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

[MIKE OSSIPOFF]

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.

But those aren't important criteria.

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.

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.

Of course different rank methods look at different things. There is no universal rule saying what rank methods must
look at. MDDTA looks at how many people rank some y over some x. (as do other MDD methods)

Your ballot says that you don't agree with x's majority defeat by y. Your ballot says that you don't think that x is worse than
y, or that, if you do think so, you're too lazy to say so.

Therefore, there is no majority saying that x is worse than y. x has more approvals than F does. F loses, rightly.

You have nothing to complain about.

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.

Mike Ossipoff










Mike Ossipoff