Is the answer "of ballot box" or "darning sox"? Is it dodging brickbats or receiving bouquets?

Overview

The Women's Political League decides to find a female candidate for mayor and their choice is Kay Gerson who, they figure, will win votes from the men because of her looks. But the town's political boss, Jim Bradley, counters with his own good-looking candidate, Freddy Bleeker, who he thinks will get the women's vote.