[EM] Duncan Proposal Draft

[C.Benham]

>
> Michael Christened our new Q&D burial resistant method "Duncan"...

What does "Q&D" mean?

Am I right in assuming that the Borda counts are based on the 
symmetrically completed ballots?

> 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.

So another way of putting it is:  "If there is no CW, elect the member 
of the Smith set with the second-worst score".

To put it bluntly, that is bound to have monotonicity problems and 
doesn't fly philosophically.

Trying to deter or frustrate order-reversal Burial strategy is fine, but 
the algorithm should "appear fair" and be able to be justified when
we assume that all the votes are sincere (or even just all equally 
likely to be sincere).

So if the score-order is  A>B>C and there is a A>B>C>A top cycle (aka 
Smith set) then this "Duncan" method elects B.

That breaks (at least one version of) "Double Defeat".  B is pairwise 
beaten by a candidate with a higher "score".


Chris B.


On 14/10/2023 4:43 am, Michael Ossipoff wrote:
> 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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