Wiktionary
balance the ticket
vb. To pick a vice-presidential candidate who represents a different constituency than the presidential candidate.
Usage examples of "balance the ticket".
Of course he would need someone like Burden to balance the ticket.
He'll certainly have to take someone like Clay to balance the ticket, someone who is, well .
The grown-ups in your party weren't about to accept a loony tune like you as nominee, even for what was supposed to be a kamikaze run, without a sane moderate to balance the ticket.