Exaggerated opinions

[Saari]

Markus -

Thanks for the carefully reasoned reply.  Although I disagree (see next), I
approve of your approach to use careful reasoning instead of rhetoric in order
to reach a conclusion.  In particular, your logic (that a non-preference
system must occasionally produce a non-preference outcome and is therefore
flawed) is entertaining and probably valid.  But I must dispute one of your
premises.

As to your conclusion, you say (excerpted):
   I want to consider a situation with only two candidates
   (A and B), where an absolute majority of the voters
   prefers candidate A to candidate B.
   -and later-
I believe, that, if there are only two candidates (A and B)
and if an absolute majority of the voters prefers candidate A to
candidate B, then every sensefull democratic voting method would
necessarily elect candidate A.

I disagree the very obvious-sounding second paragraph.  Here is my
counterexample.  Consider the following hypothetical situation:
60% rate Coke as "Excellent" and rate 7-Up as "Very Good".
40% rate Coke as "Detestable and poisonous" and rate 7-Up as "Very Good".
These are honest, true feelings - not exaggerated.

I personally think that 7-Up may be the best outcome here, but this is only an
opinion.  I cannot "prove" this, and I do not need to.  The "best" outcome for
such a situation can and must depend on the decision method already chosen by
the group.

My point is NOT an argument as to which outcome is actually best. 
MY POINT IS that this counterexample calls into question the assertion that
"if an absolute majority prefer A to B, then EVERY sensefull democratic voting
method must necessarily choose A."

The fact that I can define a simple example where at least a good case can be
made that B is a better overall choice, even though more than half of the
voters prefer A to B, means to me that the assertion that every sensible
voting method MUST choose A is highly suspect.

Mike Saari