Mike Ossipoff wrote (12 Nov 2011):
ABucklin and Mono-Add-Top:
In the criterion-compliance table that I posted, I said that ABucklin
meets Mono-Add-Plump, Mono-Add-Top
and Participation. Actually, it only meets Mono-Add-Top.
It isn't possible for a method to both meet Mono-add-Top and fail
Mono-add-Plump. Ballots that plump for X are
also ballots that top-vote X.
(Just before posting this I've noticed that your quoted text isn't
consistent with your Subject line)
ABucklin meets Mono-add-Plump and fails (as shown in my last post)
Participation.
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.
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. (Also it looks like you have
some other method in mind, but my comments still apply).
25: A>B
26: B>C
23: C>A
04: F
(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.
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.
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.
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, or even just extra information that might have
caused the algorithm to be (perhaps) forgivably "confused."
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.
Here again it sounds more like you are talking about Mono-add-Top
instead of Mono-add-Plump.
Chris Benham
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