please help solve this, industrial engineering problem thank you

7. (Total: 10 points) Consider the following mechanism for voting with 3 candidates. In the first . second round, the winner of the first round's vote competes with the remaining third candidate in a random vote ie, instead of holding another majority vote we randomly pick a winner from the two candidates in the second round, Is this mechanism IC? If yes, give a proof. If not, justify with an example