the.com/swing vote

means A vote (or voter, or bloc) not firmly committed to either side, whose choice will decide a close election or decision.

from A 20th-century American political coinage, built simply from 'swing' — the sense of swaying back and forth, undecided — plus 'vote.' It grew out of the older idea of a 'swing state' or 'swing district,' places that could tip either way, and the same imagery (a pendulum, a door swinging on its hinge) was extended to the individual voter or justice whose uncommitted ballot could swing the outcome either direction.