How will tie votes work? Will there be some kind of leader that can break ties like in a regular mafia game?
By default a tie means that nobody dies or no decision is made.
A majority is required, once that majority is reached the discussion is automatically over and that candidate wins. So for example today, once someone receives seven votes, that person is thrown out. If nobody reaches seven votes, nobody is thrown out.
Once the decision to move forward receives the majority of votes, the decision is made. If it doesn't, the party doesn't move.
Note that every answer I give has the exception: Unless someone has a role that makes it otherwise.