Ostracize comes from a Greek word meaning “voting tablet,” and the ritual of “blackballing” someone was a democratic process of elimination.
A group decided if a suspect member would be banished or allowed to stay by dropping black and white balls into a ballot box.
The word ballot means “little ball.”
If the majority were black, the candidate lost and was said to have been blackballed.
When someone has been banished or ostracized by a group we say they’ve been “blackballed”.