[EM] Trying to out-do Condorcet//IRV (via method generator)

[Kevin Venzke]

Hi,

Some may recall that I created an election method generator/fixer. I will
go over it again briefly.

The assumption is that in each election there are three factions and three
candidates, and that no faction is a majority. So with the letters A,B,C
we can denote both a faction and their candidate, in descending order of
faction size.

Each faction votes sincerely for their first choice but for the second
choice may truncate or vote for one of the other two candidates. This means
there are 3*3*3=27 possible elections. With three possible results for
each election, there are 3^27=7.6 trillion possible election methods. You
can describe a method with a 27-letter "DNA" sequence giving each result
in a certain order.

Here are a few of interest.
AAAAAAAAAAAAAAAAAAAAAAAAAAA (FPP)
AAAAAAABAAAAAAAABAAAAAAAACA (DSC)
ABAABAABAABAABAABAABAABAABA (IRV)
ABAABAABAABAABAABAABAABACCC (Condorcet//IRV)
ABAABACBCABAABAABBAAAACACCC (Schulze etc., Winning Votes)

Within this framework I'm a little limited in which criteria I can
check for. For instance I can only catch a couple of special cases of
participation, mono-raise, and mono-add-top.

As for burial, I have three checks implemented:
"Can [changing] A to A>C make A win?" named "abc"
"Can B to B>C make B win?" named "bbc"
"Can C to C>A make C win?" named "cbb"

More types of burial are possible but I felt these were the ones I have
run into the most. If I proceed I may suggest why these three are enough:

I'll list which criteria the above methods fail:
FPP: Cond-net, Cond-gross, minimal defense, strategy-free
(Ossipoff's, on votes cast), CLoser-net, CLoser-gross (which basically
equals mutual majority in this setting)
DSC: Cond-net, Cond-gross, MD, SFC, LNHelp, BBC, CBB (described above)
IRV: Cond-net, Cond-gross, MD, SFC, "ALP" (largest bloc's last preference
can't win)
C//IRV: MD, SFC, ALP, LNHarm (LNHelp or burial vulnerabilities are not
detected)
WV: LNHarm, LNHelp, ABC, BBC, CBB.

So to summarize, I detect burial vulnerabilities in DSC and WV as we
would hope, but not in Condorcet//IRV, which suggests perhaps I can find
more methods that are interesting in the same way as the latter.

Requesting methods that satisfy Condorcet(net) and the three burial
criteria, I get 16. Of those, 12 sometimes make B faction wish they had
received fewer votes (Mono-add-top special case). And 8 of those can also
see a candidate lose due to receiving more lower preferences. Almost all
of these 12 also have detectable LNHelp failures.

The remaining four, which includes C//IRV, differ in only two scenarios.
One method is strictly best, in that in addition to C//IRV's criteria it
also satisfies minimal defense. This is of interest to me because it means
the method should behave more like WV.

I actually discovered this method last year, fairly quickly, but, as now,
faced the big problem: I don't know how to define the method in plain 
English. Here are the two scenarios where a difference is required:

A. B>C. C.
A>B. B>C. C.
In both scenarios, C//IRV elects A, but would need to elect C.

I will see if I can figure out a way to define this method, at least for
three candidates.

---

I am working on some other problems too... I have wanted to find a good
way to give *some* voters under MCA a LNHarm guarantee. There seem to be
at least a few options.

---

Also, a note on something I wrote to Kristofer. I said that if you want
both LNHs, you are stuck with FPP and IRV. It turns out (at least within
this simulation) that if you insist on LNHarm, LNHelp, and Plurality,
you get one more choice: The method where A wins unless the B bloc votes
B>C, in which case C wins. (It is impossible for B faction's candidate
to win.)

Kevin