Increase the number of competitors. You can have up to 30 poll options at once and if you enable multiple voting, we could get through a large number of votes with only a single thread per round. For example, if there are 16 competitors, simply make a poll with 16 results and multi-voting enabled. Then make the poll options as follows:

1) A v B - A wins
2) A v B - B wins
3) C v D - C wins
4) C v D - D wins
etc.

Each person can then vote once in each 'pair'. If anyone votes for both competitors in a certain matchup for whatever reason, just don't count their vote.

I like the idea of matching up people from the same time frames, at least in early battles. If you've got a larger pool of competitors, you could give each 'division' a specific era. For instance, in a contest with 16 generals, you could have 4 divisions of 4 generals each, with each group of 4 being from similar time periods and/or military bacgrounds.