathy are candidates in an election.

The first-choice vote finishes in a three-way tie.

To try to break the tie, the voters' second choices are counted, but the second-choice vote also finishes in a three-way tie.

Amy proposes the following procedure:

1. Bob and Kathy first face one another in a head-to-head election.
2. The winner of that election then faces Amy in a final head-to-head election.

Assume the number of voters is odd, so no head-to-head election can tie.

Assume every voter has a strict ranking of all three candidates and votes in each head-to-head election according to that ranking.

Bob says this procedure is unfair because it favors Amy over both Bob and Kathy.

Subproblem A

Is Bob right?

Subproblem B

Given the two tie conditions, can any candidate beat both of the other candidates head-to-head (a non-cyclic outcome)?

Subproblem C

Who wins under Amy's procedure if the pairwise preferences form a cycle?

For your submitted answer, choose the statement that best answers Subproblem A.