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

[Dave Ketchum]

On Mon, 26 May 2003 23:05:27 +0200 (CEST) Kevin Venzke wrote:

> 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."


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.

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

> 
> 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."
> 

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.

> 
>>>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.
> 

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.

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

> 
>>>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

-- 
  davek at clarityconnect.com    http://www.clarityconnect.com/webpages3/davek
   Dave Ketchum    108 Halstead Ave, Owego, NY  13827-1708    607-687-5026
              Do to no one what you would not want done to you.
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