[EM] Chris: Plurality & Markus' copied criterion

[MIKE OSSIPOFF]

Chris--

You said:

As I understand it, there are only three basic types of voting methods:
(1)ranking methods (like IRV, Borda, and First Preference Plurality)
(2)rating methods (like Approval)
(3)hybrids of 1 and 2 (like Approval Elimination Runoff, and Condorcet 
completed by Approval).

I reply:

Maybe, and I suppose Plurality could be considered to be in either (1) or 
(2), not as a full member, but as a limited specail case. Most would 
probably consider Plurality a rating method, a point system, in whidh the 
voter is allowed to give 1 candidate 1 point, but must give 0 points to the 
rest.

But it seems pointless to try to write a list of balloting types that 
include all methods. My criteria say nothing about balloting type.

You continued:

Since giving a higher rating to A than to B in a rating method implies that 
the voter ranks A over B,
and ranking A over B in a ranking method implies that the voter rates A 
higher than B, I don't see
any real point in your disinction between "rank over" and "vote over".

I reply:

I don't deny that we could agree that, for Pluraltiy, "rank over" could be 
interpreted as "vote over". My point was just that the criterion didn't 
_say_ that. When it specifies ranking, maybe it is intended to apply only to 
rank methods. And no, Plurality isn't a rank method (as you say below in 
this message).

You continued:

Later in the same message you wrote:

"Let me copy your criterion definition here:


    "Any ordering of the alternatives must be an admissible vote,
    and if more than half of the voters rank y over x and x no higher
    than tied for bottom, then x must not be elected."

Say the method is Plurality, and that more than half of the voters vote for
y. Then x won't win.

Therefore Plurality meets your criterion."

In the first place Plurality doesn't normally allow equal first preferences 
(the version that does I
have seen referred to as "Single-seat Cumulative Voting"), so therfore it 
doesn't strictly meet
"Any ordering of the alternatives must be an admissable vote".

I reply:

Ok, you've suggested another interpretaton of "Any ordering of the 
alternatives must be an admissible vote".

That sentence could mean that the criterion only applies if every voter 
votes admissibly. A requirement on the voting, not a requirement on the 
method's rules.

You're interpreting that sentence to mean that the methods' rules must admit 
any ordering of the alternatives.

By your interpretation, Plurality fails the criterion, because it doesn't 
meet that rules-requirement.

By the other interpretation, Plurality passes the criterion, because there's 
no such rules-requirement.

So you've made a good point: It can't be determined from the wording whether 
or not Plurality passes that criterion.

Does that mean that that criterion is equivalent to SDSC? No, because of the 
unproposable ranked Plurality that you define below. That method passes the 
criterion that Markus posted, but doesn't pass SDSC. And letting that 
criterion pass is contrary to the motivation that Markus posted. So Markus 
was still wrong.

You continued:

(BTW,"admissable" means "capable of being allowed;permissible", in other 
words eligible to be counted
according to the rules of the method.)

I reply:

Ok. It had seemed to me that an "admissible ballot" had to also not be a 
dominated strategy for the person who voted it. But maybe it's a different 
term, other than "admissible" whose meaning  combines 
balloting-rules-compliance and undominatedness.

You continued:

In the second place,in ranked methods such as First Preference Plurality,to 
"vote for y" means to rank
y first and is not the only way to "rank y over x".

I reply:

It sure is.

You continued:

Take this example:

40:x>y=z
25:y>z>x
35:z>y>x

"More than half the voters rank y over x, and x no higher than tied bottom" 
and yet x is elected.
Therfore "Plurality" fails this criterion.

I reply:

A method is a combination of a balloting system and a count rule. Plurality 
doesn't collect rankings. The method you're talking about is not Plurality.

You can re-define Plurality in that way if you want to, but, in any country 
that uses Plurality, there isn't an elections department that would agree 
with you. I re-emphasize that you or anyone else, of course, can re-define 
Plurality, or anything else, in any way that you want to. You aren't wrong 
to do that.

I merely point out that your definition of Plurality is different from the 
one used by election departments that administer Plurality elections. Which 
doesn't mean that you're wrong to define it differently.

You continued:

It is true that the lower prefences are ignored by the method and so as a 
convenience to all concerned
they are not entered on the ballots

I reply:

No, not just as a convenience--as a requirement. Enter your 2nd & 3rd 
choices on your Plurality ballot, and it will be thrown out. The method 
doesn't allow complete rankings. You yourself defined  an admissible ballot 
in terms of what the method allows. And you know that complete rankings are 
inadmissible in Plurality, and that therefore a method that collects 
complete rankings is not Plurality.

Unless you use a new definition of Plurality.

, but that is not relavent to our analysis.

I reply:

What's relevant is that Plurality doesn't allow complete ranking. You 
yourself spoke of what kind of vote is admissible in a method. What kind of 
votes is admissible is part of a method's definition. You said so yourself 
when you defined "admissible".

You continued:

If the rules stated
"voters rank the candidates, no equal first preferences allowed, and the 
winner is the candidate with
the most first preferences", wouldn't that be a "rank method"?

I reply:

Of course. And it wouldn't be Plurality, do to different voting 
admissibility.

You continued:

A method that is exactly equivalent to
a rank method, in my book *is* a rank method.

I reply:

No, not at all. Anything can be "equivalent" to anything, depending on what 
you choose to look at.
Some would say that, in a certain particular regard, a doughnut is 
equivalent to a teacup. But if you go into a doughnut shop and ask for a 
doughnut, and  are given a teacup, you wouldn't agree that a teacup is a 
doughnut.

Your unproposable method is "equivalent" to Plurality in the sense that both 
only count indicated favorites. But because different voting is admissible 
in the 2 methods, they are not the same method, in keeping with your own 
definition of "admissible".

"Equivalent to [in some particular specified regard]"  most definitely does 
not mean "is".

You continued:

As Alex Small put it (Tue.Jul.15,03):
"Plurality does not _need_ preferential ballots, but the results of a
plurality election could be inferred from preferential ballots:  Count the
number of voters who ranked each candidate first.  If the results of an
election method can always be uniquely determined from preferential
ballots, then the method is equivalent to a preferential method

I reply:

"Equivalent to [in some regard]" is not the same as "is".

Now, first saved Markus, but then you let him back down.

You saved him when you pointed out that _maybe_ , depending on 
interpretation, Plurality fails the criterion that Markus posted. So I have 
to agree that it isn't possible to establish whether or not Plurality passes 
that criterion.

But you let him back down when you mentioned your unproposable ranked 
Pluralitiy. Because that unproposable method passes the criterion that 
Markus posted, but fails SDSC, and fails the requirement that Markus's own 
"motivation" calls for.

Mike Ossipoff

_________________________________________________________________
Choose now from 4 levels of MSN Hotmail Extra Storage - no more account 
overload! http://click.atdmt.com/AVE/go/onm00200362ave/direct/01/