How about this:
In the event of a tie, a new referendum begins with the countdown of 1 day. This new referendum is only between those nobles that were tied, and all nobles that voted for the two that tied originally automatically begin the referendum with their votes cast in favor of that candidate. Anyone can change their vote during the course of the referendum. This repeats until a tie is broken. (Purposefully possible for it to continue for a long time, because if a real stalemate occurs, the amount of character interaction will increase dramatically as the two candidates try and break the stalemate in their favor. Meanwhile, the realm falls into anarchy because no ruler is chosen, and so they can say that the other is hurting the realm interests by not withdrawing their candidacy)
