[EM] Chris reply, 9 Feb. '04, 1048 GMT

[MIKE OSSIPOFF]

I'd defined ROC:

"Plurality is a rank method? Ok, now I'm going to define a new method, which
I call Ranked Ossipoff Choice (ROC).  Here are its rules:

Voters vote rankings. The rankings are collected from the voters. Then I
make the choice, disregarding the rankings.

By your reasoning, that's a rank method too."

Chris replied:

This (Tue.Jul.15,03) quote from Alex Small in the "Arrow's Theorem" thread 
has become more relevant:

"In the formal derivations of Arrow's Theorem that I've seen, an election
method is defined as a mapping from the set of voter preferences to the
set of candidates.  Show me the preference order of each individual voter,
and (barring the case of ties) I'll show you who the winner is.  No
ambiguity."

That definition is good enough for me. "Ranked Ossioff Choice" is not a 
ranked method, because it is
not a method.

I reply:

There's a criterion called the Non-Dictatorship-Criterion. There'd be no 
point having a criterion unless it's possible for a method to fail it. A 
method can fail Non-Dictatorship and still be a method. ROC is a method.

If Alex's quote implies that no method can fail Non-Dictatorship, then 
obviously we've got some disagreement about what a method is.

Alex said that a method is a mapping, but he didn't say that it's a mapping 
that doesn't change.
If it's one mapping today, and another mapping tomorrow, then on any 
particular day, including today,  it's a mapping.

He didn't say that it will always be the same mapping. He just said that 
it's (at any particular time time that we're looking at it) a  [some] 
mapping.

ROC could is a mapping from all the possible configurations of voted 
pairwise comparisons to the set of candidates. But all the configurations 
map to one same candidate--the one that I say they map to in any particular 
election. For any particular election, ROC maps the possible admissible 
configurations of voted pairwise comparisons to the set of candidates--in 
the way that I say it does for that particular election. And, for any 
particular election, I say that every one of the possible configurations of 
voted pairwise preferences maps to a certain particular alternative that I 
specify, for that election.

Besides, I could make a tiny change in ROC: Delete the part that says the 
rankings are ignored, and say that, when I vote, my 1st choice wins. That's 
ROC2. There's nothing in the rules that says I'm not allowed to vote.

That's clearly a mapping from the possible configurations of voted pairwise 
comparisons to the set of candidates. It's just that my preferences are the 
part of that configuration that matter in ROC2.
And that mapping is a constant one.

You said:

You didn't like that Alex quote?

I reply:

Did I say that? I merely corrected 2 statements in it.

Youi quoted me:

"That isn't correct. Voting systems have, as  their input, votes, not
preferences. ...
It's a mapping from the set of all of the  configurations of voted pairwise
comparisons that would be admissible for a given set of voters, to the set
of candidates."

You reply:

Too much clarity and profundity for me to handle.

It isn't quite clear what you're trying to say. Maybe you're saying that it 
doesn't have enough clarity for you and that you don't understand it. But I 
can't help you if you don't tell which part you don't understand.

You quoted me:

"You'll protest that at least Ranked Plurality gets some information from 
the
rankings."

You replied:

Yes, "Ranked" Plurality gets "some" information from the rankings, but the 
point is that it gets
information from NOWHERE else.


I reply:

What part of Alex's statements says that the mapping can't change from one 
election to the next?
The fact that it's a mapping doesn't mean that it has to remain the same 
mapping in a different election. He didn't say anything about whether the 
mapping can change.

Besides, ROC2 doesn't get information from anywhere but the rankings. ROC2 
and Ranked Plurality have much in common: They both get information from the 
rankings, and from nowhere else, but they both disregard most of the 
information in the rankings.

So ROC2 is a better likeness to Ranked Plurality than ROC is. I hereby 
replace ROC with ROC2.

You continue:

"FPP(First-Preference Plurality) is the same as FPTP(First Past The Post): 
it elects the candidate
with the largest number of first-preference votes." Woodall

I reply:

Oh, if Woodall says so, that's different :-)

You continued:

In response to me saying:

For the purpose of rationally analysing voting methods, the fact that 
"different voting is admissible"
is only relevant if that can possibly give a different result. (And then it 
is only interesting if it
makes a different viable strategy available,like equal ranking in RP versus 
equal ranking not allowed
in RP.)
In FPP, the only restriction on vote admissibilty that is relevant is that 
the voter can mark as
favourite one candidate only. Obviously it makes no difference whether 
voters are not allowed to enter
lower rankings or are compelled to enter lower rankings or anything in 
between.

You wrote:
"It makes a difference when the ballot is thrown out because it ranks
candidates. That can change the outcome of the election."

On that logic, a version of Plurality that requires the voter to check a 
single candidate with a tick
is a different method from a version that requires the voter to check a 
single candidate with a cross,
and a version that requires the voter to use a ballpoint pen is a different 
method from a version that
allows the voter to use a pencil, and so on.

I reply:

No. Plurallity is defined as: Each voter votes for one candidate. The 
candidate with the most votes wins. Those variations you describe all fit 
the definition. Your Ranked Plurality fails the definition of Plurality.

Yes, you're going to say that 'Woodall doesn't define Plurality in that way 
:-)

Mike Ossipoff

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