At 03:06 PM 5/17/2010, Warren Smith wrote:
(3) Condorcet therefore indicates we need a more-practical very simple
alternative and proceeds to fill that bill by inventing APPROVAL
VOTING!!
I had seen it stated that Condorcet did propose an Approval method,
but had never seen evidence for it.
http://books.google.com/books?id=e7IXFcvyEMUC&pg=PA49&lpg=PA49&dq=Approval+Geneva+Condorcet&source=bl&ots=BOc9d3PIfk&sig=zP1YvpxllyOWw6Y59JBMGXHL8Vc&hl=en&ei=w73xS-LwNcH38Aa-oOD9Cg&sa=X&oi=book_result&ct=result&resnum=1&ved=0CBIQ6AEwAA#v=onepage&q=Approval%20Geneva%20Condorcet&f=false
I'm most interested in Warren's statement of the Condorcet criterion
that indicates that Range satisfies it. Warren had mentioned this
many times without specifying the exact way in which Range could be
considered to satisfy the criterion.
If the votes on a set of ballots are such that a single candidate
prevails in all pairwise races, if the votes for all other candidates
besides the pair are struck, this candidate is the Condorcet winner.
Given Range ballots, of course, this statement is true for the Range winner.
In these pairwise elections, the voters have possibly, by the nature
of Range ballots, voted in that pairwise race with varying voting
power. "Prevails" must be understood as "following the method,"
whereas some statements of the Condorcet criterion assume that it is
the number of voters preferring the candidate over the other vs the
reverse which matters. Obviously, if, after we strike all the
non-pair votes, we get
2: A, 1; B, 0
1: A, 0; B, 10
B wins this pairwise election(and wins it by a large margin) even
though more voters preferred A.
In the book I link to above, there is a discussion of preference
strength, and an argument that using preference strength was
preposterous because, then, the most intense feelings would dominate.
But that argument does not address systems where the expression of
preference strength is limited; in particular, with Range Voting,
preference strength is limited to the range of 0 (no preference) to 1
vote (full preference). The anti-strength argumetn assumes some kind
of absolute preference strengths, which is only possible to collect
in certain special cases where preferences are commensurable.
1-person, 1-vote systems force commensurability of preference to the
individual's voting power.
It's fascinating to see how the old arguments were afflicted with a
poverty of the imagination, so that a knee-jerk objection simply was
assumed to be generally applicable. This same argument about the
incommensurability of preference strength was accepted by Arrow and others.
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