[EM] ABucklin doesn't meet Mono-Add-Top or Participation, but meets Mono-Add-Plump. MDDTR and Mono-Add-Plump.

[C.Benham]

Mike,

> You continued:
>
> (Also it looks like you have
> some other method in mind
>
> [endquote]
>
> How so? As I said, I'm referring to MDDTR.


Because in the description of your example you referred to information 
that MDDTR
ignores:

> Say the method is MDDTR, and your favorite candidate is F. F doesn't 
> have a winning approval (top + middle) score,
> because x has significantly more approvals.

MDDTR takes no account of approval scores. It is only interested in 
majority-strength pairwise defeats and TR scores.
It looks more like you were describing MDDA.


> But x is disqualified by having a (bare) majority voting y over hir.
> With x disqualified, F wins with the most approvals of any 
> undisqualified candidate. F isn't close to having a top-rating
> majority.

Nor is MDDTR (explicitly) interested in a "top-rating majority". Now it 
looks more like you are describing  MDD,ABucklin


> But I'll post an example of that particular kind of Mono-Add-Plump 
> failure within
> the next few days.


I look forward to seeing it.

Chris Benham



Chris Benham wrote:

It isn't possible for a method to both meet Mono-add-Top and fail
Mono-add-Plump.

[endquote]


I hope that I didn't say that ABucklin fails Mono-Add-Plump. If I did, 
it was an error
and I retract the statement. In the subject-line, I said that ABucklin 
passes
Mono-Add-Plump.

So yes, that was a typo. I meant what I said in the subject-line: 
ABucklin doesn't meet
Mono-Add-Top, but it meets Mono-Add-Plump.

You (Chris) said:

(Just before posting this I've noticed that your quoted text isn't
consistent with your Subject line)

[endquote]

Yes, there was a typo in my message, regarding that.

I'd said:

 > MDDTR and Mono-Add-Plump:
 >
 > Say the method is MDDTR, and your favorite candidate is F. F doesn't
 > have a winning approval (top + middle) score,
 > because x has significantly more approvals. But x is disqualified by
 > having a (bare) majority voting y over hir.
 > With x disqualified, F wins with the most approvals of any
 > undisqualified candidate. F isn't close to having a top-rating
 > majority.
 >
 > Then you and a few other people show up, and plump for F. (You top
 > rate F, and don't rate anyone else).
 >
 > Now your presence in the election increases the requirement for a
 > majority, with the result that x
 > no longer has a majority ranking y over hir.
 >
 > Now, x wins instead of F, because x has significantly more approvals
 > (F was behind x in approvals by more than
 > the number of newly-arrived voters.
 >
 > By plumping for F, you and the other newly-arrived voters have made F
 > lose.

You wrote:

Mike, I'd like to see an example election of what you are talking about.
If this way of  MDD,TR failing  Mono-add-Plump
is possible it isn't the one I know about.

[endquote]

I admit, not assert, that MDDTR fails Mono-Add-Plump. We agree that it does.

But I'll post and example of that particular kind of Mono-Add-Plump 
failure within
the next few days.

You continued:

(Also it looks like you have
some other method in mind

[endquote]

How so? As I said, I'm referring to MDDTR.

Here's my definition of MDDTR:

3-slot method: top, middle, and bottom (unrated)

Disqualify every candidate who has another candidate voted over hir by a 
majority.

The winner is the undisqualified candidate with the most top ratings.

[end of MDDTR definition]

That is the method that I was referring to when I said "MDDTR".

You wrote:

25: A>B
26: B>C
23: C>A
04: C

(78 ballots)   B>C  51-27,   C>A 53-25,   A>B 48-26 

TR scores: C27,   B26,  A25.      Approval scores: C53,  B51, A48.

All candidates have a majority-strength pairwise defeat, so no candidate
is disqualified. MDD,TR and MDD,A and
MDD,ABucklin (as you call it) all elect C.

Now say we add 22 ballots which plump for C.

25: A>B
26: B>C
23: C>A
26: C

(100 ballots)   B>C  51-49,   C>A 75-25,   A>B 48-26

TR scores:  C49,    B26,    A25.       Approval scores: C75,   B51,   A48.

Now there is one candidate (B) without a majority-strength pairwise
defeat, so all except B are disqualified and B wins.

[endquote]

Thank you for that example showing the MDDTR Mono-Add-Plump scenario 
that I described. No, your
example is not different from my scenario. It's a numerical example of 
my scenario. The plump-ballots
took away B's majority defeat, allowing B to win. The only difference 
was that, my scenario, B beat C by
higher Approval score, whereas, in your example, B wins by being the 
only undisqualified candidate. Unimportant
difference. In both stories, the plump-ballots take away B's majority 
defeat by raising the requirement for
a majority.

You wrote:

BTW, unrelated to the Mono-add-Plump issue, C in both elections is
uncovered and positionally dominant so I think
a method needs a much better excuse for not electing C in both cases
than any that the MDD methods can offer.

[endquote]

Cetainly, if uncoveredness and positional dominance can be shown to have 
great practical
importance, as opposed to aesthetic appeal.

Any method will fail many aesthetic criteria. We choose a method based 
on what we want or need from it. We need
compliance with criteria that are of practical importance.

I'd said:

 > So you storm into the Department of Elections office, to complain
 > about that.
 >
 > The person at the counter says, "Excuse me, but do you think that the
 > election was a Plurality election?"
 >
 > You see, in Plurality, 1st choice votes are what decide the election.
 > Rank methods look at more than that. They
 > look at your other preferences too. Maybe it's tempting to want 1st
 > choice ratings to decide the election in rank methods
 > too. But they're rank methods, and rank methods needn't act like
 > Plurality.

You wrote:

This explanation might be acceptable if we were just talking about a
failure of  Mono-add-Top where the complainers provided
some extra information that the voting-method algorithm might have
reasonably construed as strengthening not just their favourite
but also the winner

[endquote]

They did. Their ballots proclaimed "I am indifferent between everyone 
but my favorite!"

Either they were indifferent, or they just were too lazy to vote 
otherwise. In either case, they
have only themselves to blame. Their indifference regarding everyone but 
their favorite meant that
someone who previously had a majority defeat no longer has a majority 
defeat.

The fallacy of Mono-Add-Plump is that a plump-ballot says nothing other 
than who the voter's favorite is.

You wrote:

, or even just extra information that might have
caused the algorithm to be (perhaps) forgivably "confused."

[endquote]

The algorithm wasn't confused, forgivably or otherwise. It looked for 
majority defeats, and
didn't find one for the candidate who beat your favorite. It had a good 
reason for looking
for majority defeats--doing so allows it to meet CD, LNHa, and SFC.


I'd said:

 > Yes, it's aesthetically nice if the win is monotonically related to
 > addition of 1st choice ballots, but there is no reason why it should
 > or must be. Rank methods aren't Plurality.

You wrote:

Here again it sounds more like you are talking about Mono-add-Top
instead of  Mono-add-Plump.

[endquote]

I was talking about what I said I was talking about: MDDTR, as I define it,
and Mono-Add-Plump.

A plump-ballot contains information other than only the voter's 
favorite. It expresses
indifference among the other candidates. That indifference can obviously 
make the difference
regarding whether or not some particular candidate has a majority defeat.

We're used to Plurality. There's therefore a tendency to judge methods' 
results in terms of Plurality, and to
interpret ballots in terms of Plurality.

Mike Ossipoff