I agree with Nick Welsh that the current method of electing the mayor is flawed. He suggested a run-off election.
I suggest a ranked voting system. Each voter would select two or three candidates and list them as first, second, or third choice. First choice gets 3 points, second gets 2 and third gets 1. The person with the most points at the end is elected.
This will take less elapsed time and cost a lot less money. I think it accomplishes the same thing.