[EM] The "Turkey" problem

Tue May 27 03:51:01 PDT 2003

Dave,

 --- Dave Ketchum <davek at clarityconnect.com> a écrit : 
> 
> I stay with what I said.  The collection of candidates to which I assign a 
> worth of zero are best truncated, for this will give none of them any 
> ammunition toward winning anything other than last place.  If  I do not 
> truncate, then I give all but the one I rank last a bit of ammunition 
> toward winning over the ones I rank lower.  If other voters are enthused 
> over one of these candidates then the bit of ammunition from my not 
> truncating could help that candidate win.

If they are truly worth zero to you, then it makes no difference whether
you truncate them or order them randomly.  You merely have to fill in
more bubbles in the latter case.

We don't seem to differ much here.  My point was that there is no gain
in truncating when the worths are not the same.  May I ask: Do you think
that disliked candidates are all worth 0?  It sounds like you do.

> Coming back to "universally disliked", if this label is true this 
> candidate is not going to get ranked high by enough voters to win.

See below.  A CW doesn't have to be ranked high, he just has to be
ranked HIGHER.  There are no guarantees about how much he is actually
liked by anyone.

> > Even if the voters are agreed, nothing inherently prevents the CW from being
> > the best of the worst lemons.  The point is that Condorcet makes no
> > guarantees about the value (avg worth to each voter) of the CW, and
> > that's what the "turkey problem" is.  If that doesn't bother you, that's
> > fine.  But I'm not so sure it's an "unreasonable fear."
> > 
> 
> If the candidate field is all lemons you might get there; if there are ANY 
> candidates with some attractiveness they should attend to the worst lemons.

In the scenario envisioned, the candidates who are not lemons are a "love 'em
or hate 'em" deal, who all have more opponents than fans.  I'll spell this out
for you:

34: A>D...
33: B>D...
33: C>D...

D is the CW.  We cannot discern whether D has the greatest worth (possible)
or whether he's an incompetent but innocuous fool and everyone knows it 
(also possible) or whether no one knows much about D but would rather take
their chances with him than with the two "major" candidates they know they 
don't like.

> 
> > 
> >>>Here's an example, as you asked:
> >>>
> >>>48: A>B>C  (A worth 100, B worth 15, C worth 0)
> >>>2: B (B worth 100, A and C worth 0)
> >>>48: C>B>A  (C worth 100, B worth 15, A worth 0)
> > 
> >>I do not understand "worth" in this context - but think I do not need to.
> >>
> > 
> > "Worth" refers to the degree to which each group of voters likes the
> > candidates.  It's crucial to the discussion to know how much each
> > candidate is worth to whom.
> > 
> 
> Apparently you see value here that I do not.  I assumed the topic was 
> Condorcet, for which I can say A>B, A<B, and perhaps A=B, but cannot say 
> whether the difference is 1 or 99.  You seem to be talking of a more 
> complex method with a ballot in which the voter can specify a worth value. 
>   Even given such a method, I do not see how you can come up with a 
> yardstick in which voters attach the same meaning to a worth value of 10.

The topic IS Condorcet.  I am not talking about a different ballot.
I am specifying candidates' values to voters in terms of numbers.  I
am reading their minds, not asking them to estimate their own feelings.

I can't believe you don't see the motivation for this.  I'm trying to
persuade you that a generally disliked candidate can be the CW.  How
on earth can I give you an example of that without a measure of
"dislike"?

Merely looking at a candidate's rank to decide how "liked" he is
amounts to using a point system like Borda, which is inadequate
for the point I'm trying to make.  Candidate D, in my latest
example, has a Borda score of 200, I believe.  Surely the highest.
But that's not enough information to decide that D must really be an
awesome candidate.  He could be nearly terrible.

> 
> Given this confusion, I will have little to say about other paragraphs.

So have I ameliorated the confusion?

Kevin Venzke
stepjak at yahoo.fr

> 
> > 
> >>>If they vote as above, B is the CW.  His average utility is only
> >>>16.4, while A and C are both worth 48.  If the A and C supporters
> >>>truncate, A and C tie.  But say there isn't a tie, and one of the
> >>>B supporters votes B>A>C, so that A is the CW.  Now the C supporters
> >>>regret truncating, because they could've at least gotten B elected.
> >>>B is still pretty bad, but he's better than A.
> >>>
> >>As I said above, it is not proper to truncate until you have said ALL you 
> >>care to say (also note that votes of A>B and C>B are not true truncation, 
> >>given a total of 3 candidates).  Here about half the voters say A is the 
> >>best available, and about half say A is the worst available, and almost 
> >>all agree that B is neither best nor worst.
> >>
> > 
> > It sounds like you think I'm claiming that the Condorcet Loser could be
> > the Condorcet Winner.  I'm not, except in cases where there is only one
> > candidate.
> > 
> > 
> >>You strain to call B "pretty bad" 
> >>
> > 
> > B being "pretty bad" was from the perspective of the C supporters.
> > I can say that because I said in the example that B is only worth 15 to
> > them.  Compared to 100, that is "pretty bad."  I should've been clearer.
> > 
> > 
> >>- all you know is that few call B best 
> >>of the 3, BUT ALSO, few (actually none) call B worst of the 3.  For 
> >>example, assume A and C promise to implement opposite extreme positions on 
> >>abortion, and B promises to hold the middle ground.
> >>
> >>Again, you talk of A and C backers truncating before expressing their full 
> >>desires, and then regretting their own suicide - they should have learned 
> >>the rules BEFORE voting.
> >>
> > 
> > Without considering the "worth" values I gave, you can't help but miss
> > my point here.  My point is that B is the CW despite being worth only
> > 15 to 96 of the voters.  My other point is that if the A or C supporters
> > truncate, they don't improve the result from their own perspectives.
> > 
> > 
> >>>In Approval, unless A or C look hopeless, only the 2 voters will
> >>>approve B.  The other 96 voters are better off trying to break a
> >>>100-15 tie than a 15-0 one.  Thus the average utility of the winner
> >>>is improved by collecting information on preference priorities.
> >>>
> >>Depends.  If either A or C backers can be confident of winning, they vote 
> >>only their desires in Approval.  If they expect the above strategy to 
> >>lose, they properly include B with their favorite as better than a worst 
> >>class loss (see what I said about abortion above).
> >>
> > 
> > Again, my paragraph here depends on the fact that the 96 voters prefer
> > Favorite>B much more than B>Worst.  If A and C are believed to have
> > equal odds, then B's odds are irrelevant to the decision of whether
> > to approve him.  The relative worth makes the decision.  I should've
> > been clearer about all that.
> > 
> > 
> > Kevin Venzke
> > stepjak at yahoo.fr

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