[EM] Re: Approval doesn't meaningfully meet Majority or Mutual Majority.

MIKE OSSIPOFF nkklrp at hotmail.com
Sun May 1 22:52:48 PDT 2005


I'd said:

>I claim that my PMC gives answers more in accord with the intent of the 
>majority criterion than does FHC or the original votes-only MC.

You reply:

	I disagree with that claim. Here is your PMC...
Preference Majority Criterion (PMC):

>Preference Majority Criterion (PMC):
>A method fails PMC if it's possible to contrive a configuration of 
>candidates, voters, and voter-preferences such that a set of voters 
>consisting of more than half of the voters prefer X to each of the other 
>candidates, and it isn't possible to contrive a votes-configuration such 
>that everyone votes sincerely and X wins.


>If a set of voters consisting of more than half of the voters prefer X to 
>each one of the other candidates, then they should have a sincere way to 
>elect X.

I reply:

"Or"? Which is it?: Are you saying that I define PMC in two ways, or are you 
saying that you aren't sure which definition is my definition of PMC.

Would you like me toi give you a clue?: When I posted the 2nd one, I said 
that it replaces my earlier definition.

	This is not a meaningful way to do preference criteria for approval
voting, at least not for criteria like majority, mutual majority,

I reply:

1. You shouldn't have different versions of a criterion for different 
methods. You should use criteria that can meaningfully and usefully be 
applied to all methods.

2. Maybe you should talk about one criterion at a time. Maybe you could tell 
of your objections to my Condorcete's Criterion and Mutual Majority in a 
different posting, so as to discuss one thing at a time.

3. Approval fails my Condorcet's Criterion and my Mutual Majority.

4. But don't hesitate to say why you think that my criteria aren't the 
meaningful way. I've often suggested that it would be better for you to look 
over what you're about to send before you send it, so that you won't make 
statements like that, which you can't defend.

You continue:

, etc. Consider that if you write preference criteria for
approval this way, approval once again passes almost anything, as with the
votes-only criteria.

I reply:

Approval doesn't pass any of my preference criteria except for PMC, FBC, and 
WDSC. Approval fails SFC, GSFC, SDSC, Condorcet's Criterion, Smith 
Criterion, Condorcet Loser, Mutual Majorilty, etc., as I define those 

So, by "almost anything", did you mean three out of ten? :-)

Approval passes some criteria and fails others. Amazing.

You continue:

	For example, I'm pretty sure that approval passes "preference" Condorcet
criterion, if you word it this way.


But I don't word it that way. Here's the preference Condorcet's Criterion:

If there's a CW, and if everyone votes sincerely, then the CW should win.

[end of Condorcet's Criterion definition]

James, I've posted that definition many times, and it's at the barnsdle 

You continue:

	Do you really think that it is meaningful to say that approval passes the
Condorcet criterion?

I reply:

No, but of course that doesn't stop you from saying that it does.

You continue:

Similarly, I
assert that there it is not meaningful to say that approval passes the
majority or mutual majority criteria.

I reply:

Mutual Majority Criterion (MMC):

If a set of voters consisting of more than half of the voters prefer all the 
candidates in set S to all the other candidates, and vote sincerely, the 
winner should be from set S.

[end of MMC definition]

I should probably instead say "No candidate outside S should win".

Either way, Approval doesn't pass.

You continue:

	These sort of criteria (i.e. majority, mutual majority, Condorcet, Smith)
aren't about whether the "correct" candidates *can* always win given
*some* sincere vote-configuration of any preference ordering; they're
about whether the "correct" candidates *will necessarily win* given *any*
sincere vote-configuration of any preference ordering.

I reply:

What is a vote-configuration of a preference ordering??

Condorcet's Criterion and the Smith Criterion are usually about votes-only. 
I've told what's wrong with that, and why my preference versions of those 
criteria better comply with the intent of those criteria.

Mutual Majority is about what I say it's about, because I defined it. Well, 
it's based on a criterion of Bruce Anderson, and I must admit that I don't 
remember whether his was votes-only or preference. If it was preference, 
however, it left out the necessary stipulation about how voting is based on 

And, as I said, my MMC definition is as a preference criterion, a criterion 
that Approval fails.

Yoiu're making a typically large number of mis-statements in this posting. 
You asked me if I would please state some specific mis-statements of yours. 
There are plenty of them in this posting that I'm replying to.

You continue:

	Approval is simply not designed to meet any majority criteria.

I reply:

Did Approval's modern 1st proponent, Robert Weber tell you that? :-)

This is a long posting, so I'll reply to it in two parts. This is part I. 
Part II will be along tomorrow, or soon after.

Mike Ossipoff

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