[EM] The "Turkey" problem and limited ranks

[Dave Ketchum]

On Sun, 25 May 2003 10:10:12 +0200 (CEST) Kevin Venzke wrote:

> Dave,
> 
> The problem with the truncation solution is that it is never in the
> interests of the individual voter to rank two candidates equally
> when he truly does have a preference.  (Ignoring the possibility of 
> cycles for the moment.)  In other words, it is potentially useful
> to vote X>Y while disliking both.


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.
      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.

> 
> 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.

> 
> 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.

> 
> 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.

You strain to call B "pretty bad" - 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.

> 
> 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).

> 
>  --- Dave Ketchum <davek at clarityconnect.com> a écrit : 
> 
>>>The "turkey problem" is the fear that an unknown, or even
>>>universally disliked candidate could be the CW if there are no
>>>candidates with broad support.
>>>
>>Seems like an unreasonable fear.
>>
>>I favor permitting and using truncation, but this requires an 
>>understanding that those you do not list must be those you like less than 
>>any you do list.
>>
>>Given the above understanding, a universally disliked candidate will never 
>>get voted better than any other candidate by any voter, and thus have no 
>>chance to become a Condorcet Winner.
>>
> 
> For it to be as you say, the voters have to quite selflessly say, "Although
> I prefer X to Y, I dislike them both, so I'll not stop Y from beating X
> if that's what other voters prefer."
> 
> That's a commendable attitude, but Condorcet doesn't reward it.  With
> limited ranks (including Approval), every voter has to make such concessions
> to some extent.  Instead of "I dislike them both" as the thought, it would
> likely be "I can't expect to gain as much from trying to break an X-Y tie."
> 
> 
>>I can picture listing an unknown candidate before one who threatens to 
>>vote "wrong" on abortion, but i do not see this becoming a problem unless 
>>many of us vote for the unknown - but you are talking of getting in 
>>trouble with Condorcet with a collection of candidates for which Approval 
>>would not have a problem.
>>
> 
> "Unknown" may be too strong.  The candidate may be tight-lipped, poorly
> understood, or not covered well by the media.  It's conceivable that
> voters would prefer to take their chances with him over a candidate they
> know they hate.
> 
> 
>>How about a sample collection of votes to make the picture clearer.
>>
> 
> 
> 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
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