I don't see how IRV's failure to elect the Condorcet candidate is
necessarily linked to its "non-monotonicity".
There are monotonic (meets mono-raise) methods that fail Condorcet, and
some Condorcet methods that fail mono-raise.
(For information: I think Bucklin would be an example of the former, and
one of the Borda-elimination methods be an example of the latter.)
I think Smith (or Shwartz),IRV is quite a good Condorcet method. It
completely fixes the failure of Condorcet while being more complicated
> (to explain and at least sometimes to count) than plain IRV, and a Mutual
> Dominant Third candidate can't be successfully buried.
But it fails Later-no-Harm and Later-no-Help, is vulnerable to Burying
strategy, fails mono-add-top, and keeps IRV's failure of mono-raise
> and (related) vulnerability to Pushover strategy.
At the risk of taking this thread away from its original topic, I wonder
what you think of Smith,X or Schwartz,X where X is one of the methods
Woodall says he prefers to IRV - namely QTLD, DAC, or DSC.
(Since QLTD is not an elimination method, it would go like this: first
generate a social ordering. Then check if the ones ranked first to last
have a Condorcet winner among themselves. If not, check if the ones
ranked first to (last less one), and so on. As soon as there is a CW
within the subset examined, he wins. Schwartz,QLTD would be the same but
"has a Schwartz set of just one member" instead of "has a CW".)
DAC and DSC only satisfy one of LNHelp/LNHarm, but they're monotonic in
return. According to Woodall, you can't have all of LNHelp, LNHarm, and
monotonicity, so in that respect, it's as good as you're going to get. I
don't know if those set methods are vulnerable to burying, though, or if
they preserve Mutual Dominant Third.
Then again, satisfying one of the LNHs may not matter since combining it
with Condorcet in that manner makes the combination fail both LNHs.
Combining a method that satisfies LNHarm with CDTT gives something that
still satisfies LNHarm, but the result fails Plurality, and that's not
good either... and the Condorcet method of Simmons (what we might call
"First preference Copeland") resists burial very well, but it isn't
cloneproof.
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