[EM] RE: improved approval?

[Abd ulRahman Lomax]

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.