In response to a quite plausible, poltical spectrum-based 5 candidate example of IRV performing poorly , you stated :
"I recognise the problem very well, but what is the practical solution? I am very sympathetic to Condorcet, but there must be serious questions about the public acceptability of some of the results it is likely to produce."
This has prompted me to unveil my idea for Improved IRV (an IRV-Condorcet hybrid), which I think you might like.
At each step where IRV eliminates the candidate with the lowest tally of votes, this method instead eliminates, from the set of candidates whose vote tallies are below average and also not above 25%, the Condorcet loser . If there is a circular tie for this spot all the tied candidates are eliminated.
Repeats of this step may result in the field being condensed to three candidates, each with more than 25% (of the votes left in play). In that event the Condorcet winner of those three wins.
The big weakness of IRV lies in how it decides which candidate to eliminate. To me the normal IRV rule is too arbitary. The figure I use of "above 25%" represents a majority of an "STV quota", and is therefore almost not arbitary.
I think that this proposed method should appeal to those who like IRV and are repelled by the pure-Condorcet possibility that a candidate with almost a majority of first-preference votes could lose to a candidate who gets no first-preference votes.
The example I referred to at the top: 10: FR > R > C > L > FL 10: R > FR > C > L > FL 15: R > C > FR > L > FL 16: C > R > L > FR > FL 15: C > L > R > FL > FR 13: L > C > FL > R > FR 11: L > FL > C > R > FR 10: FL > L > C > R > FR
With 5 candidates, the average number of votes is 20. So FL and FR with 10 votes each make up the initial "set of candidates whose vote tallies are below average and also not above 25%" , so they runoff : FR d. FL 51-49, so FL is eliminated (and FL's 10 votes are transferred to L.)
New tallies are L: 34 C: 31 R: 25 FR: 10
With 4 candidates, average number of votes is 25%, so FR is only candidate for elimination so is eliminated.(and FR's 10 votes are transferred to R.)
New tallies are R: 35 L: 34 C: 31
All tallies are above 25%, so no more candidates for elimination.
C pair-wise beats L 66-34, and C pairwise beats R 65-35 ; so C wins.
Chris Benham
---- Election-methods mailing list - see http://electorama.com/em for list info
