A matrix (a table of rows and columns for nonmath majors) results from the
various head to head pairings of candidates in the Condorcet method. The question is what part of the matrix should be looked at to resolve circular ties (or whether additional matrices should be made) when there is not any candidate who beats each other candidate head to head in the first round. In a circular tie situation, the subject "Which Condorcet tie breaker?" can be rephrased as "The first choice votes cast for which losing candidates should get transferred?" (to produce the single winner) or "Which voters should have their votes transferred (to produce the single winner) ?". One answer is the least absolute vote difference (least beaten) among the worst defeats of the candidates involved in the tie (which assumes that all candidates except the two in each pairing need to lose to produce a winner). Another answer is the candidate with fewest first choice votes (or first choice votes plus transferred votes) in repeated cycles of dropping such losing candidate and redoing (repeat, redoing) the Condorcet head to head math. The logic/ standard/ test is that such a losing candidate had his/her chance to win in all head to head pairings with the other candidates in the circular tie. Every other candidate has more voters who presumably want to stay with such candidate as their first choice as long as possible. Somebody must lose. Should it not be the candidate in the circular tie with the fewest first choice votes (or first choice votes plus transferred votes in second, third, etc. tie breaker rounds) (i.e. the smallest minority in each round) ? That is, should not such fewest number of voters be the ones to have their votes transferred in a circular tie situation ? Note- It is possible to add to the complexity of the ballot by having 2 or more candidates to indicate that they agree to be eliminated by the voters in a certain way (with advance notice to the voters) (Case 1- such candidates would have a mini-election between each other with one of them going against the other candidates) (Case 2- if such 2 or more candidates were in a tie with each other or 1 or more other candidates) Note- It is possible to add to the complexity of the ballot by having each voter to indicate when he/she wants his/her vote transferred in cases of circular ties (i.e. immediately, when the first choice candidate has votes below a certain percentage of the total votes, etc.) Some of the tie breaker difficulty arises from the repeated use of 3 candidate examples when there most likely will be many more than 3 candidates in a single winner election for major public offices (President, Governor, Mayor, etc.) (noting that the recent 3 apples plus chocolate example caused some rethinking about changing plain Condorcet regarding majority disapproved candidates who are defeated head to head by each other candidate). A Condorcet tie breaker must be simple enough for John/Mary Q. Voter to understand (besides much less intelligent politicians and judges). If a different result (i.e. a different single winner) occurs if the voters change their rank orders, then so what ? Different starting conditions almost always produce different results. |
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