[EM] Oops! Markus explained it, I missed it. No repetition today.

[MIKE OSSIPOFF]

I'm sorry! Because Markus had been repeating things, I must have
not thoroughly read one of the paragraphs in his most recent posting.
I thought that I did, but I must have missed that sentence, where
he stated that the assumption is that the voters report vN-M
utilities, sincere or not, and then the voting system takes from
those that information that it needs, and would normally get from
its own balloting procedure.

So I take back the statement that Markus didn't explain it.

But my criticisms of those assumptions mostly still remain valid.

My answers to some of Markus's statements are different based on
what I've just noticed, though.

I still say that it's a contrafactual assumption. Why assume that
people vote ratings, and that the voting system takes from them
the information that it needs, when we could instead just say that
the voting system collects the kind of input that it actually does
collect when in actual use??

Also, I still ask how it would be applied to Approval and single-winner
Cumulative. If it can't be applied to them, then its value & meaning
are seriously compromised. I suspect what the answer will be. Tell
me if I'm correct: The assumption is that the ballot is marked as
it would be for optimal 0-info strategy, based on the ratings that
the voters are assumed to have cast.

Now that's a lot of questionable assumptions. That it's 0-info, when
we know that our elections are not 0-info. That voters vote a certain
specified strategy in nonrank methods.

Markus invited me to suggest another concept for balloting for
method definitions, and now I assume that he meant for the purpose
of applying criteria.

Yes I will. I have 2 answers. One is the same as before. We can
just assume that the method's own balloting system is used. I've shown
how that works fine with all the criteria. I've rewritten Condorcet
& related criteria so that they apply fairly, reasonably & naturally
& seamlessly to all methods.

What would by my way of solving the problem that the assumptions that
he describes are intended to solve. Evidently the purpose of Markus's
assumptions is so that criteria will apply to all methods seamlessly.
But it's an awkward patchwork mess, forcing us to say that it's a
0-info election, forcing us to interpret the voters hypothetical
ratings so as to vote optimal 0-info strategy with the method's
own balloting system. Requiring a bizarre false assumption about how
voters vote.

Seamless applicability to all methods is only a problem with some
criteria, such as Condorcet's Criterion, Condorcet Loser Criterion,
Mutual Majority Criterion, Majority Loser Criterion, Beatpath GMC,
and maybe a few others. Oh, and SFC & GSFC too.

Ok, my solution? For those criteria, we need only specify that some
voters have certain sincere preferences, and stipulate that they
vote sincerely. In the case of CC, that's all the voters. In the
case of SFC & GSFC that's only some of the voters.

Sure, I too am assuming something that may not be true, when I
assume sincere voting. But in the case of SFC & GSFC that makes
sense because the freedom to vote sincerely is what the criteria are
about. In the case of CC, it makes sense too, largely for the same
reason. If there's a SCW, then he should win if we all vote sincerely.
That's really more basic to the reason for CC than saying that
someone who pairbeats everyone should win. In any case, it's just
as good, with CC.

So that's my 2nd answer to Markus's question about what I'd propose
instead, if he meant what would I propose to solve the problem that
his assumptions are intended to solve.

I should add that right now SFC & GSFC are written in a different
way. The way I described above would be neater, but the way I've
written them is perfectly adequate. I did something that would ordinarily be 
inexcusably high-handed and arbitrary: I stipulated
that the method is a rank method. That's still another solution--
adding that to those criteria.

SFC & GSFC could easily be written with the fix that I described above.
But, for those criteria, the arbitrary fix is ok too. Because SFC
& GSFC are intended to be about complete freedom to sincerely express
all our preferences. So when I unobtrusively stipulate rank balloting,
that doesn't seem inexcusable. Additionally, I do it an a way
that _is_ unobtrusive, and which, in fact, serves to clarify the
purpose of the criterion. Looking at the wording, it looks as if
that's the only purpose of that sentence of the criterion, whereas
actually it has the important material import of stipulating rank
balloting.

Let me use SFC (because it's briefer) to illustrate the difference:

Wording with the fix I describe here:

If no one falsifies a preference, and if a majority of all the voters
prefer the SCW to candidate B, and if they vote sincerely, then
B shouldn't win.

[end of definition]

Wording that I've been using:

If no one falsifies a preference, and if a majority of all the voters
vote the SCW over candidate B, then B shouldn't win. The members of
that majority should be able to sincerely rank all the candidates
[or it could say "express all their pair-preferences] without
causing a violation of the above requirement.

[end of definition]

That last sentence appears as a redundancy that does a good job
of telling the reason for the criterion. Actually it serves the
material purpose of stipulating rank balloting, in an unobtrusive way.

No doubt the version that I wrote first here is better, but I feel
that the 2nd one is adequate.

Oh, and BC needs that fix too. Well I mean it could use it. But
it doesn't really _need_ it, because BC isn't a primary criterion.
Its only purpose is for a convenient test of compliance with the
majority defensive strategy criteria. Since those are only met
by rank methods anyway, and since BC is only for a 1-test determination
for those 4 criteria, it seems perfectly ok to simply stipulate
that the method must be a rank balloting method, for BC. Or, of course,
BC could be made neater, not needing that stipulation, with the fix
that I describe here.

Markus asked me why my solution is better, and I've told in this
letter why I claim that it's better.

Mike Ossipoff


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