<html>
<head>
<style><!--
.hmmessage P
{
margin:0px;
padding:0px
}
body.hmmessage
{
font-size: 10pt;
font-family:Tahoma
}
--></style>
</head>
<body class='hmmessage'><div dir='ltr'>
<div dir="ltr">
<p class="ecxMsoNormal">This is a reply to a posting from Chris, on November 17th.</p><p class="ecxMsoNormal"><br></p><p class="ecxMsoNormal">The discussion is about this example:</p><p class="ecxMsoNormal"><br></p><p class="ecxMsoNormal">><i> 49: C </i></p><p class="ecxMsoNormal"><i>> 27: A>B <br></i></p><p class="ecxMsoNormal">><i> 24: B <br></i></p><p class="ecxMsoNormal"><br></p><p class="ecxMsoNormal"><br>Chris said:</p><p class="ecxMsoNormal"><br></p><p class="ecxMsoNormal">Truncation isn't a "problem" (for the full-rankers) as an "offensive
strategy". The problem is that it
isn't fair to the sincere truncators.</p>
<p class="ecxMsoNormal"><br></p><p class="ecxMsoNormal">[endquote]</p><p class="ecxMsoNormal"><br></p><p class="ecxMsoNormal">I answered that in the paragraph that you quote next.</p>
<p class="ecxMsoNormal"> </p><pre>><i> How does A lack legitimacy? Among the candidates not majority-defeated, A
</i>><i> has more favoriteness-supporters than any other candidate.
</i>
Translation: "I love this arbitrary algorithm, so any winner it produces
is by definition legitimate."</pre>
[endquote]<br><br><p class="ecxMsoNormal"><br></p><p class="ecxMsoNormal"><span style=""></span>Chris’s
interpretation loses something in the translation :-)</p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">Someone is confused. </p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">I was answering a claim that MDDTR’s way of choosing<span style=""> </span>lacked legitimacy, justification or rightness.</p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">So forgive me if, to that end, I mentioned MDDTR’s way of
choosing :-)</p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">So then, how wrong, illegitimate or unjustified is MDDTR’s
way of choosing?:</p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">I’ll say this again: A majority has the power to get its
way. So that it won’t have to do so by undesirably drastic strategy, it’s
desirable that the method itself enforce majority rule in some way. Different
methods do that in different ways. One way, not the only way, would be to
listen to people when they say that they’d rather have x than y. There is
someone more preferred than y, by a majority of the voters. One way for a
method to respond to that statement (but not the only way) would be to
disqualify y. That’s what MDDTR does.</p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">Now, the question is: How to choose among the undisqualified
candidates?</p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">Again, there are many good ways, many standards. Here’s an
obvious standard: Act on the fact that more people want x as favorite than want
y as favorite. That isn’t the only way of choosing, or the only right way of
choosing. </p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">As I’ve said, by itself, as a whole method, that standard
wouldn’t be enough, because it doesn’t provide majority-rule protection. But
MDDTR’s first stage, the majority-defeat-disqualification, accomplishes that. </p>
<p class="ecxMsoNormal"> </p><p class="ecxMsoNormal">Chris continued:</p><p class="ecxMsoNormal"><br></p><pre>A's win lacks legitimacy simply because there is another candidate that
was vastly better supported on
the ballots.</pre>
<p class="ecxMsoNormal"><span style="">[endquote]</span></p><p class="ecxMsoNormal"><span style=""><br></span></p><p class="ecxMsoNormal"><span style=""> </span>Oh, so now we
must do the election by Plurality’s standard :-)<span style=""> </span></p>
<p class="ecxMsoNormal"> </p><p class="ecxMsoNormal">Chris continued:</p><p class="ecxMsoNormal"><br></p><p class="ecxMsoNormal">If we add between 2 and 21 ballots that plump for A, then C's
"majority-defeatedness" goes away and
the winner changes from A to C, another failure of Mono-add-Plump</p>
<p class="ecxMsoNormal"><br></p><p class="ecxMsoNormal">[endquote]</p><p class="ecxMsoNormal"><br></p><p class="ecxMsoNormal">Perhaps Chris has forgotten that I answered that last
time he said it. We’ve already been over that, and I’ve replied regarding the
Mono-Add-Plump criticism of MDDTR. </p>
<p class="ecxMsoNormal"> </p><p class="ecxMsoNormal">Chris continued:</p><p class="ecxMsoNormal"><br></p><p class="ecxMsoNormal">If we nonetheless accept that C but not A should be immediately
disqualified, electing the undisqualified
candidate with the most top-ratings is just another arbitrary feature of
the algorithm.</p>
<p class="ecxMsoNormal"><br></p><p class="ecxMsoNormal">[endquote]</p><p class="ecxMsoNormal"><br></p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">This from someone who has just finished advocating Plurality’s
standard :-)</p>
<p class="ecxMsoNormal"> </p><p class="ecxMsoNormal">Chris probably doesn’t know what he means by
“arbitrary”.<span style=""> </span>As I already said, each
method uses different ways of choosing, judging by different standards. That’s
why they’re called “different methods”, you know. </p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">One could come up with all sorts of competing standards, and
it could be argued that the choice between them is arbitrary,<span style=""> </span></p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">There’s certainly obvious and undeniable justification in
preferring the election of someone who is favorite to more people.</p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">Then why don’t we just keep<span style="">
</span>Plurality, or (along with Chris) adjudicate the ABE<span style=""> entirely </span>by Plurality’s standard?</p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">…Because we want majority rule, in some form, that’s why. A
good reason for wanting that is to avoid the strategy problems that result when
the method doesn’t, in some way, honor majority rule. One way to do that is to
disqualify majority-defeated candidates. That isn’t the only way.</p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">Other good methods implement majority rule in different
ways. MMPO, MDDTR, MTAOC, and MMT do so in their own different ways, via
different rules. But doing so in some way is necessary in order to avoid the
worst strategy problems.</p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">Anyway, not knowing exactly what Chris means by “arbitrary”
I’ll say that I didn’t choose MMPO, MDDTR, MTAOC and MMT arbitrarily. I chose
them for their properties.</p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">In the ABE, I’m not saying that A must win, though I prefer
that outcome. If C wins, because a majority against C fail to mutually
co-operate, I have no objection to that. That’s one of the solutions to the
ABE. MTAOC and MMT solve it in that way.</p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">In other words, not recognizing one-sided “coalitions” is
one solution to the ABE.</p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">Or, alternatively, make it that one-side is all that is
needed to define a majority and assure that the winner must come from that
majority. MMPO and MMT do that. But don’t use that majority support, the
support that makes the winner be one of the favorites among that majority,
against the candidate(s) of the people who gave the support. Use any other
reasonable way to choose among the favorite candidates among that majority of
the voters.</p>
<p class="ecxMsoNormal"> </p><p class="ecxMsoNormal">Chris continued:</p><p class="ecxMsoNormal"><br>Why that candidate and not the one that is most approved? Based on the
information actually on the ballots,
no faction of voters has a very strong post-election complaint against B.</p>
<p class="ecxMsoNormal"><br></p><p class="ecxMsoNormal">[endquote]</p><p class="ecxMsoNormal"><br></p><p class="ecxMsoNormal"><br></p>
<p class="ecxMsoNormal">I’m not saying that the approval numbers themselves
argue against a win by B.</p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">But, when B wins--because the majority-support that ensures
a win in {A,B} is also naively, mechanically and crudely used for determining
_which_ {A,B} member should win, that means that, within that majority, the
helping side loses. I suggest that that isn’t the message that we want to send
to people wanting to help support the {A,B} majority: I’m referring to the
message: “You help, you lose”.</p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">Yes, Chris said that maybe the B voters might really not
like A better than C, and that the approval numbers themselves don’t</p>
<p class="ecxMsoNormal">argue against electing B.</p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">And I’m saying this:</p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">While it’s necessary for a method to honor and enforce
majority rule, that isn’t enough. It’s better if the method doesn’t deter
intra-majority-support and coalition. If it does, then the method’s
majority-rule protections often can’t be used.</p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">For that reason, I suggest that “You help, you lose” isn’t
what we should want the method to say to people who’d like to give support for
a majority.</p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">As I said, there are two solutions:</p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">One: The method doesn’t recognize one-sided coalitions;</p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">Two: Even one side, among two factions in a majority of
voters, can, by helping the other side, ensure that one of that majority’s
candidates wins.<span style=""> </span>…ensure that the
winner must come from {A,B}—but that majority support isn’t counted against
those who give it, when choosing among</p>
<p class="ecxMsoNormal">The favorite candidates among that majority. Some other
method is used for that choice.</p>
<p class="ecxMsoNormal"><br>
If there are two such candidates, and we want to choose between them other than
by “You help, you lose”, then how should we choose?</p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">The size of the factions in the majority, the number of
people considering a candidate their favorite, is an obvious way. And no, that
isn’t “arbitrary”.</p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">MMPO, like MDDTR, uses solution number two. One faction of a
majority, one helping faction, can, by itself, establish and define a majority,
ensuring that the winner comes from among the candidates who are favorite among
that majority of voters. </p>
<p class="ecxMsoNormal">In the ABE, that means ensuring that the winner comes from
{A,B}.</p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">Of course MMPO doesn’t explicitly refer to majority. But if
A and B’s supporters add up to a majority, they can give a stronger defeat to
the other candidates than the other candidates can muster. So, without
explicitly mentioning majority, the effect is the same. One faction of the
majority can unilaterally make the winner come from {A.B}, by supporting the
other faction’s candidate. One helping faction can establish the majority’s
win. </p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">How should MMPO choose the winner from the favorite
candidates among that majority? Not identically with MDDTR (which is why we
call them different methods), but nevertheless plausibly and justifiably. </p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">Again, the choice shouldn’t (for strategy reasons described
above) be made by using the helping faction’s majority-support against it.</p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">Least maximum pairwise opposition. The candidates other than
those of the majority aren’t going to have that. Someone among the candidates
favorite among that majority will have it. If two of those are tied for least
maximum pairwise opposition, then it isn’t grossly and blatantly unfair :-) to
look at the tie-members _next-to-maximum_ pairwise opposition, as does MMPO2.</p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">The point is that the choice among the favorite candidates
of that majority isn’t made by using the helping faction’s majority-support
against it. </p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">So, the choice between the two methods MMPO and MDDTR,
versus the two methods MMT and MTAOC is:</p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">One: Do we want one-sided support within a majority to be
able to establish the majority and its win? …but not be used against those
giving it?</p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">Two: Or do we want to not recognize one-sided coalitions?</p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">Solution One, when it explicitly speaks of majority-defeat,
allows the fallacious criticism involving Mono-Add-Plump.</p>
<p class="ecxMsoNormal">And when it doesn’t, comparing maximum pairwise opposition
that needn’t be of majority-magnitude, it can elect C in</p>
<p class="ecxMsoNormal">Kevin’s MMPO bad-example, an outcome that is opposed by some
people here due to aesthetic impressions.</p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">I’d hoped that the latter solution would avoid both of those
nonproblems, to avoid confused or dishonest criticism from public proposal
opponents. Regrettably, such methods still “fail” Mono-Add-Plump. (But MMT2
does not fail FBC).</p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">But that “failure” of Mono-Add-Plump, in MMT and MTAOC, is
more difficult for opponents to try to sound convincing about. I’ve already
discussed that. </p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">Apparently MMMPO avoids both of those fallacious criticisms
mentioned above.</p>
<p class="ecxMsoNormal"> </p>
<p class="ecxMsoNormal">Mike Ossipoff</p>
<p class="ecxMsoNormal"> </p>
</div> </div></body>
</html>