[EM] The "Turkey" problem

[Kevin Venzke]

Dave,

We seem to be having communication problems.  I wonder if you would have
an easier time accepting these claims:

1. There are no guarantees that the CW would not have received the
FEWEST votes, had the same election used Approval as the method.
2. The "Approval loser" can arguably be called the "worst" candidate.

I am quite happy to weaken my claim to the above.


 --- Dave Ketchum <davek at clarityconnect.com> a écrit : 
> I qualify that a bit.  Given candidates I personally see as close to tied, 
> and a bunch of issues involved, I could assign a personal worth to each 
> candidate for how well they did on each of these issues - thus developing 
> a personal valuation to guide my own voting.

Ok.  Suppose you and I both say, BEFORE the election, "I don't really like
candidate A."  Would you deny that my statement and your statement can be
compared in meaning?

> > Well, numeric values aren't even necessary if all one wants to show
> > is that the CW might displease EVERYONE (in ABSOLUTE terms, keep in mind;
> > I'm fully aware that no one ranks B last).  In the ABCD scenario where
> > everyone ranks D second, I could simply say, "Everyone thinks D is a
> > twit, and he is the CW."  No interpretation is involved here.  I'm
> > telling you that's how it is.
> > 
> > If you agree that this situation is possible, we can be done with this.
> > Note the wording is "D is a twit," not "D is the biggest twit" or "D
> > is everyone's least favorite."
> 
> And I read the votes as saying D PLEASES everyone.

That's a fair interpretation, but since I'm now telling you that D
is universally believed to be a twit, surely there is a place for the
word "displeasure" here.

> True that A backers 
> would prefer their candidate but, considering that that is an impossible 
> dream, they should be thankful that D protects them from having B or C 
> win (and B and C backers should have similar thoughts).

They probably are "relatively pleased," but that is a different beast
from what I'm talking about.  They can be relatively pleased, and displeased
(in absolute terms) at the same time.

> And, again, it could be that all the voters agree that D is a good and 
> qualified candidate - A, B, and C get in the act because each of them 
> convinces some of the voters that they are even better.

I agree that this was possible BEFORE I added that everyone believes
D is a twit.

> Could be that some or all rate D lower - but none assign D the bottom of 
> the barrel - each rates 2/3 of the other candidates as worse.

No "could be" about it, that's the way it was.  (Everyone truncated after
D.)

> > It is one possible definition of "worst."  "Condorcet Loser" is another
> > possible definition.  If the election method is Condorcet, you cannot do
> > any better than the latter definition.  I'm not saying you can.
> > 
> Do not remember seeing "Condorcet loser" elsewhere, but it could have the 
> almost useless meaning of "all candidates except Condorcet winner".

It means a candidate who is beaten by everyone else.  I take that to be
Condorcet's definition of the "worst" candidate.  Not a bad definition
at all, but not the only one, either.

> > Agreed.  It sounds like you think I'm saying we could pick someone
> > better using an identical, Condorcet ballot.  I am not saying that.
> > 
> > I am saying that Condorcet cannot guarantee anything about the "total
> > worth" of its winner.  Since you think "worth" can't be defined, even
> > in a hypothetical situation, you should be willing to concede that point.
> > If "worth" can't be defined, how can Condorcet make any guarantees about
> > it?
> 
> While we cannot usefully attach numbers to it, the point is that we are 
> looking for the candidate to which the voters collectively attach the most 
> worth.  Gets tricky for cycles such as agreement that A>B, B>C, _AND_ C>A - 
> but then we have to decipher which is the strongest assertion.

Your description of what we are "looking for" doesn't seem to be what
Condorcet attempts.  Condorcet is about majority rule, not maximizing worth.
It doesn't collect the information needed to attempt the latter.  I am
not saying that's BAD, I am saying that as a consequence we cannot say
anything about the "collective worth" of a CW.

> >>I see no value in a numeric value for worth with Approval - either they 
> >>are good enough that I choose to rank them as acceptable, OR they are not.
> > 
> > I don't believe you.  If this is true, then there are potentially cases
> > where you would be willing to approve all the candidates on the ballot,
> > despite the fact that this "strategy" doesn't improve your prospects.
> > 
> I can see them as equally good or equally bad.  If so, my best strategy is 
> to not interfere with the other voters deciding on the winner.

True.  But what if there are only three candidates, who make you 99%, 97%,
and 93% happy respectively?  I'm assuming 93% is high enough for you
to deem "acceptable."  Do you sit this election out, or do you put those
"worth" figures to use in making a decision?


Kevin Venzke
stepjak at yahoo.fr


___________________________________________________________
Do You Yahoo!? -- Une adresse @yahoo.fr gratuite et en français !
Yahoo! Mail : http://fr.mail.yahoo.com