[EM] Trying to have CD, protect strong top-set, and protect middle candidates too

Thu Nov 24 19:27:17 PST 2016

Kevin suggested IC,MMPO, as a method that meets FBC, avoids
chicken-dilemma, and has MMPO's (uncertain) kind of protection of a
middle-ranked CWs.

MMPOsc achieves that too,and the symmetrical completion avoids the
Hitler-with-2-votes bad-example.  But the symmetrical completion that it
needs spoils its truncation-proofness.

So an advantage of IC,MMPO over MMPOsc is truncation proofness, because the
IC avoids MMPO's bad-example, and so the symmetrical completion isn't
needed.

Forest's MDDAsc could be used with IC too. IC,MDDAsc would add a sort of
Condorcet-Criterion compliance. I guess the symmetrical completion would
still be needed, to keep Mono-Add-Plump,but, it doesn't do any harm to
MDDA's solid, positive protection of a middle-ranked CWs to whom approval
isn't denied..

So that's four related methods:

MDDAsc
MMPOsc
IC,MDDAsc
IC,MMPO

Some advantages among them:

MDDAsc:

Protection of a middle-ranked CWs is positive & solid, if approval isn't
denied that candidate.

MMPOsc:

Chicken-dilemma deterrence is automatic. All middle-ranked candidates would
receive some (uncertain) protection if they're CWs. But the protection of
_any_ middle-ranked CWs is uncertain, and might or might not be there.

The necessary symmetrical completion spoils the truncation-proofness that
MMPO would otherwise have..

Deterrence of burial and truncation depends on the would-be buriers knowing
if the strength of pairwise oppositions favors them, or will result in
penalty. It depends largely on whether the candidate under whom they bury
the CWs has strong pairwise opposition other than by the CWs. Maybe that
threat would depend on the voters of the defending wing, between the median
and any possible burying-candidate,  purposely leaving hir only weakly
pairwise-opposed (other than by the CWs). If there are a number of
candidates under whom the CWs could be buried, and who could receive strong
pairwise opposition, then it might be necessary to give low opposition
(other than by the CWs)  to a number of them.

Anyway, the protection of a middle-ranked CWs is always uncertain.

IC,MDDAsc:

Compiance with Improved Condorcet Criterion is added to MDDAsc's properties.

IC,MMPO.

Same as above. Also, because symmetrical completion isn't needed, due to
IC, this method has, as an advantage over MMPOsc, that it's
truncation-proof.

-------------------------------------------------

MDDAsc & IC,MDDAsc seem to win the comparison because the voter can give
full, sold, positive protection to a candidate to whom s/he doesn't deny
approval.  Chicken dilemma will be relatively uncommon, and so approval
won't usually be denied.

Michael Ossipoff

On Wed, Nov 23, 2016 at 8:09 AM, C.Benham <cbenham at adam.com.au> wrote:

> On 11/23/2016 10:59 AM, Kevin Venzke wrote:
>
> Hmm, with a movable cutoff MDDA already violates Plurality with three
> candidates. Do you think symmetric-completion of the bottom can save it?
>
>
> Yes.
>
> Something Toby Pereira wrote  (9 Nov. 2016) regarding "Irrelevant Ballots"
> got me thinking. The criterion I defined just talks about ballots
> that plump for nobody, but there can also be a problem with ballots that
> only vote nobodies below, say, equal-top.
>
> Under MDDA with symmetric completion only at the bottom, adding  ballots
> like that can wash away  "majority-defeat"
> disqualifications and make the result less Condorcet-consistent.
>
> This has led me to think of a modification to fix this problem that looks
> to be too good to be true, but so far I can't see how.
>
> *Voters submit rankings with an explicit approval cutoff. (I prefer
> default placement to be just below candidates ranked below no-one).
>
> On the ballots that have been symmetrically completed at the bottom, find
> the smallest set S of candidate/s that majority-strength pairwise
> beat all the outside-S candidates.
>
> Disqualify the outside-S candidate/s and delete all the ballots that make
> no distinction among the inside-S candidates.
>
> Repeat as many times as possible.  If at the end of this process more than
> one candidate hasn't been disqualified, elect the
> one of those by normal MDDA (SC).*
>
> I am fearful that this might fail FBC  and/or mono-raise, but I can't
> (yet) see how it does.
>
> 45: A>B>>C
> 10: A=B
> 40: B
> 05: C
>
> 100  ballots. After symmetrically completing at the bottom we get  A>B
> 47.5 - 42.5,    A>C  75-25,    B>C  95-5.
>
> Normal MDDA(SC)  disqualifies only C and then elects the most approved
> candidate, B.
>
> My suggested version first disqualifies C and then deletes the 5 C  and
> 10 A=B  ballots and then disqualifies B leaving  A (the CW)
> as the winner.
>
> What do you think?
>
> Chris Benham
>
>
> On 11/23/2016 10:59 AM, Kevin Venzke wrote:
>
> Hi Chris,
>
>
> ------------------------------
> *De :* C.Benham <cbenham at adam.com.au> <cbenham at adam.com.au>
> *À :* Michael Ossipoff <email9648742 at gmail.com> <email9648742 at gmail.com>
> *Cc :* EM <election-methods at lists.electorama.com>
> <election-methods at lists.electorama.com>; Forest Simmons <fsimmons at pcc.edu>
> <fsimmons at pcc.edu>
> *Envoyé le :* Mardi 22 novembre 2016 10h51
> *Objet :* Re: [EM] Trying to have CD, protect strong top-set, and protect
> middle candidates too
>
> On 11/22/2016 9:25 AM, Michael Ossipoff wrote:
>
> >>With MDDTR, if your plump for X makes hir lose, it's because you added
> a ballot. It has nothing whatsoever to do with the fact that the new ballot
> plumped for X.
> >>Your ballot made X lose in spite of the fact that it was a plump for X,
> not because it was a plump for X.
> >>But in IRV, when you make X lose by raising hir from last place to 1st
> place, that raising of X was the only thing that you did, and it is the
> reason why X lost.
> >
> >That "distinction" is meaningless and completely useless.  The idea that
> adding a ballot is "something you did" that rates a mention is ridiculous.
>
> I'm not sure about this specific example but I think this kind of
> distinction could be a useful defense. For IRV I might argue that a
> mono-raise failure happens not just from raising the winner but also
> *lowering* some other, incidental candidate. The reason mono-raise
> failures are offensive is that supposedly the voter has done nothing but
> aid the preexisting winner. But at least in IRV it is not so clear as
> that.
>
> >Regarding MDDA,  symmetrically completing the ballots only at the bottom
> and having a moveable approval cutoff fixes its failures of Mono-add-Plump
> >and Plurality and Irrelevant Ballots Independence and in my opinion makes
> it a good/acceptable method.
>
> Hmm, with a movable cutoff MDDA already violates Plurality with three
> candidates. Do you think symmetric-completion of the bottom can save it?
>
> For whatever interest it may be, I calculated the "DNA" for the method you
> describe and got the exact same 343-digit code as for ICA(explicit). That's
> the first time I've hit a method I already had...
>
> Chris Benham
>
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