[EM] The "official" and "unofficial" defns of "Condorcet", range voting, & red herrings

[Warren Smith]

OK, I can see I'm hitting a wall of opposition here.  This whole issue is
a red herring (i.e. distraction from my main point) so let us not be
too distracted by it.  The central issue which we had started from is the 
question of which is better - range voting or Condorcet methods?

So instead of me foolishly trying to blast through that wall,
let me simply concede for the purposes of further argument that the "official"
Condorcet definition should be:  

CONDORCET(C for short):   
Elects a winner W, whom the voters based on the COUNTS of X>W and W>X type votes,
agree is pairwise-superior to all others X (if such a "Condorcet winner" exists - in
the sad case where none exists, then no claim is made).   
Only applicable to: voting systems in which candidate rank orderings
are deducible from the votes.

OK?  Then the "unofficial Warren D. Smith Condorcet property" of a voting system
(which is related and also interesting) is

WDS-CONDORCET (WC for short):   Elects a winner W, whom the voters would
agree is superior to all others (if such a "WDS-Condorcet winner" exists - if none exists,
then no claim is made) in each paired-off 2-candidate election "W versus The_Other",
using the same voting system but with all but these two candidates erased from
all votes.  Only applicable to: voting systems in which "erasing all candidates from all votes,
except for a preselected pair of candidates" has a meaning.

1. WC is applicable to a strict superset of the voting systems to which C is applicable,
so in that sense it is a more useful, important, and valuable property.

2.  WC and C happen to be equivalent on all "ranked-ballot voting systems which
reduce in the 2-candidate case to majority vote."  I.e. every system C has ever been tested
on, in all preceding literature.  But they are NOT equivalent if
applied to voting systems more general than that.

3. Is C a desirable property for a voting system to have?  It sounds that way at first, 
but it is a known theorem that any voting system obeying C must exhibit
"add top" and/or "add bottom" failures (e.g. adding a new vote ranking the current-winner 
top, can cause him to lose).  That makes C sound less like a desirable property.

4. Also, an instance where C clearly is undesirable, is the "free the slaves" vote
in the early USA, where, say, 60% of the voters would vote to keep slavery,
and 40% (we assume the slaves are allowed to vote) would vote to ban slavery.
However, the right decision is to free the slaves, and a voting system that were
somehow able to weight the votes based on the utility to that person (slaves: freedom
has high utility.  slaveowners: having a slave has utility, but a lot less) would
produce a superior result utility-sum-wise.

5. Is WC a desirable property for a voting system to have?  Sounds that way, yes.

6. Both Range voting, and all so-far-constructed "Condorcet voting methods",
obey WC.

7. Range voting elections (ignoring exact ties) ALWAYS produce a WDS-Condorcet winner.

8. All other so-far-constructed "Condorcet voting methods" do NOT always
produce a WDS-Condorcet winner.

9. So in that sense, which is very highly related to the yardstick used by Condorcet proponents
themselves, range voting is superior to every so-far-constructed Condorcet voting method.

wds