[EM] Approval & MMC, contd.

Michael Ossipoff email9648742 at gmail.com
Thu Jun 6 12:50:13 PDT 2013

Mr. Lomax says:

Michael has a bit of misunderstanding floating in his head about this.

When someone is as vague as Mr. Lomax, no one can be blamed for not
knowing what he meant.

 I pointed out that definitions have been manipulated with certain
voting systems criterion, in general, in order to generate "failures."
And, of course, they can be manipulated in the other direction. This
was on the Center for Election Science mailing list, which Michael
just unsubscribed from, saying there were no open issues.
So he brings one here? Ah, well, to each his own.

Yeah i decided to answer Mr. Lomax's confusion about Approval & MMC,
though of course I didn't expect to thereby help his confusion.

 He did clearly misunderstand the issue.

Forgive me if I misunderstood what Mr. Lomax meant :-)

 First of all, the definition of "sincere vote" was not the issue.

Sure it was. Mr. Lomax said that I contrived to define sincere voting
so as to make Approval fail MMC.

But now Mr. Lomax apparently wants to change what he said, after
finding that it didn't work.

In Approval Voting, there is a large set of possible sincere votes.

That's right. If some voters prefer A>B>C, and others prefer B>A>C,
then we all agree that it would be sincere in Approval for the A
voters to approve only A, and for the B voters to approve only B.
Therefore with all of the A voters and B voters voting sincerely, C
can win, even though the A voters and B voters comprise a majority.
That's why and how Approval fails MMC.

In Approval, those voters have a strategy decision that they need to
make. 'Should I approve A, in addition to B, to reliably defeat C, or
should I just approve B, so that I'm doing the best I can in the
contest between B and A?"  In the 1st Approval election, maybe the A
and B voters would approve both, but soon the B voters might want to
find out if B could win. Maybe they aren't defecting. Maybe they just
want to find out if B has a majoriity--a legimate reason to approve
only B.

In Beatpath, IRV or Woodall, those B voters can find that out while
still supporting A, in case B alone doesn't have a majority.
Therefore, in Beatpath or Woodall, the B voters and the A voters don't
have the strategy decision that they'd have to make in Approval.

With methods that meet MMC, you can vote for, and benefit from voting
for, any majority that exists in your ranking, for some higher ranked
set over some lower ranked set, wherever the dividing line is that
demarks such a higher-ranked majority.  That's why I said that
MMC-complying methods guarantee automatic majority rule enforcement,
something that Approval most decidedly does not do, for which reason
Approval requires strategy decisions that Beatpath, IRV, Woodall,
Benham, and Schwartz Woodall don't require.

That's what MMC measures for. That's what Beatpath, IRV, Woodall,
Benham and Schwart Woodall pass, and Approval fails. The
above-described strategy problem is the real-life practical
consequence of Approval failing MMC.

As I said, MMC measures for a genuine tangible advantage, in spite of
Mr. Lomax's long, unintelligible, and thoroughly-confused ramblings.

Rather, the issue is about the question of whether or not a vote that
does not express a preference that is at the foundation of a voting
system criterion satisfies the precondition for applying the test of
the criterion.
Michael, here, did not give the relevant definitions.

I gave a very thorough definition of MMC, and I've told why MMC
measures for something of practical importance, offered by Beapath,
IRV, Woodall, Benham and Schwartz Woodall, but not by Approval.

That is irritatingly typical. There were two definitions examined:
>From Wikipedia:

 The mutual majority criterion is a criterion used to compare voting
systems. It is also known as the majority criterion for solid
coalitions and the generalized majority criterion.

Incorrect. Wikipedia is mistaken. I introduced MMC. I wrote it, and
named it. Its definition is as I specified. the Majority Criiterion
For Solid Coalitions (MFSC) is defined quite differentlyl from MMC.

The criterion states that if there is a subset S of the candidates,
such that more than half of the voters strictly prefer every member of
S to every candidate outside of S, this majority voting sincerely, the
winner must come from S.

Here "prefer...to..."  is being used to mean "vote...over...".  Fine,
just so we agree on what is meant.

This is similar to but stricter than the majority criterion, where the
requirement applies only to the case that S contains a single
The Schulze method, ranked pairs, instant-runoff voting, Nanson's
method, and Bucklin voting pass this criterion.

So do Approval and Plurality. MFSC doesn't measure for the automatic
majority-rule advantage that I discussed above. No problem, just so we
all understand the difference between MFSC and MMC.

The plurality vote, approval voting, range voting, the Borda count,
and minimax fail this criterion.

Incorrect. Approval and Plurality pass MFSC.

For an organization that prides itself on reliability, the wikipedia
can be quite sloppy and incorrect.

The point I have made is that "strictly prefer" must require that the
voter actually vote the preference.

Mr. Lomax wants to make an issue of that, implying that it's something
that I've missed, or that it's the crux of his disagreemnt with me.
Actually, I've acknowledged from the start that that definition of
MFSC is using "prefer...to..." to mean "vote...over...".

Otherwise we have what I call Space Alien Failure. Under Space Alien
Failure, Plurality fails the Majority criterion, because the voter,
being informed by Space Aliens that their favorite cannot win the
election, vote for someone else. No, the voter must *actually vote the
preference* to set up the condition for the test.
Otherwise we are led to a series of preposterous conclusions.

I won't pretend to know what that means. If Mr. Lomax means that
"prefer...to..." is being used to mean "vote...over...", in that
wikipedia definition of MFSC, then he's correct. As for the part about
Space Aliens, Mr. Lomax isn't being entirely clear with us about what
he's trying to say.

The term "stricly prefer" is ambiguous, unless we interpret "prefer"
as "act to prefer."

Yes, we've established that the wikipedia definition of MFSC uses
"prefer...to..." to mean "vote...over...".   :-)

With Approval voting, a voter acts to prefer A to B by voting for A
and not for B. The voter acts to prefer a set by voting for every
member of the set and not for every non-member.

Yes, I suggest that we've established that that's what wikipedia means
in their MFSC definition, when they refer to preferring A over B, or
preferring one set to another.
By "prefer...to....", they mean "vote...over...".   Haven't we already
established that?  :-)

I'd said:

One way to answer his objection is to ask him to compare Approval with
methods that meet MMC, and ask himself if he notices a difference.

 That's not an answer, it's a socratic question, and it requires me to
study matters where I have little interest.

It was a demonstration of why it's better to meet MMC than to fail it.
It was a demonstration of what it means to meet or fail MMC.

That was the topic on which Mr. Lomax was posting. He shouldn't post
on what he isn't interested in.

I see no sign that Michael has understood the objection.

Have I not understood what Mr. Lomax was trying to say? Maybe only Mr.
Lomax knows what he was trying to say.

But what he "meant" seems to change, when what he previously meant has
been answered or refuted. That's the nice thing about meanings that
are vague or variable.

I'd said:

The methods that I recommend for the Green scenario, IRV, but
especiallly Woodall or maybe Benham, also are free of chicken dilemma,
and so maybe comparing Approval with them would be unfair--because
we're only trying to show the benefit of MMC.

So then, let's compare Approval with a method that has chicken
dilemma, but passes MMC. Let's compare Approval with Beatpath:

The A voters and the B voters all prefer both A and B to C. The A
voters and the B voters are, together, a majority of the voters.

They are a mutual majority, and {A,B} is their MM-preferred set.

Let's assume that there is no chicken dilemma. The A voters and the B
votes are co-operative and amicable. None of them are inclinded to
defect against eachother. The A voters and the B voters have no
chicken dilemm need to not rank eachother's candidate.

So, voting sincerely, the voting looks like this:


Because the A voters and the B voters add up to a majority, C is defeated.

The A voters and the B voters succeeded in getting a winner from their
majority-preferred set by merely ranking sincerely.

If the A voters are more numerous than the B voters, then A will win
instead of B. The A voters can gain that, while still fully supporting
B againist C.

Can they do that in Approval?

 It's entirely a different question.

...from what? I was merely demonstrating what it means to meet or fail
MMC. with an example.

Approval does not allow ranking beyond two ranks.

...and that contributes to its failure of MMC. MMC describes and
measures for something that is desirable in its own right. MMC wasn't
written to make Approval look bad.Approval fails MMC because of
something valuable that Appproval indeed fails to offer or gurarantee.
  ...something that Beatpath, IRV, Woodall, Benham, and Schwartz
Benhalm guarantee.

The method that is analogous could be Bucklin, which is "instant
runoff approval." That allows ranking. The voters vote the same way as
described above, and the winner must come, under the stated
conditions, from (A,B). Voters may choose to second-preference their
less-favorite, or may drop this candidate to third rank (original
What about raw Approval? What can the voters do?

I'd said:

MMC measures for something of practical importance that Beatpath, IRV,
Woodall, Benham, and Schwartz Woodall have, but  which Approval
doesn't have.

 Michael has a point, but it should not be based on mind-reading.

Any mindreading is in the mind of Mr. Lomax.

Approval  has a strategy need that MMC-complying methods don't have.
MMC measures for that.



It's crazy to compare Approval, a very simple voting system, with far
more complex systems that allow full or enhanced ranking. ----

Nonsense. Simple, nonranked Approval can't do what the better rank
methods can do. For example, they, but not Approval, meet MMC,
conferring MMC's guarantee of automatic majority rule.

Yes it's fair to compare something simple and modest like Approval
with something more deluxe that offers more.

Michael Ossipoff

I trust that I've shown that Mr. Lomax's objections to MMC, to the
extent that we, or even he, knows what he's trying to say, can be

I expect that it won't be necessary for me to continue answering Mr.
Lomax's confusion.

If I don't reply, that won't mean that Mr. Lomax has said something
irrefutable. It will just mean that I've already sufficiently
answered, more than his rambling confusion deserves, and that he's
already showed that he doesn't know what he's talking about, or even
what he means.

Though I reserfe the right to answer if Mr. Lomax says something new
that genuinely calls for a reply, I probably won't reply to Mr. Lomax

Michael Ossipoff

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