After rethinking the problem of Condorcet circular ties, I note that such ties occur because any tiebreaker method using additional rankings beyond the first choice ranking has the potential for strategic voting (i.e. attempted candidate manipulation of such additional rankings depending on the tiebreaker that uses such additional rankings-- a sort of manipulation- tiebreaker method feedback loop). A possible remedy if there is a circular tie would be to ignore the additional rankings. Namely, 1. Do the standard head to head pairings. 2. Drop all candidates who cannot beat or tie any other candidate. 3. If there is a circular tie, then drop the candidate with the lowest number of first choice votes. (Such candidate has had his/her chance to beat the other candidates). 4. Relook at the head to head pairings of the candidates remaining in the circular tie. 5. If the circular tie continues, then move up the rankings of the candidate dropped in step 3 (or step 6). (e.g. a second choice vote becomes a revised first choice vote on a ballot that has the dropped candidate as the first choice candidate). 6. Drop the candidate with the lowest number of revised first choice votes. 7. Repeat steps 4, 5 and 6 as necessary. Relative rankings would remain intact. Moving up the votes in step 5 after a choice is dropped would encourage the making of additional rankings and discourage truncated votes (i.e. a single winner just might end up with a majority of all the votes). As much as it might shock some folks, the above is a combination of the head to head part of Condorcet along with the often attacked Instant Run-off.
