[EM] Majority winner set

[MIKE OSSIPOFF]

Markus said:

you wrote (21 Nov 2000):
 > Plurality doesn't have rank balloting. Plurality isn't just a
 > count rule to be applied to rank-ballots. Plurality, like any
 > voting system, is a combination of a balloting system and a
 > count rule.

I don't agree with you that the ballot design is a part of the
election method. To my opinion, the ballot design --especially
questions like (1) how the candidates have to be sorted on the
ballot, (2) whether there should be party affiliations, (3)
whether there should be write-in options, (4) whether there
should be a NOTA option, (5) what should be done when NOTA is
chosen or (6) whether the ballots should be counted by hand or
by computer-- is a part of the electoral law but not of the
election method itself.

I reply:

I didn't say that the shape, size & color of the ballot, and the
order of the candidates on the ballot, and whether there should be
party affiliations, and whether there should be write-in options,
and whether the ballots should be counted by hand or by computer--
is part of the voting system. Also, adding NOTA to the alternatives isn't 
part of the voting system either, as you said.

Those things are details of balloting, but they aren't part of the
intrinsic balloting system any more than they're part of the voting
system.

Now I'll tell you something that _is_ the intrinsic balloting system:

The basic rules for how voters may express preferences for candidates,
disregarding size & shape of ballot, which candidates are allowed on
the ballot, in what order the candidates are listed, etc.

Either you're real sloppy today, or you're being a little less than
honest with us
, if you're claiming that the basic rules governing
how voters may express preferences for candidates isn't part of the
voting system. Has it occurred to you why they call it a _voting_
system? "Doo...oing" :-)

Markus continues:

However, I don't have the impression that your statements have
anything to do with majority winner sets or beat path GMC.

I reply:

Wrong. My initial comment was that your definition of Beatpath GMC
was worded in such a way that no method can pass it. Then you changed
your definition from being about preferences to being about votes.
Then I told you that, by your new definition, Plurality meets
Beatpath GMC.

Then, wanting to be nice, I said that it isn't just Beatpath GMC,
but also Condorcet needs the fix that I described. Then I began
using Condorcet's Criterion as an example, because it's a simpler
criterion, and a much more widely-used one than Beatpath GMC.
But the discussion was still about Beatpath GMC, and whether or
not it's met by Plurality, and whether your newest statements about
BPGMC make any sense.

By the way, you never did say whether Condorcet's Criterion, according
to your way of looking at it, as met by Approval. While you're at
it, you can tell me whether it's met by Cardinal Ratings and
single-winner Cumulative.

As I said, the fact that you can't answer that shows that your
definitions of CC & BPGMC don't work.

Look, it just fortuitously happens that a ranking reveals a 1st
choice, and so you can call that 1st choice the Plurality vote.
But it isn't always the case that a balloting system for one type
of voting system can be counted by another voting system's count
rule. To base a criterion's definition on an attempt to do that
is silly.

If you wanted CC & BPGMC to mean what you're saying they mean, then
you ought to say what you mean when you write the definition.
You should say, for example: "If we have the voters rank the
candidates, and then we count those rank ballots according to
a certain voting system's count rule, then..." If you don't say what
you mean when you write the definition, then people have no way of knowing 
what you man. Anyway, don't bother rewriting your BPGMC definition in that 
way, because it wouldn't make any sense, as I've
already explained.

Mike Ossipoff





Markus Schulze



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