Warren--
You said that WMDDA isn't Smith//Approval, because the approvals are
expressed in the rankings. But it's still Approval, regardless of how the
Approvals are expressed. It could be on a separate Approvsal section of the
ballot. It could be by an Approval cutoff in the rankings. And it could be
by a rule that all the candidates you rank are counted as approved by you.
You start by disqualifying the candidates who aren't in the Smith set. Say
there's a one-candidate Smith set, a CW. The CW must win. Your method meets
Condorclet's Criterion. Kevin demonstrated that Condorcet's Criterion is
incompatible with FBC. Smith//Approval fails FBC.
Here's an example in which Smith//Approval fails SFC:
Sincere rankings:
40: ABC
25: BAC
35: CBA
Ballots:
40: A (approving only)
25: BA (approving B and A)
35: CB (Approving C and B)
These approvals could be like that because of a rule that (only) all ranked
candidates are approved, or it could be that people place their approval
cutoffs in that way.
B beats A beats C beats B. The Smith set consists of all the candidates. So
Approval choses among them.
Approval scores:
A: 65
B: 60
C: 35
A wins.
Buit a majority prefer the CW (B) to A. And they vote sincerely, voting all
of their preferences.
And no one falsifies a preference. So SFC says that A shouldn't win. But A
wins. Smith//Approval fails SFC.
I've told why Smith//Approval fails FBC & SFC.
Now, where are the errors in the demonstration claims?:
* satisfies SFC because if no majority prefers anyone to X, then X will
not be disqualified. If X has a majority-strength win over Y, then Y will
be disqualified, so that Y can't win.
WDSmith adds: WMMDA also satisfies SFC because of the same proof.
I comment:
Kevin said that if X has a majority-strength defeat over Y, then Y will be
disqualified. But that's only if it's a majorilty-strength defeat.
Smith//Approval disqualifies nonmembers of the Smith set, but it doesn't
disqualify everyone who has a majority defeat. There could be majority
defeats in the Smith set, and they wouldn't disqualify anyone. So that
sentence in Kevin's proof doesen't apply to Smith//Approval.
If I say "A majority of the voters rank X over Y", that has to mean more
than half of the voters. Yes, sometimes I"ve gotten careless and said "A
majority rank X over Y". When the sentence doesn't say what it's a majority
of, shouldn't the assumption be that it's a majority of the electorate?
Anyway, I'll start saying "a majority of the voters".
* satisfies FBC because if X wins, and a faction has ranked Y insincerely
low, then if this faction raises X and Y to the first position, the winner
will then be either X or Y. This is because X and Y can only lose defeats in
this way, and other candidates can only gain them. Also, X and Y's
approval can only increase.
NOTE: this FBC proof only works if the "ranking" is allowed to include
EQUALITIES not
just ">" relations, e.g. A>B=C=D>E=F>G=H.
WDSmith adds: WMMDA also satisfies FBC because of the same proof.
I comment:
It doesn't work for Smith//Approval. It can't be said neither X nor Y can
get a defeat when you move Y up to 1st place with X. Say X is CW. X barely
beats Y. Some X>Y voters move Y up wilth X. Now X doesn't beat Y. Now
there's a cycle. I could contrive the approvalls so that neither X nor Y
would win Smith//Approval then. So moving Y up wilth X can change the winner
from X to someone other than X and Y.
Now, though moving Y up with X can give X a defeat, it can't give him a
majority defeat. That's because: X was BeatsAll winner. If there were a
majority ranking Y over X, it would be impossible for X to beat Y, before or
after those people moved Y up with X. So, when moving Y up wilth X gives X a
defeat, it isn't a majority defeat. MDDA only disqualifies for majority
defeats. So moving Y up with X can't get X disqualified, Or Y either. Nor
can it lower the Approval score of either. So it can't cause the win to
leave {X,Y}.
Here, Y is those voters' favorite. The question is: Will somone other than X
and Y win if they move their favorite up to 1st place, rather than burying
him by voting X over him?
You pointed out that if _everyone_ ranked all the candidates, then there'd
be an approval tie. But generallly ranking all the candidates isn't good
strategy, because you can hurt your several bottom-most ones most by the
approval difference resulting from not ranking them.
Sure, maybe you intend to make use of SFC compliance, and you believe that
you're in a majorilty
of people who like the CW better than the worse candidates, and that no one
will falsify. These are all reasonable assumptions, and if you don't
perceive an a/ua situation, you might rank all the candidates, because you
expect the conditions under which SFC compliance makes it safe to do so. But
all it takes is one person who doesn't think so, who isn't counting on those
assumptions, and who wants to use approval-difference against some of the
candidates.
Or maybe one person who perceives an a/ua situation and therefore truncates
the unacceptables. With thousands or millions of voters, it would be rare
for everyone to rank all the candidates.
Of course if I were sure that everyone else would, then I could cast the
deciding vote, by ranking only my favorite, so that s/he'd win unless the
other voters got him/her disqualified with a majority defeat.
You asked why Deluxe MDDA doesn't deter offensive order-reversal as well.
Consider ordinary MDDA:
Say it's Favorite, Middle, and Worst. Favorite is your favaorite. Worst is
your last choice. Say you want to try to give Middle a majorilty defeat by
helping Worst get a majority against Middle. That's because you perceive
your chief rival to be Middle. The trouble is, to do that, in ordinary MDDA,
you forfeit your right to vote an Approval difference for Favorite over
Worst. That would tend to be a mistake, to abstain in Favorite vs Worst, in
order to maybe give Middle a majority defeat. Middle isn't even as bad as
worst.
But with a separate Approval cutoff, of course you cn rank Worst over Middle
without giving an approval to Worst. So MDDA has less offensive
order-reversal problem than does Deluxe MDDA. I pretty much don't propose
Deluxe MDDA anymore, for that reason.
What does it mean to you if offensive order-reversal is well-deterred? It
means that you can feel safer when you rank your 2nd choice below your
favorite. You don't have to worry that your vote for Favorite over Middle
will be augmented by Worst voters who likewise vote Favorite over Middle.
You said that in MDDA there's no reason to equal-top-rank. Well, in the
previous paragraph, I told why ordinarily there's little reason to. No
reason to fear that you'll hurt Kerry by ranking him below Nader.
But, what if you believe that the Republican is completely unacceptable. As
I said, it's unlikely that ranking Kerry 2nd instead of 1st could cause
Kerry to lose. But it's possible. Maybe some Republicans _will_
order-reverse, and augment your Nader>Kerry vote, to disqualify Kerry, who
was the only wone with enough approval to beat Republican.
The fact that that is unlikely is irrelevant if Republican is completely
unacceptable to you and if Kerry is acceptable to you. Anytyhing that you
can do to reduce the probability of a Republican win, you'll do it. That
includes moving Kerry up to 1st place.
Speaking for myself, though Kerry is really completely unacceptable, I, in
MDDA, would vote all the acceptable candidates equally in 1st place. I'd do
the same thing in SSD(wv). In Condorcet(margins), I'd probably rank the
acceptables in order of winnability, maybe burying my favorite.
Of course, because SSD(wv) meets Condorcet's Criterion, it fails FBC, and I
could regret that I didn't rank a more winnable acceptable over my favorite.
Some will do that. Maybe many will.
But Condorcet is off the subject. My point was that I would equal-rank all
the acceptables in 1st place. In Condorcet I'd eiether truncate the
unacceptables or rank them strategically in reverse order of winnability. If
offensive order-reversal seemed likely, I'd truncate them.
In MDDA, likewise, I have those two choices. Ranking them in reverse order
of winnability, I could try to make one unacceptable have a majority defeat
against the most winnable acceptables. Sometimes that could be the best
idea. But usually I'd expect that the chance of defeeating the unacceptables
in that way is less than the chance of defeating them by voting an approval
difference against them, by truncating them. Especially the unacceptables
that I rank relatively high won't be much hurt by the strategic rankings,
whereas all the unacceptables will by hit with an approval difference if I
truncate them. In general, then I'd suggest that truncating the
unacceptables is the best strategy in an acceptable/unacceptable situation
in MDDA.
If power truncation is available, I'd power truncate the unacceptables.
Here's what power truncation is:
The voter may mark a box on his/her ballot so that every candidate s/he
doesn't rank will be scored as if s/he had ranked all the other candidates
over him/her.
That option makes acceptable/unacceptable strategy as simple as that of
Approval or RV.
By the way, as I judge these methods and the power-truncation enhancement,
the rank method is at its best when its a/ua strategy is as easy as that of
Approval. That means that, in public elections, Approval or RV is the
standard against which to measure the rank methods. And it means: Why bother
with rank methods then? Why not just use Approval or RV? Good question.
Mike Ossipoff
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