[EM] Duncan Proposal Draft

Sat Oct 21 12:38:58 PDT 2023

On Sat, Oct 21, 2023 at 11:05 C.Benham <cbenham at adam.com.au> wrote:

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

Are you referring to how equal-ranking is counted in Borda? I advocate
that, in these methods’ Borda-count,  a ranking give each of its
ranked-candidates a number of points equal to the number of candidates in
the ranking who aren’t ranked over hir.

> 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".
>

Would you mind telling why that’s another way of putting it?

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

How doesn’t it 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).
>

Remember that sincere top-cycles are vanishingly rare. That’s why
Sequential-Pairwise’s Pareto failure isn’t important, & it’s why
MinMax(wv)’s Condorcet Loser failure isn’t important.

It matters much more what happens in a strategic cycle. Does the method
reward or penalize burial?  …or neither?

Duncan tends to often do neither, because it will likely disqualify both
Bus & BF. (I defined those usages when I defined CTE.

I prefer CTE to Duncan, because it more often penalizes, instead of merely
not rewarding.

But I remind you that these methods are intended to deter
probabilisticallly, but aren’t claimed to penalize burial in every possible
example.

>
>

>
> 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
>>
>>
>>
>>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20231021/6a7e15eb/attachment-0001.htm>