Young's translation of Condorcet (was RE: Left or right loser)
Mike Ossipoff
dfb at bbs.cruzio.com
Sun Jan 26 13:27:09 PST 1997
Hugh Tobin writes:
>
> 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
You're saying that Demorep was right to say that the translation
of Condorcet's instructions is different from saying to
elect the alternative whose worst defeat is the least? But
I, & also Steve, demonstrated why Condorcet's translated
words do mean that, and that Demoprep was mistaken to
suggest otherwise.
>
> 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.
You believe that this statement by Demorep is correct? Check out
my explanation of why it isn't so, in the letter to which you're
replying. You're one of those people who replies to, & tries
to rebut, letters that you haven't even read.
> >
> > 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.
You haven't re-posted the entire quotation, but it seems to
me that it defined an "opinion" as a result in which there
was an unbeaten alternative, and then said to stop the
count when an "opinion" exists. I believe that Demorep's
quotation did say that. If Demorep neglected to quote that
part, then check Duncan Black's translation, in his book
_The Theory of Committees & Elections_.
> Moreover, it appears that to Condorcet an "opinion" is more than a
> winner, it is a whole set of propositions (pairwise races). From the
Wrong. It's a whole set of pairwise comparisons in which there's
an unbeaten alternative--and that's the winner according to
Condorcet's proposal.
> 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
How could it lead to indeterminate results? You neglect to say.
The way Demorep said it could is the result of Demorep's misunderstanding
of what Condorcet's proposal was. Demorep though that, as long
as there was still a cycle, there couldn't be a winner, even
though there was an unbeaten alternative.
> point that Condorcet's tiebreaker is different from EM. But this is no
Wrong again. Condorcet's tie-breaker is the same as saying to
pick the alternative whose greatest defeat is the least. Doing
that is Condorcet's method. The magnitude of a defeat can
be measured in various ways. Condorcet(EM) measures it by
votes-against. Young's translation, and Duncan Black's
translation of Condorcet is not different from how I've
been defining Condorcet's method. Condorcet(EM) is one of
the several ways of implementing Condorcet's method. It
isn't different from Condorcet's method any more than
a Hershey Bar is different from a candy bar.
And if all you're trying to say is that Condorcet(EM)
is "different from" Condorcet's method because it's
one of the ways of doing Condorcet's method, then
you're wasting our time. You are anyway.
> argument against using a tiebreaker that works; Mike is surely right
> that for SW, once one has an "unbeaten" candidate one can stop, rather
...as Condorcet said to do.
> 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?
Sorry, but Demorep didn't, & Young didn't even try to. What
we've been calling Condorcet, or Condorcet(EM)
does what Condorcet said to do: It picks the alternative
whose greatest defeat is the least. In terms of being a
version of Condorcet's method, a way of doing what Condorcet
said to do (without specifying how to measure defeats),
Condorcet(EM) is a version of Condorcet's method. Whether
that's the best name to use when offering it to the
public is another issue.
>
>
> -- Hugh Tobin
This list has become a babysitting service, in which we
indulge people who engage in sloppy disorderly discussion.
>
> .-
>
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