To spoil one's ballot, to spoil one's vote, to spoil one's ballot paper.
"
Since she supported none of the candidates, she spoiled her ballot paper."
Cambridge Dictionary Online.
Members of that religion are required to
spoil their votes in all elections.
In News:
"Some voters say they deliberately spoiled ballot papers to register dissatisfaction with PCC election process."
The Guardian(UK).
"Yes, I have a ballot for the upcoming US presidential election, and I
shall send it. However, it will not be counted, as I shall deliberately
spoil it."
Inquirer Opinion.
"I’m sure we would all wish our police force to become ever more
effective, but asking people to deliberately to
spoil their ballot
papers is not exactly the way to do that. "
Derbyshire Times.
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