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

[C.Benham]

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>
> *À :* Michael Ossipoff <email9648742 at gmail.com>
> *Cc :* EM <election-methods at lists.electorama.com>; Forest Simmons 
> <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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