The Modified Ball-Hollingsworth Voting Algorithm
Mathematics Department, University of Georgia

We begin with a nomination round. In the first and subsequent voting rounds, one can vote for a "live nominee" or one can vote "abstain". The definition of "live nominee for the nth voting round" is as follows: when n = 1, any nominee (from the nomination round); when n > 1, a live nominee from the previous voting round who has received at least n votes on that round and who was not the unique low vote getter (among live nominees) on that round. The voting rounds continue until either: one candidate receives a majority (of votes cast, or votes eligible to be cast, depending on circumstances), in which case that candidate wins; or "abstain" wins a majority of the votes cast, in which case none of the nominees from this round wins. If there are still positions to be filled, then we begin again with another nomination round.