Chris Benham wrote:
Kristopher,
All Condorcet methods are vulnerable to Burial. Smith,IRV has in
common with IRV but not the other well-known Condorcet methods
that a Mutual Dominant Third winner can't be buried. But like all other
Condorcet methods it is not absolutely invulnerable to Burial like IRV.
37: A>B
31: B>A
32: C>B
B is the CW, but if the A>B voters bury B by changing to A>C then
the Smith,IRV winner changes from B to A.
For the advantage over IRV of the difference between Smith and
Mutual Dominant Third (MDT), we lose Burial Invulnerability and
Later-no-Harm and Later-no-Help and Mono-add-Top.
So I think the argument that Smith,IRV is really much better than the
simpler plain IRV is weak. Likewise the case that Smith,IRV is the
best Condorcet method.
I wouldn't say Smith,IRV is the best Condorcet method, either, but it
may be the closest thing if people are very inclined towards burying
candidates (and we want Condorcet).
"Is it possible to make a monotonic method that's resistant to burial?"
Yes, FPP fills that bill. Other methods have incentives to "bury" only
by truncating, not order-reversing. (According to a definition I'm not
entirely happy with this qualifiies as "burying"). I have in mind the
methods
that met Later-no-Help and not Later-no-Harm, such as Bucklin and
Approval.
It would seem that in order for a method to be completely resistant to
burial (including truncation), it must meet both LNHelp and LNHarm. That
makes sense, because Burial involves altering the position of those
lower down on your ranking to help the candidate that's higher up in
your ranking. However, we know from Woodall that we can't have both
LNHs, mutual majority, and monotonicity, nor can we have LNH* and
Condorcet. Thus a method that's completely resistant would seem to need
to be nonmonotonic or fail mutual majority, and in either case fail
Condorcet.
There is one way out: consider a method that fails LNH* only in such
ways that are not conducive to burial. For instance, it may be that if
you vote A>B>C, then moving B last would cause C to win (instead of B).
This is like Warren's claims about Black (Condorcet else Borda). You
gave an example where burial works in Black, so Black is somewhat
susceptible to burial, but it's theoretically possible there may be a
method that works this way.
There's also another caveat in the other direction: consider a method
with compulsory full ranking and a fixed number of candidates. It may be
susceptible to burial (order reversal) even if LNH* no longer make any
sense.
-
FPTP works, but really just because you can't bury. This can technically
be "fixed" by treating FPTP as a ranked voting method where only your
first preference matters. Still, it's a bit of a trick, so let me try
something a bit more detailed. I wonder if there's a method that meets
Condorcet and Dominant Mutual * burial resistance (the lesser the
fraction the better), and is also monotonic. Both Smith,IRV and "first
preference Copeland" meet Dominant Mutual Third burial resistance, but
they're both nonmonotonic. While I'm wishing, having it summable would
also be nice.
Or, for that matter, do we have a method that meets DMTBR, mutual
majority, and monotonicity? Perhaps DAC (since it meets LNHelp), but it
has other problems, and it doesn't meet plain DMT.
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