The correct answer is influence.
Sway means to move slowly backwards and forwards or from side to side. It also means to control or influence a person or a course of action.
The politician could not sway voter opinion means that the voters couldn't be convinced of his ideas and therefore, refused to vote for him.
In politics, this term refers a way of influencing potential voters that are not sure whom to vote for.
To reject means to dismiss as inadequate, to defer means to put off or delete, to question something means to ask questions about somebody or something.
