[EM] Some numbers (LNHs, compromise/withdrawal, burial games)

[Kevin Venzke]

Hello,

I have my generator looking over the method DNA and counting scenarios
from which we can find a LNHarm failure, LNHelp failure, compromise/
withdrawal incentive (i.e. the faction would have preferred to not vote
for their favorite), and two types of burial games. Let's call them 
truncation-deterred "TD" and reversal-deterred "RD." In a TD game the
attacker will hesitate to bury if he fears the defender faction will
truncate support for the attacker. In an RD game the attacker would have
to fear that the defender will vote for the candidate intended to be a
pawn. In both cases the deterrent is that the pawn may be elected, which 
neither attacker nor defender want.

To be clear, this is a burial game: X does not vote for Z, Y wins, Y votes
X>Y; and if X changes to X>Z, X wins; and if Y faction then changes their
vote (to what, depending on TD vs RD), Z wins. XYZ can be anybody.

I get numbers overall and by faction. Even then I realize some of these
numbers may not tell a complete story. For example, one method may have
greater LNHarm failures than another method, but we don't see what happens
with the new preference when LNHarm isn't failed.

I'm including numbers for margins methods, but it produces 7 DNA sequences
depending on the exact faction size ratios. I produce them all.

Here's a list. I won't break out by faction for everything for now. The
format is method name, LNHarm (failure scenarios), LNHelp, compromise/
withdrawal incentive, TD burial games, RD burial games.

FPP 0 0 18 0 0
IRV 0 0 9 0 0
DSC 0 3 12 1 1
DAC 9 0 6 0 0
Bucklin 12 0 5 0 0
WV 1 4 2 6 0
C//App 4 4 3 5 0
C//IRV 3 0 6 0 0
QR 0 3 7 4 0
MMPO 0 6 2 6 1
BklnVariant 5 2 6 2 0
C//KH 6 0 5 0 0
KH 6 0 7 0 0
margins 0 6 2 6 1 (= MMPO)
margins 1 4 4 2 2
margins 0 6 3 5 2
margins 1 4 3 5 1
margins 1 4 2 6 0 (= WV)
margins 1 4 4 4 2
margins 2 2 6 2 1

I was surprised that DSC and MMPO have RD games. In DSC it is: AB, B, CB.
A wins. B can vote B>C and win. If A thinks the B voters would be lying,
they will have to make B voters fear that the vote will be AC. This is
unusual from what we usually discuss because the "attacking" faction B is
actually defending the CW, and so could be said to be using *defensive*
burial.

If we take the margins averages (which we probably shouldn't, as they
won't occur with equal frequency) margins is by a hair the best LNHarm-
failing method wrt LNHarm. WV places second. WV has a bit less LNHelp,
less compromise/withdrawal incentive, more TD games, but no RD games.

If we are supposed to expect different voting behavior from WV and margins
in the zero-info case, I don't think these numbers suggest it.

Condorcet//Approval's burial resistance advantage over WV doesn't look
all that great here. You get one less burial scenario, in exchange for a
compromise scenario and 3 LNHarm scenarios.

QR over IRV: With QR you pay a price (LNHelp and TD burial) for two
fewer compromise scenarios. Not that *much* improvement but I'm still
pleased.

Bucklin vs. my variant is interesting. Although I only aimed to give
LNHarm to the A faction, the LNHarm failures are cut by over half. Six
of Bucklin's 12 failure scenarios involved A's preference, so those are
gone, plus one more. The one more is actually a good example of how the
numbers can't show a complete picture. In Bucklin, AB B CA elects B, but
the B voters can throw it to A by voting BA. In the variant, B doesn't
win in the first place, which is (at least on its face) a worse situation
for B than when he is prone to a LNHarm failure.

Next I am working on a more thorough strategy solver. For a given scenario
(in terms of sincere utilities) I want to have the factions play
against each other, so that we can actually see which voting scenarios
occur when voters are smart. With these results we should be able to say
that such-and-such method (or lottery of methods) "maximized utility" for
instance, for the given scenario. Or, we could say which methods were
most likely to reduce to two candidates in practice. Or, which methods
occasionally produced train wreck outcomes due to gaming.

(I still want to study nomination strategy, but I'm really stuck on the
details. I want to approach strategy, without assumptions, on both the
nomination and voting sides. But then I need intelligence on both sides.
An intelligence that isn't based on my assumptions is hard to imagine,
and if it's some kind of brute force thing it will never finish running.)

Kevin Venzke