[EM] Issues with the Majority Criterion

[Kevin Venzke]

Hi Greg,

--- En date de : Jeu 16.10.08, Greg Nisbet <gregory.nisbet at gmail.com> a écrit :
> I would say it is that if X is ranked/rated strictly first
> by more than
> half of the voters, then X should win.
> 
> =What would co-first candidates imply?

Neither of such candidates would be ranked/rated strictly first by a
voter that tied them at the top. That is what "strictly" means.

> > If the method doesn't satisfy FBC, how can this be
> > regarding as a good
> > thing, isn't it just making a massive compromising
> > incentive?
> It is not regarded as a good thing to fail FBC.
> 
> =I have to make the antecedents of my pronouns more
> clear... I meant that
> FBC failure seems to seriously hurt the majority criterion
> because it is
> plausible for a compromise candidate to gain a majority
> from insincere
> candidates. I am asking, absent FBC, how valuable is
> majority compliance?

I would say it depends on how badly FBC is failed.

But also, in a method where it's possible to notice a majority's 
favorite, I don't think it will be publicly acceptable to fail majority.

> I don't understand why you say "massive."
> Methods vary widely with
> respect to how much compromise incentive they provide.
> 
> =FBC compliant methods have less compromising incentive
> than non-FBC
> compliant ones, in general. I called it massive because I
> perceived it to be
> noticeably different from FBC compliant ones. FBC compliant
> methos such as
> Range may suffer from compression to some extent, but
> Offensive Order
> Reversal will not occur.
>
> = I regard it as massive because of the Offensive Order
> Reveral thing.

You mean defensive order reversal, not offensive. Offensive means burial
strategy.

> > Does a method count as majoritarian if a majority can
> > impose its will, but
> > doesn't necessarily have to?
> I don't think the term "majoritarian" has an
> agreed-upon meaning. The way
> I define the term, it is not directly related to the
> majority criterion.
> 
> =Hmm... good point. To some extent I was probing the
> meaning of the term
> "majoritarian" that I have heard in previous
> discussions. I guess what I
> meant is, "how valuable is allowing a majority to
> force its will if it so
> chooses as opposed to always having it get its way?"

It's a partial assurance that you won't regret listing compromise
choices. You don't even have to know whether you're in a majority:
The method counts the votes first, and if you're in the majority, the
rest of your preferences are not regarded. It's doing work for you and
letting you simply say how you really feel.

It seems to me you're asking about the difference in value between
one guarantee (the majority criterion) and no guarantee at all. If a
majority has merely the ability to come up with some way to vote that
gets their favorite result, this is more like the method not being
utterly broken, than a useful guarantee.

> But the term "majoritarian" would be almost
> meaningless if it meant that a
> majority always has some method to make their first
> preference win.
> 
> =The only methods that would violate it would be silly ones
> like
> Antiplurality and Borda. I agree. But if, in reality, the
> distinction isn't
> all that meaningful, is it really worth mentioning as a
> flaw of a particular
> system.

The "flaw" of methods that fail the majority criterion perhaps isn't
the failure of that particular criterion, but the general absence of 
guarantees about how lower preferences will be used.

That does seem like a pretty big deal, whether you want to use the
majority criterion or some other mechanism to address it.

> > Also, how do you define membership in a majority.
> It depends on the criterion. For the majority criterion
> simply, membership
> in the majority is determined by you strictly supporting
> the same first
> preference.
> 
> > Let's pretend Alice votes Candidate X = 100
> Candidate Y
> > = 60
> >
> > With respect to the majority criterion, does she
> belong in
> > Camp X, or 100%
> > in Camp X and 60% in Camp Y?
> I don't know any definition of the criterion that
> doesn't refer to first
> preferences. Even your definition refers to first
> preferences.
> 
> =Exactly. Is it best to regard 60% as 60% of a 'first
> preference' or as not
> a 'first preference' at all? Rankedisms don't
> translate perfectly to Range
> Voting.

It seems to me that "first preference" means the same thing whether you
use rankings or ratings. Especially if you try to discuss voters' sincere
sentiments and not just how they vote. However:

Suppose the Range voter doesn't normalize his rating and his "top"
preference only receives a 60%. Does that mean his top preference is
only 60% of a "first" preference?

Kevin Venzke