[EM] The "Turkey" problem and limited ranks

[Kevin Venzke]

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.

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.

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)

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.

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.

 --- 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


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