At 08:08 PM 9/27/2005, Simmons, Forest wrote:
In the recent message quted below there are two questions.
1. What should we call the Approval method that allows an extra
mark to identfy the favorite candidate, thus satisfying the Approval
voter's urge to give more moal support to Favorite than to Compromise?
I suggest "Approval Plus" or A+ for short. I think it is the best
public proposal for now.
I tend to agree. It answers the common objection to Approval. A+ is
the name I am using for Approval plus indication of Favorite, which
latter information is not used for elective purposes, but for other
purposes: public campaign finance, a definitive poll, and the sheer
psychological value of being to express a preference. However:
2. What if we put this extra mark to use in pairwise contests?
Then we open Pandora's little box of cycles.
I've been looking at it with my primitive tools, and I think that
A+PW (A+ PairWise), which is essentially a Condorcet method with an
expressed Approval Cutoff, probably the simplest possible Condorcet
method, actually could be a viable proposal.
The method could also be named for various Condorcet methods, such as
DMC, specified as 2-slot or 3-rank. (Given that slots refer to voting
positions on ballots, I think the suggestion made to me that this
would be 3-slot DMC is not correct. It has only two voting positions.)
Plain A+ may be more easily implemented, politically, as it could
overcome the main objection to Approval, which does have substantial
support at least in some circles. Otherwise basic Approval would be
the easiest, I'd think -- only the momentum of IRV makes IRV arguably
more possible.
But A+PW, while it is a Condorcet-compliant method and thus
vulnerable to cycles, has a ready means of cycle resolution, using
the Approval data.
It also appears to me that the restriction of ranks to three
(Favorite, Preferred, [Not Preferred]) could make strategic voting
quite difficult to pull off without so much risk that it would be
unlikely to be attempted. Here, I'm really hoping to get detailed
criticism of A+PW from this list.
To summarize the method:
The ballot has two options for each candidate, Favorite and Preferred.
The ballots are counted pairwise, and for all pairs not containing
the Favorite, Favorite and Preferred are counted the same, as one
vote for the marked candidate. For pairs containing the Favorite,
only the Favorite vote is counted. The winner is the winner of all
pairwise contests, if any such candidate exists.
This is, I believe, a Condorcet method, so cycles are possible.
Cycles could be resolved by choosing the candidate within the cycle
receiving the largest total number of votes, Favorite and Preferred
being considered the same, one vote for the candidate receiving either.
DETAILS:
Overvoting would be permitted, there is no reason not to. So a voter
could vote for more than one as Favorite, assuming the voter is
willing to abstain in the pairwise election between the candidates so
marked. And voters could, of course, vote for more than one under Preferred.
The names seem to arouse some controversy. Favorite is obvious, but
to some, Preferred is a synonym for Favorite. I think that is an
error, for Preferred here is short for Preferred to All Unmarked
Candidates, and marking both Favorite and Preferred has the same as
just marking Favorite.
Quite a number of readers seem to misunderstand the method at first
sight, remarkable given how simple it is. It is Approval Plus
indication of a favorite, and it is counted as Condorcet, with
Approval resolution of cycles.
Because of the way that the ballot is designed, Approval cutoff is
clearly indicated with minimum ballot complexity. I don't think it
could get simpler without becoming basic Approval (i.e., no
indication of Favorite). Yet it is a Condorcet method, as I'd define
it, for it will choose the Condorcet winner if one exists given the
ballot information. Because of the sparse information, voters are
confined to only vote for "approved" candidates, so it could also be
counted as truncated DMC. But why bother?
One of the major obstacles to EM reform is that some of the better
methods are quite difficult to explain and understand. A+PW is, I
think, not difficult at all.
I've thought of it as Approval Plus, but you could also call it
Plurality Plus. It is Plurality plus the ability to specify an
additional set of candidates as Preferred over the remaining ones.
What I don't yet know about the method is its vulnerability to voting
strategies. It seems to me that it could be reasonably immune to
insincere voting, i.e., insincere voting could quite easily result in
a result other than the desired one; and once this is true, strategic
voting would become too risky, and sincere voting would be the norm.
It seems that there is no reason not to rank the Favorite as
Favorite, and to rank Not Preferred candidates as Preferred. But I'd
like to see counterexamples.
By the way, this discussion would be, I'd think, entirely appropriate
for the Approval Voting mailing list, but I was banned from that list
(arbitrarily, I'd say, without warning) and so I can't post this
there. But anyone else who is subscribed to the Approval List could
post it to that list. I do still receive the AV list -- though it has
very little traffic lately. A+, in particular, could overcome the
main objection to approval that I've found.
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