[EM] Warren: WMDDA comments

[MIKE OSSIPOFF]

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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