[EM] candidate withdrawal option and burying

[James Green-Armytage]

Hi folks,

	I've been trying to imagine how the candidate withdrawal option (CWO)
might play out, if added to something like beatpath or ranked pairs in a
large-scale public election. (Briefly, CWO is that any non-winning
candidate can order a post-election re-tally in which they are deleted
from the ballot.)
	One nice thing about CWO Condorcet is that it retains both Condorcet
efficiency and minimal dominant set efficiency; no withdrawal should
change the winner from a minimal dominant set member to a non-member.
Furthermore, I suppose that the withdrawal of a non-minimal-dominant set
candidate shouldn't ever change the result of an election.
	Although CWO may produce a kind of messy aftermath to some sincere
cycles, I'm starting to think that it may help keep the burying strategy
in check to some extent. Here are a few brief supporting arguments for
this notion:

1. The actual candidates involved (assuming that they are humans) may be
better-equipped than any deterministic voting algorithm to judge whether a
burying strategy has in fact been the cause of a particular cycle.
2. Candidates are more likely to withdraw in favor of similar candidates,
which means in effect that defeats among similar candidates are more
likely to be dropped. This effect is somewhat similar to that of the
cardinal pairwise method, and in both cases it means that the more
high-incentive burying strategies are less likely to be successful. (Let's
say A>>B>C voters vote A>C>B in order to cause a false C>B defeat that
overrules a genuine B>A defeat. Let's say that A is very different from B,
who is fairly similar to C. Thus, the A>B voters have a strong incentive,
but the C>B defeat is unlikely to overrule the B>A defeat, because B and C
are relatively similar candidates.)
3. If there is a median candidate involved in a false cycle with two
opposing wing candidates, and the median candidate is the initial winner,
then neither of the wing candidates are likely to withdraw. However, if
one of the wing candidates is the initial winner, then the opposing wing
candidate has a fairly clear incentive to withdraw in favor of the median
candidate. If a median candidate is involved in a cycle with two
candidates from the same wing (lets say left for this example), this
suggests that someone from the right wing buried the median under a
leftist candidate, and so if the cycle resolves in favor of a
left-of-center candidate, the strategizing right-wing voters have
themselves to thank.

	Anyway, I'm not suggesting that CWO is preferable to cardinal pairwise.
What I am suggesting is that if cardinal pairwise is considered to be too
complex, then CWO may be a workable substitute in some situations.
	Another interesting topic for me is CWO in the case of direct issue
voting. Obviously a proposition can't decide to withdraw by itself, so I
suppose that in order to use CWO in a multiple-issue direct issue voting
scenario, each option would have to have some sort of sponsor-type person
with the authority to withdraw it in the event of a cycle. Again, perhaps
not an ideal solution, but perhaps workable.

	Any comments?

my best,
James