Results were Liberal Democrats 20, Conservative 16 and one other.
Mr Underwood-Frost said that despite winning, he did not think councillors should be elected by the toss of a coin.
"We did ask whether we between ourselves could agree to disagree with the toss of a coin... but the law's the law, and the law needs to be changed in my view.
"Here I am re-selected by a way that I don't think anybody would agree with, but that's the law."