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

[Dave Ketchum]

On Mon, 24 Mar 2008 19:53:42 -0400 Warren Smith wrote:
> 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).

I went thru several thoughts:
      Did you make up the data?  Seemed as if you were reporting something 
you learned rather than made up.
      Did you round up 31 live voters and report what they voted?  I would 
not expect that, and doubt that you would have gotten the pattern you 
reported that way.
      Did you use what I would call a "random number generator".  I feel
certain you do use such programs to learn what you report about various
voting methods - tell it what you know and ask it to use some sort of
formula to calculate results.  In private email you say you do not do that 
here.

So, WHERE do the numbers come from - I still have a headache.

Looking at the report for Plurality voting I see two puzzles:
      Voting for candidates with 3 Ys was POPULAR - 16 out of 31.
      Voting for the similar candidate with 4 Ys got zero votes.
      Voting for the 4 candidates with 3 Ns was UNpopular - each got 1 vote.
      But the similar candidate with 4 Ns got 5 out of 31.

Mixed in with all this, a voter can use any of the methods Plurality, 
Approval, Range, or Condorcet to vote for a single candidate - why would 
the method used influence their thinking for such voting?

The methods we promote allow voting for multiple candidates, and doing 
that gets into method differences having an effect.
> 
> 
>  >  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
-- 
  davek at clarityconnect.com    people.clarityconnect.com/webpages3/davek
  Dave Ketchum   108 Halstead Ave, Owego, NY  13827-1708   607-687-5026
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