Specifically, if the vote card had a cost, when is it payed? Before
the referendum or after? More importantly, before Voter Captivation or
after?
Political action cards are a type of action cards.
Action cards' costs are paid when the action succeeds (reaches resolution
unblocked) but before resolution (you have to pay the cost in order to resolve
the action's effect).
For political actions, this means the cost is paid before conduction the
referendum (before setting terms, before casting votes, and long before Voter
Captivation).