[EM] James--Majority rule definition, 29 March, 0632 GMT

[MIKE OSSIPOFF]

I'd said:

>If a majority prefer X to Y, that's a majority pairwise preference (MPP).
>The strength of that MPP is measured by the number of voters who prefer X
>to Y.

You say:

	Well, obviously that's one way to define the strength of a pairwise
defeat. Margins provides another way, and cardinal pairwise yet another.

I reply:

No, that obviously is _not_ a way of defining the strength of a pairwise 
defeat. It's a way of defining the strength of a majority pairwise 
preference, however.

One way (but only one way :-) of defining a majority pairwise preference is 
as an instance of a majority praeferring one candidate to another. 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 :-)

I'd said:

>
>An MPP for X over Y is outdone if there is a sequence of MPPs from Y to X,
>consisting of MPPs that are all at least as strong as the MPP of X over Y.
>
>To violate majority wishes means to elect someone who has an MPP against
>him
>that isn't outdone.


You say:

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

I reply:

The Smith set has nothing to do with majority.

You continue:

This is close to your definition

I reply:

No. It bears no resemblence to my definition.

You continue:

..., except
that you get more specific by assuming that there is a single normative
definition for "defeat strength"

I reply:

We all have heard that there are other definitions for "defeat-strength". 
Whether they're normative or not, I've told why they aren't as useful for 
meeting criteria about guarantees of minimizing strategy need. And I've told 
why they aren't as good in terms of the goal of not overruling avoidably 
many voters. If saying that something is normative means saying that it's 
what should be, then I've told you why wv is normative.

Now you're talking about majority rule, and so now, instead of majority 
pairwise preferences, it's majority pairwise votes (MPVs). I suggested 
measuring the magnitude or strength off such a vote by the magnitude of the 
majority. Call me original :-)

You continued:


, and then proceeding to define majority
rule along the lines of what Jobst calls the "uncovered set". (I think
that's basically it, right?)

I reply:

You'd have to ask Jobst. But even if my definition of majority rule is the 
same as Jobst's definition of the uncovered set, then if that means that I 
defined majority rule along the lines of the uncovered set, that was purely 
accidental and coincidental.

You continue:

	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

I reply:

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.

You don't say how you'd rather define the magnitude of a majority pairwise 
vote. Margins? You'd like to define the magnitude of a majority vote in 
terms of the majority and the minority? Most of us woiuld define the 
magnitude of a majority vote by the magnitude of the majority.

In fact, that fundamentally makes more sense than defining the magnitude of 
a majority vote in terms of the minority. It's normative :-)    ...,even 
though I hadn't said that before.

Note that I don't say that you can't define it differently, but you must 
accept that it's ok if we don't all define it as you do.

You continue:

, and I doubt that very many other people will
either [accept my definition of majority rule]


I reply

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

For me, the value of my definition of majority rule is that it's used in my 
definition of offensive strategy. But my definition of offensive strategy 
isn't important, even to me. As you've no doubt heard, defensive strategy, 
the need for defensive strategy, is my strategy concern.

So maybe you could change what you're saying, and say that you object to my 
definition of majoritiy pairwise preference (MPP) and say that you want to 
define it in terms of margins, instead of being so arbitrary as to derfine 
the magnitude of a majority pairwise preference in terms of the majority 
that it refers to. What I said about MPV applies to MPP.

But what makes you think that it's important if people accept my definition 
of the magnitude of a majority pairwise preference, and, hence, my 
definition of defensive strategy.

The defensive strategy criteria aren't based on my definition of defensive 
strategy. Only their name is based on that definition. So are you fighting 
about a name? The matter of whether or not a method meets a criterion is 
unaffected by the criterion's name.

My definition of defensive strategy isn't something that I ask anyone to 
accept. It would never have occurred to me to ask anyone to accept it. It's 
just my way of saying what I mean when I speak of defensive strategy, when I 
tell what shouldn't be needed in its more drastic forms, and give to it a 
name.

So, sure, don't accept my definition of the magnitude of majority pairwise 
preferences, or my definition of defensive strategy. And don't accept my 
definition of majority rule, which means that you then won't accept my 
definition of offensive strategy.

Now, of course there's something that you don't like about my definition of 
majority rule: When Cardinal Pairwise elects Kerry in your example, instead 
of Bush, CP is violating majority rule, as I define majoritly rule. I stand 
by that definition and that conclusion that CP violates majorilty rule when 
it elects someone who has an un-outdone majority defeat.

But I'm not saying that CP shoudn't do that. Or, in your terminology, I'm 
not saying that it's un-normative for CP to do that :-)  It's a good thing 
when CP elects Kerry in that example, a good thing that CP has and uses 
information other than the pairwise votes, when that can thwart offensive 
order-reversal, or when it can resolve a natural circular tie in a way that 
is fairer.

By the way, AERLO too is useful in natural circular ties. With AERLO, I'd 
have no strategic reason to not rank all the acceptable candidates in order 
of preference, instead of equal-ranking all of them in 1st place.

But, though I stand behind my definition of majority rule, and the 
conclusion that CP violates majority rule (for a good cause) when it elects 
Kerry in your example, I _don't_ stand by my definition of offensive 
strategy. According to my definition of offensive strategy, voters in CP who 
adjust their ratings intentionally to protect Kerry from offensive 
order-reversal by the Bush voters are themselves engaging in offensive 
strategy. That means that what they're doing is both offensive strategy and 
defensive strategy (because they're doing it to protect the CW, in violation 
of majority rule*).  Is that nonsense? Sure. I said previously that I wasn't 
entirely satisfied with my definition of offensive strategy.

*But note that that isn't a problem for my defensive strategy definition, 
because defensive strategy is defined in terms of majority wishes, not 
majority rule.

CP provides a case in which my definition of offensive strategy gives an 
answer that is the opposite of what we expect offensive strategy to mean. I 
won't defend that definition of offensive strategy. It would be better to 
re-write it so that it won't give answers that aren't what we mean by 
offensive strategy. I might re-write it eventually, and anyone else is 
welcome to also.

But, for one thing, my definition of offensive strategy usually works fine, 
in keeping with what we expect offensive strategy to mean--its failure with 
CP is an exception. For another thing, offensive strategy isn't my main 
concern anyway. Need for defensive strategy is more important. So, in the 
meantime, till a better offensive strategy definition is written, I don't 
consider it a problem that there isn't a better one yet.

My point is that this isn't important.

You continued:

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

I reply:

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

You continue:


	Do you really think that it would be a majority rule violation to choose
Kerry rather than Bush in the example above (in part I, that is)? I don't
think so at all. But I think it would be if we accepted your recent
definition.

I reply:

Yes. But that just means that Cardinal Pairwise (CP) protects the CW in 
spite of that being a majorilty rule violation due to falsified preferences. 
I define majoritly rule in terms of votes rather than preference, and that's 
how we all expect majority rule to be defined. For instance, we all probably 
agree that Pluralitiy meets the Majority Criterion: A candidate who is voted 
favorite by a majority should win. And majority rule should be defined in 
terms of pairwise votes, but not in terms of the preference intensities, 
expressed or otherwise.

But I agree that my offensive strategy definition is fouling-up when it says 
that those voters in CP who protect Kerry with their voted preference 
intensities are using both offensive and defensive strategies when they do 
so. They obviously aren't using offensive strategy in any meaningful sense.
The offensive strategy definition is wrong in that instance.

Mike Ossipoff

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