[Election-Methods] Fwd: YN model - simple voting model in which range optimal, others not

[Warren Smith]

On Sun, Mar 23, 2008 at 11:21 PM, Dave Ketchum <davek at clarityconnect.com> wrote:
 > On Sat, 22 Mar 2008 19:35:13 -0400 Warren Smith wrote:
 >  > The "YN model" - a simple voting model in which range voting behaves
 >  > optimally while many competing voting systems (including Condorcet)
 >  > can behave pessimally:
 >  >
 >  > http://rangevoting.org/PuzzAggreg.html
 >  >
 >  When I stare at this all I get is headaches:
 >
 >  Why would Plurality voters be attracted to candidates with 3 Ys, or no Ys
 >  - yet reject 4 Ys?

Some voters prefer N on some issues.   All of society, if
asked to vote on any given issue, prefers Y by (in the b solution) 16 to 15.
That means there are 15 voters who prefer N on issue 1.

You seem to have the idea in this question that all voters prefer Y.  That is
not the case.  The voters are as specified in the table in the answer
(in the case of answer b).


 >  Why would Condorcet voters seem to be attracted to Ns?  If the answer is
 >  that they truly are, why should Condorcet be blamed as if a bad method?

The voters are whoever they are. I am simply saying that IF
the voters happen to be as specified in the answer "e", then
the candidate NNNN...NN  will win a pairwise matchup with
the candidate YYYY...YY
even though, on every issue represented by a single letter in the
candidate-names, Y beats N pairwise with those exact same voters.
You can simply verify those facts by counting.

Is Condorcet a bad method?  Well, in this case yes.  Condorcet in
the artificial, but valid, scenario of answer e,
makes the worst candidate NNNN beat the best YYYY
pairwise.

However, it may not be as bad as I initially thought.
I initially thought in answer e that NNNN was the "Condorcet (i.e. beats
all) winner."
But in fact, that is not true.  NNNN is pairwise preferred over YYYY but
not over EVERY candidate.   In which Condorcet rules-flavors does NNNN
win and in which does it not?   I am not sure right now.

Also, it could be claimed that this scenario is artificial and will
rarely arise.  If
so, then Condorcet is not so bad.  The less-rare this is, the worse Condorcet
looks.  I have no idea how rare this kind of thing is.   But as a matter of
PRINCIPLE, it is interesting.   I mean, you would hope that a voting
method would be "self consistent" in the YN model.   If Y's
win,  then YYYY ought to win.  You would hope.

That kind of self consistency
appears to be correct for range voting but false for
practically every other single-winner voting method.

--
Warren D. Smith
http://RangeVoting.org <-- add your endorsement (by clicking "endorse"
as 1st step)
and
math.temple.edu/~wds/homepage/works.html