[EM] Duncan Proposal Draft

[Michael Ossipoff]

Yes, I like Duncan because burying the CW in an attempt to help your
favorite won’t help hir when it causes hir disqualification, as it probably
will.

…& Duncan is remarkably briefly-defined, needing only a very slight
modification of Black’s method.

On Fri, Oct 13, 2023 at 10:11 Forest Simmons <forest.simmons21 at gmail.com>
wrote:

> 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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