Left or right loser

[Mike Ossipoff]

DEMOREP1 at aol.com writes:
> 
> Prof. Young gives the following example of his (Young's) interpretation of
> Condorcet's comments (that I quoted in the original Left or right loser
> posting)--
>          Table 1- 13 voters
>            a         b          c
> a        --        8            6
> b        5        --           11
> c        7          2          --
> 
> Prof. Young's comments- Let us apply this rule [Condorcet's comments that I
> quoted in the original Left or right loser posting] to the situation in Table
> 1.  First we are to choose the three propositions having a majority, namely b
> > c with eleven votes, a > b with eight votes, and c > a with seven votes.
> Since these three propositions form a cycle, however, we delete the
> proposition with the smallest plurality, namely c > a.  This leaves the
> combination b > c and a > b (and implicitly a > c), which implies the ranking
> a > b > c. 
> ---
> 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. When you "delete the
proposition with the smallest 'plurality'" that means that
the alternative beaten in that "proposition" (pairing) is
no longer beaten and is now the winner. Had there been
a more complex situation, with more alternatives, it's
still true that when you keep deleting "propositions" as
described in translations of Condorcet, you're finally going
to make something unbeaten. When you do that, you've
"deleted the proposition" that represents' the minimax
defeat: The proposition you've just deleted is obviously
that alternative's biggest defeat, since you've been
sequentially eliminating the smallest ones. And it's 
smaller than anything else's biggest--that's why your
sequential procedure is deleting it before theirs.

Nope, the wording you've described is the same as
"The winner is the alternative whose biggest defeat
is the smallest".

The only question is how we measure defeats. As I've
repeatedly explained to you, Condorcet didn't say. So
each way of measuring defeats can be called "Condorcet's
method", since they're all consistent with it. I"ve
already talked about why votes-against is the best
measure.

As for the word "plurality" in your translation, it seems
to me that the translation in Duncan Black's book says
"the smallest majority". Either way, they mean the smallest
pairwise defeat.

As explained above, Young's wording is thge same as ours,
so is it really necessary to ask us to wade through the
following long, long passage?

> ----
> 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.

> ----
> My comment-- b beats a head to head 13 to 12.

Irrelevant. Everything is beaten by something. I thought
you understood that. The idea is to pick a winner even though
nothing is unbeaten, even A.

Demorep, I suggest that you pay some attention to what you're
quoting before you post it. You're spamming us with quotations,
rather like your state constitutions. At least check out what
they mean before you post them. Obviously you didn't.

> --- 
> Prof. Young goes on with his own idea about reversing the lowest
> proposition(s) to eliminate any cycles.
> ---
> The general problem is, of course, that the pairings of the candidates
> involved in a cycle can be looked at in 2 simple ways (noting truncation
> possibilites)--
> Votes For at left in high to low order
> L1 > R1
> L2 > R2
> L3 > R3
> L4 > R4
> L5 > R5
> etc. (That is, L1> L2> L3, etc.)

This is why no one ever knows what you're talking about. What
are R1...R5? What's that supposed to mean?

>  or
> Votes Against at right in high to low order (assuming some truncations such
> that the left number of votes plus the right number of votes may not be the
> same in all pairings)
> L3 > R3
> L1 > R1
> L2 > R2
> L5 > R5
> L4 > R4
> etc. (That is, R3> R1> R2, etc.)

Has Demorep discovered that defeats can be judged by either
votes-for or votes-against? After we've been discussing that
fact for quite a few months?

You left one out, Demorep: votes-against minus votes-for, or
"margin of defeat" in worst defeat.

As I said, we've thoroughly discussed the various ways
of measuring defeats, & we've explained repeatedly why we
chose votes-against.

> 
> I suggest that all Condorcet fans take a look at-- Condorcet's Theory of
> Voting by H. P. Young, 82 American Political Science Review 1231 (Dec. 1988).

Thanks, but it may surprise you to find that Condorcet fans have
already checked out Condorcet's wording of his proposal. I suggest
that you check out the meaning of quotations that you post before
you post them, with erroneous commentary. And I suggest that
if you're going to take part in this discussion, it's necessary
for you to pay some attention to what others have said. Your
informing us what the translation says, and informing us that
there's such a thing as votes-for & votes-against shows that
you're quite blissfully ignorant of what's been said over
the past year.

Mike

> 
> .-
> 


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