This episode's broadcast date of November 7, 1966 nearly coincided with the United States Senate elections of 1966 (Midterms). The election was held the next day, on November 8, 1966, for the United States Senate.
As county clerk Howard might have problems with what offices he could legally run for without a conflict of interest: he might have to resign as county clerk for the duration of his council career, or not draw a salary as councilman, or not even be able to run at all.
Logically Andy could've solved his problem by simply supporting Bee and her candidacy in public, and voting for Howard in private. But without the conflicting situation and personalities there would be no comic story.