[EM] The "Turkey" problem (to Dave)

[Kevin Venzke]

Dave,

 --- Dave Ketchum <davek at clarityconnect.com> a écrit : 
> We are mixing two topics:
>       My topic is that I insist on having the right to truncate after 
> ranking as many candidates as I choose to.  There can be 10 or a dozen 
> candidates and there is no value in forcing me to rank among the lemons 
> whose rottenness is equally unacceptable.

Ok, but this isn't the point I was replying to.  I don't think, and I
don't know anyone who thinks, that permitting truncation is bad.

>       Your topic seems to be about ranking those when I see a difference 
> as a voter.  CERTAINLY I should rank according to the preferences I do have.

Ok.  The point of my last message was to argue against your apparent
claim that a "universally disliked" candidate would never have an opportunity
to become the CW.  Your claim seemed to be based on the notion that a
voter has no reason to strictly order candidates who are both "disliked."

Perhaps we mean something different by "universally disliked."  I'm
talking about a candidate who is worth very little to most voters.  In 
the example I gave, B is the most disliked candidate, on average.

> > 
> > If people did agree to truncate before the bad candidates, the
> > winner's average utility would be higher (we would have a guarantee
> > that someone thought he was a good choice), but some voters might
> > have gotten a better result by not truncating.
> 
> 
> PROVIDED the voters are agreed as to which are the worst lemons, it will 
> not matter whether they are truncated, for NO candidate can be CW without 
> at least some voters ranking the candidate as better than others.

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."

> 
> > 
> > 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)

Oops, that doesn't add to 100 voters.

> 
> 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.

> > 
> > 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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