Only political cards in hand may be traded or given away. Once played the cards stay where they are until finished (voting cards only stay for one vote) or forced to discard (influence card discarded by broken coalition).
Is this stated anywhere in the rules? We have argued that since cards played in front of you count towards your hand limit, they are treated like cards in players' hands, only they are revealed. We therefore play with:
* Yes, you can trade or give away face up influence card.
* But if you do, they must remain face up for the receiving player. (Our interpretation of "where it remains".)