Young's translation of Condorcet (was RE: Left or right loser)

[Steve Eppley]

Mike O. chided Demorep for not seeing that Young's interpretation of
Condorcet's writing closely matches the EM interpretation.  I think
the criticism was a little harsh, since it might take a bit of
thought to realize the following two points:

1. Eliminating pairings in order of smallest support is the same 
as eliminating in order of largest opposition, when voters aren't
allowed to express indifference between any pair.  (It was and is 
common to ignore the possibility of indifference, but we in EM don't 
ignore it since we choose to adhere to Arrow's "universal domain" 
axiom: all preference orders are allowed.)

2. Eliminating pairings in "smallest support" order until the cycle
is broken leads to the same outcome as picking the candidate with the
smallest largest pairloss.  Here's an example to illustrate:

   35: ABC
   33: BCA
   32: CAB

        A    B    C 
   A        67L  35 
   B   33        68L
   C   65L  32      
      ---- ---- ----
   LL: 65   67   68

   Opinions:   A>B  B>C  C>A  (a cycle)
   Plurality:  67   68   65
L'opinion avec the smallest pluralite' est:  C>A
(Pardonez moi my French.)
Discarding C>A leaves:  A>B B>C  (no cycle)

M. Condorcet presumably intended that the winner of "A>B, B>C" is A, 
since the cycle has been broken with A ranked transitively first.  
A is also the alternative with the best (smallest) Condorcet(EM) 
score (65), since this is the C>A total and C>A is A's largest 
pair-loss.

---Steve     (Steve Eppley    seppley at alumni.caltech.edu)