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

[Hugh Tobin]

Steve Eppley wrote:
> 
> 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 [snip]

I agree that Mike was harsh, but I also think Steve is a bit
patronizing, expecially because DemoRep seems to be right on this one. 
See below

Mike Ossipoff wrote:
> 
> DEMOREP1 at aol.com writes:
> >
> > ---
> > My comment- It appears that Prof. Young says that Condorcet's  tiebreaker is
> > different from anything written about on the EM list.
> 
> Correction: It appears _to you_ to be different from what has
> been written here. Actually it's the same. 

[snip]
> 
> > ----
> > Prof. Young goes on with a 4 candidate cycle example--
> > 25 Voters
> >          a       b         c         d
> > a     --       12      15       17
> > b    13        --      16       11
> > c    10         9       --       18
> > d     8         14       7        --
> >
> > In step 2 of Condorcet's algorithm one would select the six propositions
> > having greatest majorities.  In descending size of majority, these are c > d
> > [18 > 7] , a > d [17 > 8], b > c [16 > 9], a > c [15 > 10] , d > b [14 > 11]
> > , b > a [13 > 12].  According to a literal reading of [Condorcet's] step 3,
> > one would first delete the proposition b > a, as it has the smallest majority
> > in its favor.  But this does not result in an "opinion" because one cycle
> > still remains: b > c, c > d, d > b.  Therefore one would delete the
> > proposition d > b, as it has the next- smallest majority in its favor.  All
> > cycles are now eliminated.  But there is a difficulty: in the resulting
> > partial order both a and b are undominated.  Either one of them could be
> > interpreted as the top- ranked candidate, so the outcome is indeterminate.
> 
> Nonsense. There's an "opinion", a winner, if when you
> deleted B>A, A was no longer beaten. The fact that a cycle
> remains among the others is irrelevant. Read Young's translation
> again. It says to stop when you no longer have  a paradoxical
> situation with everyone beaten.
> 

I could not find where it says that in DemoRep's posted excerpt. 
Moreover, it appears that to Condorcet an "opinion" is more than a
winner, it is a whole set of propositions (pairwise races).  From the
quotations posted (for which I thank Demorep), it seems one is not to
pick the winner until one has a "possible" opinion.  Young's point that
this could lead to indeterminate results seems valid, as does Demorep's
point that Condorcet's tiebreaker is different from EM.  But this is no
argument against using a tiebreaker that works; Mike is surely right
that for SW, once one has an "unbeaten" candidate one can stop, rather
than inventing a second-order tiebreaker.

Perhaps DemoRep and Young provide another justification for using a new
name for what has been called Smith // Condorcet? 


-- Hugh Tobin