[EM] Truncation and 4 dimensional voting

[josh at narins.net]

I bet some people would not look fondly on being forced to choose
whether they liked John Hagelin or Lenora Fulani better.

Remember when I mentioned three dimensional voting? 

Well, how about four dimensions!

Voting on a matrix, instead of a ranked or approval ballot, allows the
voter the most freedom to express themselves EXCEPT when confronted by
the following...

Each voter Vx has a different ballot Bw for each state of the world
W[1..x]

IF the recent allegations concerning Buddy's friends are true...

  Able Buddy Chuck
A        A     A
B  A           A
C  A     A

Otherwise, as long as the Able doesn't come out for free ice cream...

  Able Buddy Chuck
A       B      B
B  B           B
C  B    B

But if aliens hit Earth before inauguration day...

  Able Buddy Chuck
A        B     C
B  B           C
C  C     C

Since the number of possible states of the world are infinite, I doubt
anything more than the first question would ever become necessary.


On Sun, May 25, 2003 at 10:10:12AM +0200, 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.
> 
> 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 ?crit?: 
> > > 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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