[EM] Misc notes; approval-less version of "Venzke-Bucklin"

[Kevin Venzke]

Hello,

I was trying to design a new method, and when I finally wrote code to
determine its 27-digit DNA string, I found with some bemusement (and
also amusement) that its DNA was identical to VBV, the inspiringly named
"Venzke Bucklin Variant."

I think this method was mainly interesting because it plotted near DSC
and DAC, which stake out a large but sparsely populated area of my 
method map.

It's sort of like an MCA which gives LNHarm to the largest bloc.

A recap of the VBV method definition:

1. Three-slot ballots.
2. Count all the preferences except the lower preferences of those top-
rating the top rating winner (TRW).
3. If the TRW has the most preferences, he wins. Otherwise count all the
preferences and elect whoever now wins (which would be the Approval
winner).

Here is "ranked VBV" for lack of a better name, which is based on
majority-strength wins rather than approval concessions:

1. Rank ballots. Equal ranking and truncation allowed.
2. If the TRW (let's keep using this name) has a majority pairwise win
or doesn't have a majority pairwise loss, he wins.
3. Otherwise he does not win. Elect a different candidate using this
hierarchy:
a. Prefer lack of any majority pairwise loss to having one
b. Prefer having a majority pairwise win to not having one
c. Prefer more "top ratings"

In the three-candidate case, step 3's terms can be described (and
rationalized) like this:

a. If B or C have a majority over the other, that winner wins. (This
will be the second preference of the TRW supporters.)
b. If B or C has a majority over the TRW and the other does not, the
one who does wins. (Without thus rule we could fail Plurality.)
c. B wins.

One thing I like about this (and also QR) over, for example, King of the
Hill (KH) or IRV is that the largest bloc will get their second choice if
they don't win.

A downside (in common with QR, again) is that the C voters can bury A
under B if they think A will pick C as their second preference. This is
could pose an unwanted dilemma for the A voters.

---

The thought process:

I usually look at elections with the expectation that there are two
strong candidates, and then a third weaker candidate who is probably
closer to one of the strong candidates, and eating away, to some extent,
at his top-rating support. In other words, the two weaker candidates
may not be in an alliance, but there might be a majority between them
that can defeat the strongest faction.

So the thought behind step 2 is this: If the TRW has some majority
behind him, or if there is no majority against him from the smaller
factions, then this situation is ambiguous enough, too different from
what I thought I might see, that I'm willing to stop the process here
and elect the TRW.

(I think it is unusual for a method to behave like this. It's probably
what plots VBV in DAC/DSC territory.)

After this, all I am trying to do is get the TRW voters their second
choice without violating Plurality. (If I can enhance LNHarm or anti-
burial properties somewhere, then that's great as well.)

---

Incidentally, I recently noticed that KH and Quick Runoff (QR) in the
three-candidate case only differ from IRV wrt the LNH criteria in
that only the supporters of the weakest candidate (by first preferences)
have a lapse of one of the two (-Harm for KH and -Help for QR).

So, if you back one of the two strongest candidates as your first
preference, you have the same LNH___ guarantees as under IRV. (That's 
true with more candidates also. It's just that supporters of all the
weaker candidates are missing one of the two guarantees.)

---

I also experimented with a version of Conditional Approval (CdlA) that
only allows two rounds. But it seems pretty unfair to the TRW. It's not
really an advantage to lead in the first round (which is what the TRW
does). In the first concession, everybody who hates you gets to react to
your leading. In the second concession, TRW supporters can only give up
some preferences. The TRW can't reclaim the lead without a third
concession. (This does stop his supporters from using burial though.)

My motivation in experimenting with CdlA is that the effect of one's
vote doesn't feel direct enough to me. Too many potential rounds, no
ability to retract conceded preferences. Seems like it's asking to be
gamed.

(I made wiki.electorama.com pages for QR, KH, and CdlA a few days ago.
I've held off on VBV because I have two methods and zero good names.)

Kevin Venzke