http://en.wikipedia.org/wiki/Alternative_voteIt's even more like the way the Conservative Party in the UK elects its leader:
If more than two candidates stand, then MPs first hold a series of ballots to reduce the number to two. On each round, the candidate with the fewest votes is eliminated. (If two or more candidates tie for last place, as happened in the 2001 contest, then the ballot is repeated, and if the tie remains, all bottom-placed candidates are eliminated.) Candidates may also withdraw between rounds (this also happened in the 2001 contest).
The series of ballots by MPs continues until there are only two candidates remaining.
sourceYou want people to phone in to say "I think X is the worst - dump them". That might be acceptable for a program like "Big Brother", where it's all about disliking people anyway, but in theory this is meant to be finding a good singer - so they ask people to vote for people they like. By making people vote positively rather than negatively, they hope that the person left will be liked - and thus will actually sell records. If they've been asking people to think "which of these is bad" for several weeks, people will think negatively about the winner.