[EM] Condorcet and other authors on Condorcet (and how does range voting fit in?)

[Abd ul-Rahman Lomax]

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.