[EM] James, 4 April, '05, 0400

[MIKE OSSIPOFF]

James--


I'll adopt your convention of putting the speaker's name before a colon, to 
indicate who said what.
One reason why that's convenient is because many of the "James:"s and 
"Mike:"s are already there before I copy and reply.

Mike (said):

>And
>one way of defining the strength of that majoritly pairwise preference has 
>to
>do with how big a majority that is. Completely arbitrary, of course :-)

James (said):

	Not arbitrary, but also not the only valid way to define it.

Mike:

But, as I already said in the message to which you're replying, it wasn't 
possible to define it in every way, and use all those deinitions when I use 
the term, and so it was necessary to choose just one way to define it.

James:

Another way
to define the strength of a majority preference is the size of the
majority times the strength of the preference on each ballot comprising
the majority. This is the definition given by cardinal weighted pairwise,
and it has an equally valid claim to be a definition of majority
preference strength.


Mike:

If you're talking about majority preference, then you aren't talking about 
majority rule, because my majority rule definition involves majority 
pairwise votes, rather than majority pairwise preferences.

Majority pairwise preferences are used in my definition of defensive 
strategy. For that purpose, I'm interested in how many prefer X to Y, 
because if a majority prefer X to Y, then it's possible to make some 
guarantees about what they won't have to do in order to keep Y from winning. 
Siimple as that. For that purpose, there's no need for me to get into the 
matter of how intensely they prefer X to Y, because the mere fact that they 
all prefer X to Y is sufficient to give them the power to keep Y from 
winning without, with the guarantee that they won't need certain degrees of 
drastic strategy to do so, with complying methods.

That's why I define majority pairwise preferences (MPPs) as I do.

But itsn't it true that majority rule is what you're really more interested 
in here? In that case, you're questioning my definition of majority pairwise 
votes (MPVs) rather than my definition of MPPs.

But it's for a similar reason that I define MPVs in terms of a majority 
voting X over Y, instead of the intensity with which a majority vote X over 
Y. Becasue the mere fact that they vote X over Y makes it possible to say 
things about what should or shouldn't happen. I'm talking about majority 
rule as the term is usually understood and used. If a majority votes X over 
Y, then electing Y violates majority rule, unless that MPV is nullified. And 
what could nullify an MPV other than it being in a cycle whose other MPVs 
are at least as large as it is? Hence my definition of majorilty rule.

Look, you know I have no quarrel with Cardinal Pairwise, and when it saves 
the CW by violating majorilty rule, violating an un-nullified  MPV, that's 
an MPV based on dishonest voting. I completely agree that it's a good thing 
to violate majorilty rule in that instance, via the preference-intensity 
voting that CP collects and uses.

There's no need to quibble about what majority rule means. I'm just telling 
you what it means to most people when they use the term. My defintion merely 
copies the term's accepted meaning.
That's all my defintion attempts to do. I had no intent to write a new 
definition, but rather only intended to put into words the usual accepted 
meaning of majority rule.

James:

	Lately, I have been defining majority rule violation as the selection of
>an option outside the Smith set.
>

Mike:

>The Smith set has nothing to do with majority.


James:

	It has everything to do with majority. The Smith set is the smallest set
of candidates who are preferred by a majority to every candidate outside
the set.

Mike:

No, I'm sorry, but that isn't the definition of the Smith set. There are two 
things wrong with that definition: 1) It speaks of majority; 2) It speaks of 
preference instead of votes.

Here's the definition of the Smith set:

The Smith set is the smallest set of candidates such that every candidate in 
that set pairwise-beats every candidate outside that set.

[end of Smith set definition]

How can any discussion get anywhere when terms are used in a way so 
different from their accepted definition?

Maybe you want "majority" to mean a majority of those voting a preference 
between X and Y. But then "majority defeat" justs becomes another word for 
"pairwise defeat". In other words, majority loses its meaning, the "more 
than half of the voters" meaning that it has in its accepted use. 
Additionally, a set of voters consisting of more than half of the voters is 
a set of voters for whom certain strategies can be guaranteed. That's my 
interest in majority.

James:

If you pick a non-Smith candidate, you are needlessly ignoring a
majority preference.

I reply:

Not at all. Maybe, due to truncation, someone is out of the Smith set 
because of a sub-majority defeat.

James:

Hence it is necessary to chose from the
Smith set in order to guarantee that no majority preference will be
unnecessarily ignored.


Mike:

Not at all, if someone is out of the Smith set due to a sub-majority defeat.

>
James:
>
>I think that the Smith set is the narrowest majority rule
>definition we can make that stands some chance of gaining general
>consensus.
>

Mike:
>...except that the Smith set isn't a majority rule definition.


James:

	Of course it is, in the following sense: If a voting method chooses a
non-member of the Smith set, I say that it has violated majority rule. If
a method chooses a member of the Smith set, I say that it has upheld
majority rule.

Mike:

Oh, ok, if you define majority rule as the Smith set, then, by your 
defintiion, it is. But, by the usual definition of the Smith set, and by the 
accepted meaning of majority, it is not.

James:

If a voting method always elects a member of the Smith set,
I call it a strong majority rule method. I argue that this definition is
meaningful and useful.

Mike:

That definition is completely at odds with the accepted definition of the 
Smith set and the accepted definition of majority.

It's possible to write definitions that don't contradict 
already-widely-accepted definitions.

James, I don't criticize you because you're new to this subject. CP is a 
perfectly good idea, a good Condorcet enhancement, and probably meets the 
criteria that I judge methods by. But, for some reason, in voting system 
discussion, some people new to the subject arrive with some degree of 
arrogance--the notion that they have it right, and that someone else has 
been wrong all this time.

Well, ok, I claim that lots of others have been wrong about some things, but 
I thoroughly defend those claims. All I'm saying, James, is that when you're 
new to a subject, be a little more tentative with your statements. Don't 
express them in the form of assertions that you're sure that someone else is 
wrong. Not till the discussion has gone on long enough for you to be able to 
make such claims with assurance.

Do you see that your definition of the Smith set suggests that you're a 
little premature with your statements about who is wrong?

James:
>
>	I have to object to the defeat strength part of your definition, in part
>on the behalf of cardinal pairwise. Winning votes is surely one way to
>define defeat strength, and it is not a bad one, but I do not accept it as
>the one and only definition
>
Mike:
>I have never said that wv is the only way to define defeat strength.
>Perhaps you would like me to define defeat strength in all of the possible 
>ways. Forgive me, but it seemed best to only define it in one way, and, if 
>it's
>ok with you, I chose wv.

James:

	My contention is that there is no basis on which to define it in only one
way. You can do so if you want, but you shouldn't expect other people to
accept your definition.

Mike:

...then I should define it in every possible way, and, then, when I speak of 
pairwise defeat strength, use every possible definition of it? Does that 
sound to you like a good idea?

What I (would like to) expect others to accept is that wv makes certain 
guarantees about strategy that aren't possible without wv. And that wv 
avoids overruling unnecessarily many individual paiirwise votes, when 
overruling a publicly-voted pairwise defeat. And that the magnitude of a 
majority defeat is most meaningfully measured by the number of people who 
favor that defeat.

But no, I don't expect anyone to accept that wv is the only possible way to 
define defeat-strength, because it obviously is not. The best isn't 
necessarily the only.

Mike:
>You don't say how you'd rather define the magnitude of a majority
>pairwise vote. Margins?

James:

	No. When it comes to choosing an actual method, I prefer the defeat
strength definition that CWP gives. When it comes to defining majority
rule for general purposes, I prefer to leave defeat strength out of the
definition, i.e. to define majority rule compliance as choosing from the
Smith set.

I reply:

I've answered your statement about the Smith set being a majority rule 
definition.

About CP as a way to judge pairwise defeat-strength, fine. Whatever is 
useful. Remember that usefulness is part of the reason I like wv. If CP is 
useful, then it's useful to measure defeat-strength as CP does. I've never 
denied that, and I don't now deny it. Are we aguing about something that 
don't disagree on?

Mike:

>But why is that important to you, how many people accept my definition of 
>majority rule.


James:

	If you don't care if anyone accepts it, why bother posting it on a
discussion list?

Mike:

This is unbelievable. I've just finished telling you, in the message to 
which you're "replying", why I post definitions of terms that I use. But I'm 
going to repeat it again for you, just one more time:

I post definitions of terms that I use because telling what you mean by the 
terms that you use is part of saying what you want to say.

Someoe's acceptance or non-acceptance of those definitions is something 
that, I must admit, had never occurred to me. Tell me if you don't know what 
I mean, but I don't know what it means for you to tell me that you don't 
accept those MPV, MPP, majority rule, or defensive strategy definitions.

Yes, I really should put all these answers into a FAQ, so that I can just 
post the FAQ when these questions and objections are repeated.

James:

By doing so, you are implicitly asking for others'
feedback.

Mike:

I always welcome feedback. But please, out of respect for yourself, consider 
your feedback more carefully.

James:

If you don't care if anyone adopts your criteria, you might as
well not mention them to other people.

Mike:

Wait--were we talking about criteria definitions?  Please note that my 
defensive strategy and offensive strategy defintiions aren't used in my 
criteria definitions. And that my MPV, MPP, and majority rule definitions 
aren't used in my criteria definitins.

Yes, the broad name that I give to my criteria is "defensive strategy 
criteria", and that makes it good to have a definition of defensive 
strategy.

As for caring about if anyone accepts what I say, as a way to decide whether 
to say it, I can't say that I agree with you. I say what I want to say 
because, for some reason, I want to. But, as I've repeated here again and 
again, I'm not interested in the outcome. I couldn't care less what anyone 
else does or doesn't do with anything that I've proposed to them. That isn't 
my department.

Having said that, of course I answer objections to my criteria, because 
that's part of proposing the criteria.

But you aren't, in the message to which I'm now replying, objecting to 
criteria, are you?

But, since you mentioned that subject, here are several grounds on which you 
can object to my criteria:

1. You don't consider important the goal of getting rid of the 
lesser-of-2-evils problem, or the goal of minimizing the need for 
favorite-burial, and other defensive strategies that conceal or reverse 
people's preferences. I'm not being sarcastic here: I've been told by a few 
people on EM that that isn't important to them. Fine.

2. You don't believe that my criteria measure for accomplishment of the 
abovementioned goal, and can tell us why.

3. You claim that my criteria aren't well-defined, and can show us an 
example where, with some method, preferably a proposable method, one of my 
criteria doesn't unambiguously say whether not that method fails the 
criterion in that example.

Go for it.

Mike Ossipoff

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