[EM] RE: improved approval?

[Abd ul-Rahman 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.

Wow. I think I agree, I've been pushing for the extra position for a 
while now, but not thinking of it as an election method other than Approval.

>2. What if we put this extra mark to use in pairwise contests?
>
>Then we open Pandora's little box of cycles.

Yes. If the extra mark is used, it becomes a ranked method. However, 
resolving cycles should be possible using the Approval information. 
In other words, if there is a cycle, the winner is the member of the 
cycle with the highest *overall* approval vote. That would be an 
exception to the rule that approval is disregarded in the pairwise 
contest between an Approved candidate and a Preferred One.

>If we want to make any instrumental use at all of the extra mark 
>without sacrificing the Strong FBC, then it has to be a tie breaker 
>only, and even then we have to be careful how we use it, or we can 
>lose the FBC inadvertently.

Given that ties in public elections are *extremely* rare, and that if 
there is a tie, it is common to toss a coin, just about any method of 
resolution, as long as it is not blantantly unfair, would seem to be 
acceptable. A technical loss of Strong FBC, but only in the case of 
tie, would hardly be a serious defect!

>I wish that someone could prove me wrong on this.  But Alex Small 
>worked on this problem for a long time, and came up with essentially 
>this conclusion, if I am not mistaken.  The only way we can graft 
>the Strong FBC onto Approval is to have the extra position at the 
>top largely symbolic.

I think we should review his work, or otherwise re-examine it.

For convenience, FBC, Favorite Betrayal Criterion
>For any voter who has a unique favorite, there should be no possible 
>set of votes cast by the other voters such that the voter can 
>optimize the outcome (from his own perspective) only by voting 
>someone over his favorite.

So, to review, A+ has two positions per candidate (i.e., each 
candidate is like a Yes/No proposition in terms of vote counting); 
the positions I'm going to call, for the moment, Favorite and 
Preferred. The reason is that calling the others Approved, as we 
often have, has met the challenge that I might not like to vote for a 
candidate, but am only voting for him as the lesser of two evils, so 
it is relative preference, which Preferred expresses (i.e., Preferred 
over all unmarked candidates), rather than true approval. It's a 
semantic issue, but it could be important.

The ballot is actually a ranked ballot with only three rankings 
(bottom ranking being assumed for unmarked positions). So, while I 
haven't studied it in detail, it should be vulnerable to cycles, 
since it can rank three candidates with unique rankings and the 
minimum Condorcet cycle size is three, if I'm correct.

All votes are counted for a candidate (both Favorite and Preferred), 
except in the pairwise contests between the Favorite and Preferred 
candidates. This is individual to each ballot, I have not worked on a 
practical counting algorithm.

One common objection to Approval has been the inability of voters to 
indicate the favorite. I see this objection again and again, it is 
asserted that, for example, Nader voters won't like a method that 
requires them to equate, for example, Gore and Nader. Further, there 
is the problem of public campaign finance money, which is allocated 
with a presumption that the voting is plurality, no overvoting 
allowed. Allowing the indication of Favorite would solve both of 
these problems.

Yes, it could mean that the widest-approval candidate would fail to 
win, unlike in basic Approval. However, I dislike that preference 
information, among approved candidates, is unavailable and thus 
completely unusable in basic Approval. A+, with the favorite 
information not being used to elect, solves the campaign finance 
problem, for the Favorite votes would be used. (And if voters mark 
more than one Favorite, the votes should be considered as fractional 
votes for such purposes.)

However, having the information and not using it for the election, I 
can predict, is going to meet with some opposition. It seems to me 
that using it only in the pairwise elections involving a Favorite and 
a Preferred candidate might be some kind of middle ground.

Is Alex Small's work on the problem accessible? Did he consider the 
votes being counted differently in the various pairwise races? I'll 
search, but any help would be appreciated.

A+ is a nice name, a *very* nice name, but we have two possible forms 
here: one with the Favorite information being used in the election 
process as described, the other with it being informational (and only 
used for funding and other purposes, not for the election itself, 
except in the case of a tie).

A+, perhaps, for the uncounted, Approval method, and A+(Pairwise) for 
the counted method? A+P for short.

A+ is really Approval, no difference strategically, but it is simply 
a question of whether or not the powers that be are willing to spend 
the extra ballot space. I'd say it would be very much worth it.