Which Condorcet tie breaker

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Which Condorcet tie breaker

Craig Carey-2
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

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.