split (one's) ticket
To vote for candidates from more than one political party for different roles in public office. It has become increasingly uncommon for voters to split their ticket by voting for candidates from both parties.
split ticket
A ballot cast for candidates of more than one party, as in I'm registered as an Independent, and indeed I usually vote a split ticket. This idiom uses ticket in the sense of "a list of nominees for office," a usage dating from the late 1700s. Also see straight ticket.