[EM] Fwd: Duncan Proposal Draft

[Forest Simmons]

Dear EM List Friends,

We need your feedback on this draft of a proposal before we submit a
version of it to the voting reform community at large.

---------- Forwarded message ---------
From: Forest Simmons <forest.simmons21 at gmail.com>
Date: Thu, Oct 12, 2023, 5:35 PM
Subject: Duncan Proposal Draft
To: Michael Ossipoff <email9648742 at gmail.com>


Michael Christened our new Q&D burial resistant method "Duncan" after
Duncan Black who popularized the idea of using  Borda's Method as a
fallback "completion" when the ballots fail to  unambiguously reveal the
sincere "Condorcet" pairbeats-all candidate.

Our Duncan method has the same form as Black's in that the official version
directly specifies electing the unambiguous Condorcet Candidate when there
is one, and falls back to another procedure that relies on Borda Scores,
otherwise.

It should be emphasized that in both cases the fall back Borda based
expedient is rarely needed. For that reason some misguided voting reform
advocates have cavalierly opined that any decisive completion/ fallback
method would be plenty adequate to supplement the Condorcet Criterion
requirement.

However, this casual attitude ignores the  feedback aspects of voting
systems in that various voting methods vary in the degree that they
encourage or discourage the creation of artificial beat cycles that
subvert/ hide the Condorcet Candidate from view, bringing the completion
method into greater prominence in a potentially unstable cycle.

Unfortunately most of the extant methods fall into this "positive" feedback
category, including Borda itself.  Some less sensitive methods like
Approval  and IRV/RCV have a built in "friction" that dampens the feedback;
but as systems engineers know, the high performance components are the ones
that need the addition of some carefully engineered negative feedback
"circuit" to stabilize the system as a whole.

In our Condorcet Completion context, our use of the Borda Count scores is
carefully designed with that stabilizing influence in mind: adventurous
strategists who are aware of this feature, when acting rationally will be
deterred from creating these cycles that come back to bite them. Those not
aware will find out when their ploys backfire or otherwise disappoint them.

How do these pesky cycles arise so easily in Borda and other rank based
methods?

Suppose that your personal preference schedule for the alphabetized
candidates looks like ...

A>C>X>Y>Z, and that C is the Condorcet Candidate projected to win the
election if nobody acts nefariously.

You, and like minded friends, get the idea to insincerely move your second
choice to the bottom of your ballot (so it now reads A>X>Y>Z>C) ... not to
be "nefarious" so much as to just increase the winning chances of your
favorite A.

Could this work?

Yes, under Black's method if your friends follow your lead, this "nurial"
of C under the "busses" X, Y, and Z, could easily subvert one or more of
C's pairwise victories over X,Y, and Z, into defeats of C by them, thereby
hiding C's identity of sincere Universal "pairbeater" status to just one
more member of a "beatcycle" of the form A beats X beats Y beats Z beats C
beats A.

Note that the buried candidate C still beats the buriers' favorite, A ...
because lowering C  does not decrease the number of ballots that support C
over A ... which is how easily and innocently beatcycles like this can be
created in Condorcet style elections ... at least in the absence of
negative feedback from the cycle resolution fallback method.

In traditional Black that fallback method is Borda. Does that fix the
problem? ... or does it exacerbate it.

Well ... the same burial that put C at disadvantage in the pairwise
contests with X thru Z, also lowered C's Borda score by 3 counts per
ballot, and raised
 the Borda score of each of X thru Z to the tune of one count per ballot.

The likely outcome is that C will end up with the lowest score, and come in
last in the finish order.

By way of contrast, under our new Duncan method, the most likely winner is
X, and the least likely winner is A, the burier faction's favorite ... thus
disappointing the burier faction supporters ... teaching them that if they
try to outsmart new Duncan with insincere ballot rankings, they are apt to
end up helping elect their third (or later) choice instead of their first
choice or their second choice ... the one that they so cleverly buried
(however innocently or without malice).

Too many dabblers in voting method reform (as well as most professionals)
are unaware of these dynamics.

But now, with your new understanding, you, at least, can become part of the
solution.

Duncan Definition:

In the vast majority of the cases ... those in which the pairwise counts of
the ballots unambiguously identify the candidate that pairbeats each of the
others ... elect that candidate.

Otherwise, elect the highest score candidate that pairbeats every candidate
with lower score.

[Nominally "score" = Borda Count, though STAR Voting scores, for example,
could also serve]

How does this Duncan fallback procedure work to prevent A from getting
elected in our scenario regarding A thru Z?

Well, could A pairbeat every lower score candidate? In particular, could A
pairbeat C, which is now at the bottom of the Borda score pile ...
certainly lower than A ...?

Well, remember that "C beats A" was the last step in the beatcycle created
by A's friends.

So A does not pairbeat every lower score candidate, and therefore cannot
win.

New Duncan is burial resistant.

Next time ... more examples and insights ...

fws
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