[EM] Re the "official" definition of "condorcet"

[Warren Smith]

1. condorcet.org definitions page:
"Name: Condorcet Criterion 
Application: Ranked Ballots 
Definition: 
If an alternative pairwise beats every other alternative, this alternative must win the election. 
Pass: Black, Borda-Elimination, Dodgson, Kemeny-Young, Minmax, Nanson (original), Pairwise-Elimination , Ranked Pairs, Schulze, Smith//Minmax, Sum of Defeats 
Fail: Borda, Bucklin, Coombs, IRV"

2. wikipedia:
"The Condorcet candidate or Condorcet winner of an election is the candidate who, when 
compared in turn with each of the other candidates, is preferred over the other candidate."

3. http://accuratedemocracy.com/z_words.htm:
"The Condorcet candidate in a multi-candidate elections that candidate, if one exists, who could 
beat each of the others in separate pairwise contests,i.e., is preferred to each of 
the others candidates by a majority."

* according to def1, range voting either is or is not a condorcet
method depending on the meaning of "pairwise beats."
Condorcet.org has a hyperlink on "pairwise beats" (that does not show up in
this plaintext snarf) that says they mean majority vote
based on the stated rankings <,> relations in the ballots.
  However, they could have left it with no hyperlink and just based it on
whatever voting method was under test, in which case their definition
would have been unchanged as far as every single method they ever tested it on
(those they mentioned under pass/fail),
or Condorcet himself ever tested it on, or (as far as I can tell) the entire
polysci literature has ever tested it on, would have been concerned.
(Note that, revealingly, they do not consider range voting or
plurality voting to either pass or fail.)

   This no-hyperlink choice is in fact a plausible way to go because then the condorcet 
criterion is about the logical self-consistency of a method, as opposed to the consistency 
of method A as judged using method B, which is kind of an unfair pre-biased way to judge A.

* According to def2,  range voting either is or is not a condorcet
method depending on the meaning of "is preferred". 

* As far as I can tell, the EM people arguing with me prefer def1 (and with hyperlink used).

* def3 and arguably def2 in fact DISAGREE with def1.
That is because as I remarked in an earlier post, voters who in an N-candidate election ranked A>B
in their vote, do not necessarily actully prefer A over B, and may prefer B over A.

>tarr:
>As a math major, you surely understand that without agreed-upon
>definitions, we may as well be arguing in different languages.  Define
>your criteria.  Call it whatever you like.  But it is not the
>Condorcet criteria, which is already well-defined and cannot be
>changed on your whim.

--Actually, as a math PhD, what I understand is that the Condorcet criterion is NOT
"already well-defined" as I have just proven by exhibiting conflicting incompatible
definitions, as well as ambiguous definitions, as well as subtleties the previous definers
obviously did not even recognize existed (and the entire polysci literature as far
as I know did not recognize existed, far as I can tell by reading re this).

I also understand that when one encounters such a situation, it is one's
duty to clear up the ambiguity and do better.  I have done so.  Tarr however
has not done so and instead has denied this reality.  I suggest to you that
that my approach in this case, is superior.  

The situation is mildly analogous to sqrt(x) which "does not exist" if x<0.
Later it was realized the reals are a subfield of the complex numbers and sqrt(x) can
and should be defined more generally.   There were indeed people who tried to say things
like "you are not allowed to on whim do this".  They are in the dustbin of history.
Now analogously, here we have a definition (Condorcet) defined for ranked ballot
voting methods by people who had never conceived of more general kinds
of numbers than reals, oh sorry, I mean more general kinds of voting methods.
We now generalize our purview to allow complex numbers not just real numbers,
oh sorry, I mean more general voting methods than ranked ballot methods.
In that case, we have to ask how best to try to generalize the definition of
"condorcet."  I have shown there are two ways to do so, both of which coincide
with the old definition whenever x is real, oops, I mean, which coincide with
the old def whenever X is a ranked-ballot mehtod, but which do not
coincide when X is range voting.

That is the situation.  It is no whim.
wds